M A T H E M AT I C AL
G EO GR A P H Y
W I LLI S
V I CE
E
N
S
N
O
H
O
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J
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PH B
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OF E S S OR OF GE OGR A P H Y A N D
S O CI A L S CI E N C E S
NOR TH E R N NOR M A L A N D
I ND US TR I A L S CH OOL A B E R D E E N
S O U TH D A K O TA
P RE S I D E N T AND
PR
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,
NE W
YORK
C I N C I N N A TI
,
C H I C A GO
A M E R I C A N B O O K C O M PA N Y
P R E F ACE
interest in the
I N the greatly
common schoo l
awakened
geography has rec eived a
s ubj ect s d uring rec ent years
large share The establishm ent of chairs of geography in
th e giving of college
some of our great est universities
courses in physiography meteorology an d commerce
and the general ext ension of geography courses in normal
may be cited as
and high sc hools
sc hools
ac ad emies
evid enc e of t hi s growing appreciat ion of th e im portan ce of
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While physiographic processes and resu lting land forms
oc cupy a large plac e in geographical control the earth in
its simple mathematical as pect s shoul d be bett er u nder
and mathematical geog raphy
stood t han it gen erall y is
d eserves a larger place in the literature of the subj ect than
th e f ew pages generally given to it in our physical geo g
astronomies I t is generally
elem entary
raphies and
conceded that the mathematical portio n of geography
is th e most d ifficult th e most poorly taught and l east
an d that stud ent s require th e most help in
u nd erstood
The subj ect matter of mathematical
u nd erstanding it
ne
a
s
o
raphy
att
r
d
about
in
m
ny
work
and
no
e
o
sc
e
i
s
e
g g
book treats th e subj ect with any d egree of thoroughn ess
or even makes a preten se at doing so I t is with the
view of meeting the need for such a volume that this
work has been und ertaken
Although d esigned for use in secondary school s and for
teachers preparation much mat erial herein organiz ed
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1 8 5 7 05
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PRE FACE
may be used in the upper grad es of the elementary school
The subj ect has not been present ed from the point of
view of a little child but an att e mpt has been mad e to
keep its scope wit h in the attainm ents of a stud ent in a
norm al school ac ad emy or high school I f a very short
course in mathematical geography is given or if st udents
are r elatively advanc ed much of th e subj ect matt er may
be omitt ed or given as special re ports
To t h e stud ent or t eacher who find s some portions too
difficult it is sugg ested that the discussions which seem
obscure at first read ing are oft en mad e clear by ad ditional
e xplanation give n farther on in t h e book
Usually the
second study of a topic w hich see ms too difficult should be
d e ferred until the entire chapter has been read over care
fully
The experimental work which is suggested is given for
the purpo se of making th e principl es studied concret e an d
vivid The measure of the educational value of a labora
tory exercise in a school of secondary grad e is not found
in the acad emic result s obtained but in the attainment of
a conc eption of a proc ess The stud ent s d etermination
of latitud e for example m ay not be of much value if its
w orth is estimat ed in t erms of fact s obtained but th e
form ing of the conc eption of the proc ess is a result of
inestimabl e educational value Much time may be wasted
ho wever if th e stud ent is required to red iscover t he fact s
and laws of nature which are oft en so simple that to see
is to acc e pt and und erstand
Acknowledgment s are d u e to many eminent scholars
for suggestions verification of data and other valuable
assistanc e in the preparation of this book
To P resid ent George W Nas h of th e Northern Normal
and I ndu strial S chool who carefully read the entire manu
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PREFACE
cript and proof and to whose thorough training clear
in sight and kindly int erest t he author is und er dee p
obligations especial credit is grat efully accord ed Whil e
th e author h as not avail ed him self of th e direct assistanc e
of his sometime t eacher Professor Frank E Mitchell now
head of th e d e part ment of Geography and Geology of t h e
S tate Normal S chool at Oshkosh Wi scon sin h e w ishes
form ally to acknowledge h is obligation to him for an
abiding int erest in the subj ect For t h e critical exam i
nation o f port ions of the manuscript bearing upon fi elds
in which they are acknowl edged authorities grateful
is ext end ed to P rofessor Franci s P
ac knowledgment
Leavenworth head of t h e d epartment of Astronomy of
the University of Minnesota ; to Lieut enant Command er
E E Hayd en head of th e d epartm ent of Chronom et ers
and Time S ervic e of the Unit ed S tates Naval Observatory
Was hington ; to P resident F W Mc Nair of th e Michigan
Co llege of Min es ; to P rof essor Cl eveland Abbe of the
United S tat es Weather B ureau ; to P resid ent R obert S
Woodward of the Carnegie I nstitution of Washington ; to
P rofesso r T C Chamberli n head of th e d epartment of
Geology of th e University of Chicago ; and to P rofessor
Charl es R Dryer head of the d e partm ent of Geography
of th e Stat e Normal S chool at Terre Haute I ndiana For
any errors or d efects in the book the author alone is
respons ible
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CONTE NTS
CHAP TE R XI
S TATE S GOV E RN M E NT LA ND S U R V E Y
CHAP TE R X I I
TRI AN G U LATI O N
IN
ME AS U R E M E NT
AND
CHAPTE R
TH E E ARTH
IN
S
S
UR V E Y
XI I I
PA C E
CHAP TE R XI V
HI S TO R I CA L S K E TC H
AP P E ND I X
GLOS S AR Y
I ND E X
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MATH E M ATI CAL GE OGR AP H Y
CHAPTER I
I N TROD UC TOR Y
OB S E R V ATI ON S
AN D
E X P E R I M E NTS
On t h e first
cl ear evening
and the polestar I n S eptem
B ig D ipper
o bserve th e
ber and in Dec ember early in t h e evening they will be
nearly in the positions represented in Figure 1 Where
is the B ig D ipper
lat er in the evening
Find out by obser
Observations
th e S tars
of
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vat ions
°
1
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Lem
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0
readily
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to 3
a
pick out Cassiopeia s Sk i es
t
Chair and th e Littl e
g
5
D i p per
Ob s e r v e
;
the ir apparent mo
Notic e
tions al so
the position s of stars
in diff erent portions of the sk y and observe where they are
later in the evening D o th e stars around th e polestar
remain in the same position in relation to each other
th e B ig D ipper always like a dipper Cass io peia s Chair
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I n Urs a Maj o r c o mm o nly c all ed th e
P lo w
The Great
No rt h S t a r
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Wago n
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or
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Ch arles
o th er co u ntries
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s
Wago n
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in E nglan d, No rway , Ge rm any,
an d
10
I NTR OD UCTOR
Y
always like a chair and both always on opposite sides of
th e polestar ? I n what sen se may they be call ed
fixed
stars (see pp 10
8
Make a sketch of the Big D ipper and the poles tar
recording t he dat e and time of observation P reserve
your sketch for future referenc e marking it E xhibit 1
A month or so lat er sketch again at the same time of
night using the same sheet of paper with a common
polest ar for both sketches I n making your sketches
be careful to get the angle formed by a line through
th e
pointers and the polestar with a perpendicular to
th e horizon
This angl e can be formed by observing the
s id e of
a building and the point er line I t can be
measured more acc u rat ely in the fall months with a pai r
of dividers having straight edges by placing
o ne out er edge n ext to t he perpendicular
sid e of a north window and Opening t he
divid ers until the other outside edge is
parallel to the po inter line (see Fig
Now lay the divid ers on a sheet of paper
rept e
and mark the angl e thus formed
senting t he po sitio ns of stars with ast erisks
Two penny rulers pinned t hrough the end s
will serve for a pair of divid ers
P h ases of th e Mo o n
Not e the positio n
of the moo n in th e sk y on successive nights at the same
hour Where does the moon rise ? Does it rise at the
sam e time from day to day ? When t he full moon may
At sunrise
When
be obser ved at sunset where is it
there is a full m oon at midnight where is it ? Assume
it is sunset and the moo n is high in the sk y how much of
t h e lighted part can be see n ?
An swers to the foregoing questio ns should be bas ed upon
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THE NOON S HADOW
first
hand
11
b rvations I f the questions can not easily
be answered beg in Obse rvation s at the first opportunity
Perhaps th e best time to begin is when both su n and moon
may be seen above t he horizon At each observatio n
notic e the po sition of the su n and of the moon the portion
of the light ed part which is turned toward the earth and
bear in mind the simple fact that the mo on always shows a
lighted hal f to the sun
I f the moon is rising when the su n
is setting or t he su n is rising when the moo n is setting
the observer must be standing directly between them or
approximat ely so With the su n at your back in th e east
and facing t he moo n in t he west you see t h e moon as
though you were at the su n Ho w much of t he light ed
part of the moon is then seen ? B y far the best apparatus
for illustrating the phases of the moo n is th e su n and
moon themselves especially when both are observed above
the horizon
Th e Noo n S h adow
S ome ti me early in th e t erm from
a convenient south window m easure upon t he fl oor t h e
length of the shad ow when it is shortest during the
day R ecord the meas urement and the date and ti me of
Mark this
day R epeat th e measureme nt each week
E xhibit 2
On a south facing window sill strike a north sout h line
s
r
s
s
e
m
thod
for
doing
thi
a
di
cu
d
on
pp
1
s
e
6
s
e
(
Erec t at the south end of this lin e a perpendicular board
say six inches wid e and t wo feet long with t h e edge n ext
True it with a plumb line ; one
the north south line
This should
mad e with a bull et and a thread will d o
be so plac ed that the shadow from t he edge of the board
may be record ed on the window sill from 1 1 o clock A M
until 1 O cloc k P M (see Fig
Care fully cut from cardboard a semicircle and mark t he
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12
I NTR ODUCTOR Y
d egrees beginning w ith the
middle radius as z ero Fast en
this upon the window sill
with t he z ero meridian coin
ciding with the north south
line Note accurat ely the
clock tim e when the shadow
from the perpendicular board
crosses the line also where
the shadow is at twelve
o clock R ecord these facts
with the d ate and preserve as
Continue the o b
E xhibi t 3
servatio n s ev ery f ew days
When the shadow
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No o n
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had
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Fi
The
is
Su n
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s
du e
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Meridian
north
carefully
measure the angl e formed
by the shadow and a level
lin e The simplest way is
to draw th e window shad e
down to th e top of a S heet
of cardboard plac ed very
nearly north and south with
t he bo ttom l evel an d then
draw the shad ow lin e the
lo we r acute angle being the
on e
sought
se
i
e
F
(
g
Another way is to drive a
d o of S u n a t n o o n
pin in the sid e of th e windo w
Pie 4
casing or in the edge of the
vertical board (Fig
fast en a thread to it and conn ect
t h e other end of th e thread to a point on th e sill where th e
shadow fall s
A still bett er method is shown on p 172
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13
CENTR I FUGAL FOR CE
hadow is north th e su n is as high in the sk y
as it will get during t he day and t he angl e thus m easured
gives t he highest altitud e of the su n for the day R ecord
the m easurement of t he angl e with th e dat e as E xhibit 4
Continu e these record s from week to week es pecially
noting th e angle o n one of t he following dat es : March 2 1
Ju ne 22 S eptember 23 Dec ember 22 This angle on
March 2 1 or S eptember 23 if subtracted from
will
e q ual t he latitud e
of the observer
S ince the
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A FE W TE R M S E X P LAI N E D
The
literal meaning of th e word
suggest s its curre nt meaning
I t comes from the Latin
centm m
center ; and
fu gere to flee A cen
trif u gal forc e is one
directed away from a
When a stone
cent er
is whirled at the end of
a string t he pull which
the stone gives the
string is call ed c entri
fugal forc e
B e cause
of the inertia of the
the w h i rl i n g
stone
e n d s to fl y o f f
T
motion given to it
Pi g 5
by the arm t end s to
make it fl y off in a straight line (Fig
and this
The measure of the
it will do if th e string breaks
I f th e
centrifugal forc e is the t en sion on th e string
string be fasten ed at th e end of a spring scal e and the
Centrif u gal Fo rc e
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This is
exp lained o n
1
7
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1
7
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I NTR OD UCTOR
Y
n whirled the scale will show the amou nt of the c entri
fugal force which is given the ston e by the arm that
whirls it The amount of this forc e ( C) varies with the
mass of t he body (m ) its velocity (v) and th e rad ius
o f the c ircle (r) in which it moves in th e following ratio :
sto e
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The instant that th e speed becomes such that the avail
able stren gth
Of
th e
tring is l ess than
s
th e
value of
7n
2
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however slightly the stone will cease to follow t he c u rve
and will immediately take a motion at a uniform speed
in the straight line with which its motion happened to
coincid e at that instant (a tangent to the circle at th e point
reached at that moment )
Cen trifu gal F orce on the S u rface of the E arth Th e
rotating earth impart s to ev ery portion of it sav e along
the axis a c entrifugal forc e which varies according to t he
forego ing formula r being the distanc e to the axi s or the
radius of the parall el I t is obvious that on the surfac e
Of t he earth the c e ntrifugal forc e d u e to its rotation is
greatest at the equator and z ero at th e poles
At the eq uator c entrifugal forc e ( C ) a mounts to about
h
d
s
e
that
of
t
arth
attraction
thu
an
obj
ct
e
s
a
n
e
(g)
fig
there which weighs 288 pound s is lightened just on e pound
by c entrifugal forc e that is it would weigh 289 pounds
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were
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arth at rest
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At
On th e u s e o f sym bo ls , su ch
see Ap p en dix, p 307
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as
latitude
C
C f o r cen t rif u gal
7
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3
3 3
fo rc e
,
i
s
that
(
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f
r latitu de,
o
5
9
15
CE NTR I PE TAL FOR CE
trifugal force is 555 the forc e of
cen
o
at
57s
For
q uare of
s
th e
the
1156
’
rth s rotatio n
ea
cosine of
the
arth s att raction ) ;
e
Q
—
lighten ing
t he
any latitud e
force du e to
60 , C
at
,
the
—
1
’
eff e
ct
e
qual
of centrifugal
_
9
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s
289
51
latitud e ( C
X
289
t he
times
’
t
g)
cos
.
.
referring to the table of cosines in the Appendix the
“
stud ent can easily calculat e th e
lightening influence
For example
o f centrifugal forc e at h is own latitud e
say the latitud e of t he observe r is
By
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°
Cosme 40
.
7660
.
x 7660
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’
289
.
4 92
Thus the earth s attraction for an obj ect
’
urfac e
°
at latitud e 4 0 is 492 times as great as c entrifugal forc e
there and an obj ect weighing 491 pound s at that latitud e
*
would weigh one poun d more were the earth at rest
Centripetal Force
A c entripetal (cen trum c ent er petere
to seek ) forc e is on e direct ed to ward a c ent er that is at
right angl es to t he direction of m otion of a body
To
distinguish between c entrifugal force and c entripetal
force the stud ent should realiz e that forc es never occur
singly but on ly in pairs and that in any forc e action there
are always two bodies conc ern ed
Na me them A and B
S uppose A pus hes or pulls B with a c ertain strength
Th is cann ot occur exc ept B pushes or pull s A by t he same
amount an d in t he oppo sit e direction
This is only a
s imple way of stating Newt on s third law that to every
on
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Th ese
al lo wan ces
cal cu l atio ns a re
f o r th e
t
b as ed u p o n
o b la en ess .
th
a s ph e ric al e a r
an d
m ak e
no
I NTR OD UCTOR Y
16
ction ( A on B ) there corres pond s an equal and opposite
reaction ( B on A)
Centrifugal forc e is the reac ti on of t he body against the
c entripetal forc e which hold s it in a curved path and it
must al ways exactly equal the c entripetal forc e I n th e
case of a stone whirled at the end of a string the nec essary
forc e which t he string exert s on t he stone to keep it in a
curved path is c entripetal force and the reaction Of the
ston e upon t h e string is c ent rifugal forc e
The formulas for c entripetal forc e are exactly t he same
Owing to the rotation of
as those for c entrifugal forc e
t he earth a body at the equator d escribes a circle wit h
uniform speed Th e attractio n of t he earth supplies the
c entripetal forc e required to hold it in the circle The
earth s attraction is greatly in exc ess of that which is
required being in fact 289 times the amount need ed
The cen tri petal force i n thi s case i s that porti on of the attrae
ti on which i s u sed to hold the object in the ci rcu la r cou rse
The exc ess is what we call t he weight of the body or the
forc e of gravity
I f therefore a spring balanc e sus pending a body at the
e q uator shows 288 po u nd s we infer that t he earth really
pulls it with a forc e of 289 pound s but o ne po und of this
pull is expend ed in changing the direction of the motion
of t he body that is the value of c entripetal forc e is on e
po und The body pulls t he earth to the same ext ent
that is the c entrifugal forc e is al so on e pou nd At t he
pol es n either c entripetal nor c entrifugal forc e is exerted
upon bodies and henc e the weight of a body there is the
full measure of the attraction of the earth
Gravitatio n
Gravitation is t he all pervasive forc e by
virtue of which every particl e of matt er in the univ erse
is constantly drawing to wa rd itself every other particl e
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I NTR OD UCTOR Y
8
are twic e as far apart
Two lines AD and A H ( Fig
at C as at B because twic e as far away ; three ti mes as far
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apart at D as at B because three times as far away etc
Now light radiates out in every direction so that light
coming from point A (Fig
when it reac hes B will be
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pread over the square of B F at C o n the square C G
at D on the square D H etc C being t wic e as far
a way from A as B the sid e C G is twic e that of B F
as we Observed in Fig 7 and its square is four times as
great Lin e D H is three times as far away is three
times as long and its square is nine times as great The
light be ing spread over more spac e in the more distant
obj ect s it will light up a given area less The square
at B rec eives all the light within the four rad ii the
’
same square at C
rec eives on e fourth of it at D on e
ninth etc The amount Of light decreases as the squ are of
the di stance increases
Th e forc e of gravitation is exerted
in every direc tion and varies in exactly t he same way
Thus t he se cond law of gravitation is that t he forc e varies
inversely as the square of the distanc e
Gravity
The earth s attractive in fl u enc e is call ed
ect is s i m ply the me asure of
O
w
ight
of
an
bj
h
r
a
v
i
t
T
e
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g
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GR AVI TY
19
force of gravity An o bj ect on or above the su rf ac e
of the earth weighs less as it is moved away from the
center of gravity
I t is d iffit
to realiz e that what we
call the we ight of an obj e ct is simply the exc ess of attrac
tion which the earth po ssesses for it as compared with
other forc es acting upon it and that it is a pu r ely relative
afl air t he sam e obj ect hav ing a diff erent weight in diff erent
places in the solar syst em Thus the same pound weight
take n from t he earth to the sun s surfac e would we igh 2 7
po und s there only one sixth of a pound at the surface of
the moon over 2} pound s on Jupit er et c
I f the earth
were more d ense Obj ects woul d weigh more on the surfac e
s
Thus if the earth retained its present siz e but contained a
m uch matt er as the su n has th e strongest man in the world
c ould not lift a silver half dollar for it would then we igh
over five tons A pendulum clock would then tick 575
times as fast On the other hand if the earth were no
d enser than the su n a half dollar would weigh only a
trifle more than a dime now weighs and a pendulum clock
would tick only half as fast
From th e table on p 266 giving th e m asses an d d is
tances of the su n moon and principal planets many
interesting problems involv in g the laws of gravitation
may be suggest ed
To illustrat e let u s take the probl em
What would you weigh if you were on the moon
Weigh t on th e Moon The mass of the moon that is
1
the amount of matt er in it is 3 1 that of the e arth
Were it the same siz e as the earth and had this mass one
pou nd on the earth would weigh a little less than one
According to the first law of
e ightieth of a pound there
s proportion :
vitation
h
a
v
e
thi
w
e
r
a
g
1 : 1h
Moon s attraction
1 E arth s attraction
Fo r a mo re accu rate an d detail ed disc ussio n o f gravity s ee p 2 79
the
.
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,
,
-
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’
,
,
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,
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,
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,
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,
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,
,
-
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,
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’
’
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,
.
.
20
I NTR OD UCTOR Y
B u t the
radius Of the moon is 108 1 m iles only a little
more than o ne f o u rth tha t of the ear th Since a person
on the moon wou ld be so much neare r the ce nter of gravity
than he is on the earth he would weigh much m ore there
than here if the m oon had the same mass as the earth
Acco rding to the second law of gravi ta tio n we have thi s
proportion :
,
.
,
.
2
.
Earth
’
s attrac tio n z
We have the n
1
.
2
.
.
Att Earth
.
:
a ttrac tion
Att Moo n
.
1
.
,
4000
‘
z ur
3
1081
.
1
Att Moon
1
.
these by m ul tiplying
Att
There fore
:
s
1
propor tions :
the two
Att Ea rth
Combining
Moo n
’
1
Ear th
:
,
we ge t
Att Moon
6
:
.
1
.
pounds on the earth would weigh only
Your weigh t the n divided by
o ne poun d on the moon
represe n ts wha t it would be on the moon There
six
you could j u mp six times as high if you could live to
jump at all on that cold and almost airless satelli te (see
pp 263
A sphere is a solid
Th e S ph ere Circ l e and Ellipse
bounded by a curve d surface all points of which are e qually
di stant from a point within call e d the c e nte r
A circle is a plane figu re boun de d by a curve d line all
poin ts of w hich are e qually di stan t from a point within
I n geography wha t we commonly call
c all e d the c en te r
circles such as the e qua tor pa rallels and m eri dians are
Wherever u sed
rea lly only the circumfere nc es of circles
six
.
,
,
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,
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,
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,
,
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.
,
,
,
.
THE S P HER E, oi nc LE AND ELLI P SE
,
this book unless otherw ise stated the term circl e
refers to the circumferen c e
E very circl e is conc eived to be divid ed into 36 0 equal
parts called d egrees The greater the siz e of the circle
the greater is t he length of each d egree
A radiu s of a
circle or of a sphere is a straight line from the boundary
to the center Two rad ii forming a straight line con
stitu te a di ame ter
Circles on a sphere divid ing it into two hemispheres are
called great ci rcles Circles on a sphere dividing it into
unequal parts are called small ci rcle s
All great circles o n the sam e sphere bisect each other
regardless of the angle at which they cross o ne another
That this may be cl early seen w ith a globe before you test
these two propositions :
°
A point 180 in any direction from on e point in a
a
great circle must lie in the same circle
b Two great circles on t he same sphere must cross
°
som ew here and th e point 180 from the On e where the y
cross lies in both of the circles thus each great circle
divid es the other into two e qual parts
An angl e is the diff erenc e in direction of t wo lines which
if extend ed w ould meet Angles are measured by u sing
t he meeting point as the c ent er Of a circl e and finding th e
fraction of the circle or number of d egrees of the circl e
includ ed between the lines I t is well to prac tic e esti
mating diff erent angles and then to test the accuracy of
t he est imates by re ferenc e to a grad uated quadrant or
circle having the degrees marked
An ellipse is a closed plane curve such that the su m Of
th e distanc es from o n e point in it to two fixed point s within
called foci is equal to the su m Of the distanc e s fro m any
other po int in it to the foci The ellipse is a conic section
In
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,
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.
,
,
.
I NTR OD UCTOR Y
22
formed by cutt ing a right cone by a plane passing obli quely
through its oppo site sides (see E llipse in Glossary )
To constru ct an ellipse
drive two pi ns at points
for foci say three inches
apart With a loop of
non elastic cord say ten
inches long mark t he
boundary lin e as repre
se nt ed in Figure 10
.
,
,
.
-
,
,
.
Orbit
of
th e
E arth
.
The
orbit of the earth
I s an ell i pse
To lay o ff
E l l ip s e
ellipse whi ch shall
an
AaA: Fo c i C D Min o r Ax/s
quite co rrectly represent
X Y Maj o r Axis A toAjFocgl
Dis tan c e AM AM ANTA”
t he S hape of the earth s
m 9
orbit place pins on e
tenth of an inch apart and make a loop of string
inches
long
This loop
can easily be mad e
by driving two pin s
inches apart
and tying a string
l o o ped ar ou n d
them
.
.
.
.
.
,
,
.
4
.
,
’
"
'
,
.
.
Shape
th e
of
The
arth
is a spheroid or a
D COHS
approaching
solid
An Ellips e
a sphere (see S phe
roid in Glossary )
The diameter upo n which it rotates is c alled the
The end s of the axis are its pole s I maginary lines on the
E arth
.
e
,
.
.
S HAP E OF THE E AR TH
23
rface of the earth extending from pole to pole are called
l
meridia n s
While any number of meridians may be
conce ived of we u sually think Of them as one degree apart
We say for exa mple the ninetieth meridian meaning the
meridian ninety d egrees from th e prime or initial meridian
What kind of a circle is a meridian circle ? I s it a true
c ircle ? Why ?
The eq uato r is a great circle midway between the po les
P arallels are small circles parall el to the equator
I t is well for the stud ent to bear in mind the fact that
it is th e earth s rotation on its axis that d etermines most of
A sphere at rest would not have
the foregoing facts
eq uat or m eridians etc
Th e te rm m e ridian is freq u en tly used to designate a g reat c irc le
i
k
l
I
n
h
h
u
h
o
s
b
o
o
su
i
t
r
o
t
h
es
h
l
i
n
t
t
e
c
c
i
s
a
ss
a
rc
d
es
i
n
e
a
a
e
d
g
p
p
g
g
su
=g
.
,
.
,
,
,
.
.
.
’
.
,
.
,
.
merid ia n
circ le, sin ce each
m e ridian is
nu
mb ered
regardless o f
its
o p po
CHAPTE R I I
THE F ORM OF
THE EARTH
Circu m n avigation
The
THE E AR TH
S P HE R E
A
tatement s commonly given as
proofs of the spherical form of the earth would oft en apply
S
e
hap
d
or
a
di
k
hap
d
as well to a cyl ind er or an e
s
S
e
gg
P eople have sailed around it
The S hadow of
body
the earth as seen in t he eclipse of th e moon is al ways cir
cular etc do not in themselves prove that the earth is a
They might be tru e if the earth were a cylind er
sphere
B u t m en have sail ed around
or had the shape of an egg
S O might they a lemon S haped
it in diff erent directions
body To make a complet e proof we must S how that m en
have sailed around it in practically every direction and
have fou nd no appreciable diff erenc e in the distanc es in
th e diff erent directions
E arth s S h adow alw ays Circu lar
The shado w of t he
B ut
earth as see n in t h e lun ar e clipse is always circular
a dollar a lemon an egg or a cylind er may be so plac ed
When in addition
as always to cast a circular shad ow
to this statement it is S hown that the earth presents many
diff erent S id es toward the su n during di ff erent eclipses of
t he moon and t he S hado w is al ways circular we have a
proof po sitive for nothing but a sphere cast s a circular
Th e fact that
S hado w w hen in many di ff erent po si tion s
eclipses of th e moon are seen in diff erent se ason s and at
diff erent times of day is abu ndant proof that practically
.
s
-
-
”
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,
”
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”
-
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,
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’
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,
,
,
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,
,
.
24
THE FOR M OF THE E AR TH
26
S hif tin g
of
S tars
an d
D ifi eren ce in Tim e
.
The
proo f
which first d emonstrated the curvature of the earth and
on e whi ch the stud ent should cl early un d erstand
is the
disappearance of stars from the southern horizon and the
rising higher of stars from the northern horizon to persons
traveling north and t he sinking of northern stars and the
rising of southern stars to south bound travel ers After
people had traveled far enough north and south to make
an apprec iable diff erence in the position of stars they
observed this apparent risin g and S inking of the sk y Now
two travelers one going north and the other g oing south
will see the sk y apparently elevated and d epressed at the
sam e time ; that is th e portion of th e sk y that is ris ing for
S inc e it is impossible
on e will be S inking for the other
that the stars be both rising and sinkin g at the same
the move ment of
time only one conclusion can follow
the stars is apparent and the path traveled north and
south must be curved
Owing to the rotation of the earth on e sees the same
stars in di ff erent pos itions in th e S k y east and west so the
proof just given simply shows that the earth is curved in
a north and south direction Only when timepiec es were
invented which could carry the time of one plac e to diff er
ent portion s of t he earth could th e apparent po sition s
of the stars prove the curvature of the earth east and
mean s of the telegraph and telephone we
have most exc ellent proo f that the earth is c u rved east
and west
I f th e earth were flat when it is sunrise at P hilad elphia
it would be sunrise al so at S t Louis and Denver S un
rays extending to these plac es which are so near together
as compared w ith t h e tre mendous distanc e of t he su n over
would be almost parall el
n in ety millions of mil es aw ay
,
,
,
-
.
,
.
,
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,
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,
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,
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,
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,
,
27
ACT UAL ME AS URE ME NT
the earth and would strike these points at about the
sam e angle
B u t we know from the many daily messages
on
.
between these cities that
hour later than it is in St
time in P hilad elphia is an
Louis and two hours later than
su n
.
When we kn ow that the curvature of the earth north
and so uth as observed by the ge neral and practically
un iform ris ing and sin king of the stars to north bound and
so uth bound travelers is the sam e as the curvature eas t
and west as shown by the diff ere nc e in time of plac es
eas t and west we have an exc elle nt proof that the earth is
a sphere
Actual Measu rem en t
Actual measurement in man y
d iff erent places and in nearly every direction S hows a prae
tically u niform curvature in the diff erent directions I n
digging canals and laying waterm ains an allowance must
always be mad e for the curvat u re of th e earth ; also in
surveying as we shall notic e more explicitly farther on
A simple rul e for finding the amount of curvature for
an y given distanc e is the followin g :
S q uare the nu mber of mi les representin g the di stanc e and
two thi rds of thi s nu mber represen ts i n feet the departu re
-
-
,
.
.
.
,
‘
,
.
,
distance is 1 mile That number squared
is 1 and two third s of that number of feet is 8 inches
Thus an allowance of 8 inches must be mad e for 1 mile
I f the distanc e is 2 miles that number squared is 4 and
two t hird s of 4 feet is 2 feet 8 inches An Obj ect then
1 m ile away sinks 8 inc hes below the level line and at 2
miles it is below 2 feet 8 inches
To find the distanc e the height from a l evel line be ing
h
s
h
t
e
h
iv
n
av
e
e
conv
r
e
of
for
going
ul
r
w
e
t
e
e
e
e
:
g
S uppose the
.
,
.
.
,
,
,
.
,
,
,
,
.
,
,
M u ltiply the
nu mber representin g
the he ight i n
feet by l 5
,
THE FORM OF THE EAR TH
28
and
the
h
s
d
u
c
t
r
i
o
t
f
p
object i s si tu a ted
squ are root o
mile s distan t the
the
represen ts
n u mber o
f
.
The
following table is based upon the more accurate
formul a :
D istanc e ( miles )
height ( feet )
.
Ht
.
ft
.
D is t m il es
Ht
.
.
ft
TH E E AR TH
AN
t
.
Ht
mi le s
.
ft
.
D is t m iles
.
OB LATE S P H E R OI D
I n th e
year 16 72 John R icher the
astronomer to the R oyal Acade m y of S cienc es of P aris
was sent by Loui s X I V to the island of Caye nne to mak e
certain astronomical observations His P arisian clock had
its pendulum slightly over 39 inches long regulat ed to
beat second s S hortly after h is arrival at Cayenne he
notic ed that the clock was losing time about t wo and a
half minutes a day Gravity evid ently did not act with
The
so much forc e n ear the equator as it did at P aris
as tronom er foun d it n ec e ssary to S hort e n the pendulum
nearly a quart er of an inch to get it to sw ing fast enough
Ri ch er
’
s
D iscovery
D is
.
.
,
,
.
,
,
.
,
,
.
,
,
.
.
AMOUNT OF OB LATE NE S S
29
R icher
re ported these int eresting fact s to his colleagues
at P aris an d it aroused much discussion At first it was
thought that greater centrifugal force at the e quator
cou nteracting the earth s attraction more there than else
where was the explanation The diff erenc e in the forc e
of gravity however was soon discovered to be too great
to be thus accounted for The only other conclusion was
that Cayenne must be farther from the c enter of gravity
than P ari s (see the discussion Of Gravity Appe ndix
p 2 79 ; al so Historical S ketch pp 2 73
R e peated experiment s show it to be a general fact that
pendulums swing fast er on t he surfac e of the earth as o ne
approaches the poles Careful m easurements of arc s of
meridians prove beyond questio n that the earth is flattened
to ward the poles somewhat like an oblat e spheroid
Further evid enc e is found in t he fact that the su n and
planet s so far as asc ertained sho w this same flatt ening
The cause of the oblaten ess is
Cau se o f Oblaten ess
the rotatio n of t he body its fl att enin g eff ect s be ing m ore
marked in earlier plas tic stages as the earth and other
planet s are generally believed to have been at on e ti m e
The reaso n why rotatio n causes an equatorial bulging
Ce ntrifugal forc e increases
is not difficult to und erstand
aw ay from the poles toward the equator and gives a lifting
or lightening i nfluenc e to portion s on the surfac e I f the
earth were a sphere an Obj e ct w e ighting 289 pound s at
the pol es would be l i ght ened just o n e pound if carri ed to
Th e form given
th e sw iftly rotating equator (se e p
the earth by its rotation is c all ed an oblat e spheroid or an
ellipsoid Of rotation
To represent a meridian circle
Am ou nt of Oblaten ess
accurat ely we should represent the polar diameter about
h
e
s
r
part
S
ho
t
r
than
e
q
uat
rial
diam
t
r
T
hat
thi
e
t
o
e
e
33
3
,
.
,
’
,
.
,
,
.
,
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,
,
.
.
,
.
,
,
.
.
,
,
.
.
.
.
.
.
,
.
30
THE F OR M OF THE E AR TH
d iff erence is
not perceptible to the unaided eye will be
apparent if the construction of such a figure is attempted
l
say t en inches in diam et er in on e dire ction and g o of
inch l ess in the opposite direction The oblateness of
S aturn is easily perc ept ible be ing thirty times as great as
that of the earth or one tenth (see p
Thus an
ellipsoid ni ne inches in po lar diamete r ( minor axis ) and
ten inches in e quatorial diameter ( major axis ) w ould rep
resent the form of that planet
Although the oblateness of the earth seems slight when
represented on a small scale and for most purpo ses may be
ignored it is nevertheless of vas t importance in many
problems in surveying astronomy and other subj ects
Und er the discussion of latitude it will be Shown how this
oblateness makes a diff erence in the lengths of degrees of
latitude and in the Appendix it is S hown how this equa
t orial bulging shortens the length of the year and changes
the inclination Of th e earth s axis (see P re c ession of the
E quinoxes and Motio n s of t he E arth s Axi s )
I t is of very great impor
D im ensio n s o f th e S ph ero id
tanc e in many ways that astronomers and surveyors know
as e xactly as po ssible t h e dimen sions of t h e sphe roid
Many m en have mad e est imat es based upo n astronomical
fact s pendulum experiment s and careful surveys as to the
P erhaps the
e quatorial and polar diamet ers Of t h e earth
most w id ely used is the one made by A R Clarke for many
years at t he head of t h e E nglish Ordnance S urvey k nown
as th e Clarke S pheroid Of 1866
,
‘
'
‘
.
,
.
,
.
,
,
.
,
,
’
’
.
.
.
,
,
.
.
.
,
,
.
CL A R K E S
A
B
.
.
t
PH E R O I
D
or
1866
.
ter
m il es
m il es
E q u a orial d iam e
P ol ar d iam eter
Obl aten ess
A
B
A
.
1
D I ME NS I ONS OF THE S P HE R OI D
31
I t is
upon this spheroid of reference that all of th e
work of the Unit ed S tates Geological S urvey and of the
United S tates Coast and Geod etic S urvey is based and
upon wh ich most of the dimensions given in this book are
d etermin ed
I n 1878 Mr Clarke mad e a recalculation based upon
additiona l information and gave th e follow ing dimensions
though it is doubtful whether these approximations are
any more n early correct than those of 186 6
,
.
.
,
,
,
.
CLAR K E S PH E R O I D
A
B
.
.
or
1878
.
ter
Eq u atorial d iame
P o l ar di am eter
A
592 m iles
m il es
B
l
A
An ot her
andard spheroid of reference Oft en referred
to and one used by the United S tat es Governmental
S urveys before 1880 when the Clarke spheroid was
adopted was calcul ated by the distinguished P russian
astronomer F H Bessel and is call ed the
st
,
,
,
,
.
.
,
B E SSE
E q u atorial diame
B
P ol ar di ameter
.
on
1841
.
ter
A
.
L S PH E R O I D
Oblaten ess
Man y
A
m iles
m il es
1
B
A
areful pendulum t ests and a great amount of
scientifi c triangulation survey s of long arc s of parall els
and m eridians within rec ent years have mad e availabl e
considerable data from wh ich to det erm in e the true
dimensions of the spheroid I n 1900 th e United S tat es
Co ast and Geod etic S urvey co m plet ed the meas u rem ent
of an arc across th e United S tat es along the 39t h parall el
c
.
,
THE FORM OF THE E AR TH
32
from Cape May New Jerse y to P oint Arena California
°
t hrough 48 4 6 of longitud e or a distanc e of about
miles This is th e most ext ensive piec e of geod etic su r
ve yin g ever und ertake n by any nation and was so care fully
done that the total amount of probable error does not
amount to more than about eighty five feet A long are
has bee n surveyed diagonally from Calai s Ma in e to
°
New Orlean s Louisiana through 15 1 Of latitud e and
°
miles Another
22 4 7 of longitud e a distanc e of
long are w ill soon be completed along the 98th meridian
across the United S tat es Many shorter arc s have also
been surveyed in this country
The E ngli sh government und ertook in 1899 the gigantic
task Of measuring the arc of a meridian ext endin g the
from Cape Town to Alexandria
entire length of Africa
°
This will be when complet ed 6 5 long about half on
and w ill be of great value in
each S id e of the equator
determ inin g the Oblateness R ussia and S wed en have
°
lat ely complet ed the m easurement of an arc of 4 30 on
th e is land Of S pitzbergen which from it s high latitud e
°
°
’
Large
76 to 80 30 N mak es it peculiarly valuable
arc s have been measu red in I ndia R ussia Franc e and
other countries so that there are n o w available many times
as much data from w hich t he form and dim en sion s of t h e
earth may be d et ermined as Clark e or B essel h ad
The lat e Mr Charles A S chott of the Unit ed S tat es
Coast and Geod etic S urvey in di scussing th e survey of the
39th parallel with whi ch he was closely id entifi ed said :
Abundant additional means for improving the existing
d eduction s conc ern ing the earth s figure are now at hand
an d it is pe rhaps not t oo much to expe ct that t h e I nt erna
,
,
,
,
’
,
.
-
.
,
,
’
,
,
’
.
,
.
.
.
.
,
,
,
,
,
.
’
,
,
.
,
.
,
,
,
,
.
.
.
,
,
,
,
’
,
th e
I n his Tran sc o n t in en tal Trian gu latio n
Parall el
.
an d
th e Am e rican Arc
of
THE FOR M OF THE E AR TH
34
nearly circul ar passin g through c entral As ia ( 105
North America and west ern S outh Am erica
east ern
°
7
W
5
(
United S tates Curved Un eq u ally
I t is int eresting to
n ot e that t he dim e n sion s of t he d egrees of the long arc
of the 39th parallel surveyed in the United S tates be ar out
°
,
.
.
Fi g
.
1 3.
Gravimetric l ines
sh ow ing variati on
in f orce of gravi ty
to a remarkable extent the theory that the earth is slightly
flattened longitudinally makin g it even more than that
just given which was calculat ed by S ir John Herschel and
A R Clarke The average length of d egrees of longitude
from the Atlantic coast for the first
miles corresponds
closely to the Clarke table and thus those d egrees are
longer and the rest of th e are corresponds closely to the
B essel table and shows shorter d egrees
,
,
.
.
.
,
,
.
35
GE OI D D E F I NE D
Cape May to Wallace ( K ansas )
Wallace to Uriah (Calif )
mi
.
E arth
not
an
E llipso id
of
Th ree Un eq u al Axes
This
.
oblateness of the meridians and oblat eness of the equa
tor led some to treat the earth as an ellipsoid of three
unequ al axes : ( 1 ) the longest equatorial axis (2 ) th e
I t h as
short est eq uatorial axis and (3 ) the polar axis
been shown however that meridians are not true elli pses
for the amount of flattenin g northward is not quite the
and the mathe matical
sam e as the amount southward
cent er of the earth is not exactly in the plane of the equator
Geo id D efin ed
The t erm geoid which means like the
is now applied to that figu re which most nearly cor
earth
Moun tains valleys
respond s to the true sha pe of the earth
and other slight d eviation s from evenness of surfac es are
treate d as d epartures from th e geoid of referenc e The
following d efinition by R obert S Woodward P resid ent of
very clearly
th e Carnegie I nstitution of Washington
*
e xplain s what is m eant by th e geoid
I magin e the mean sea l evel or the surfac e of th e sea
freed from the undulations du e to wind s and to tid es
This mean sea surfac e which may be conc eived to ext end
through t he continents is called the geoid I t does not
coincide exactly with the earth s spheroid but is a slightly
wavy surface lying partly above and partly below th e
spheroidal surfac e by small but as yet not d efinit ely known
The d et ermination of the geoid is now on e of
amounts
the most importan t problem s of geophysics
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”
.
En cycl opaed ia Am ericana
.
36
THE FORM OF TH E E AR TH
An investigatio n is now in progress in the United S tat es
for determining a n ew geoid of referenc e upon a plan never
followed hitherto The followin g is a lucid d escription
of t he plan by Jo hn F Hayford I n spector of Geod etic
Work United S tates Coast and Geod etic S urve y
.
.
,
,
.
Area Meth o d
of
D eterm in in g F o rm
of
th e E arth
The
may be
whom is
.
method of d educing the figure of the earth
illustrat ed by suppo sing that a S killed workm
an to
given several st iff wires each representing a geod etic are
e ither of a parall e l or a m eridian each be nt to th e radiu s
d educ ed from the astronomic observation s of that are is
told in what latitud e each is locat ed on the geoid and then
requested to construct t he ellipsoid of revolution which
will conform most closely to the bent wires S imilarly
t he area m ethod is illustrat ed by suppos in g that the work
man is given a piec e of sheet metal cut to the outline of
t he continuous tria ngulation w hich is supplied w ith n eces
sar y astronomic observation s and accurat ely mold ed to fix
t he curvature of t he geoid as S ho wn by t he astrono mic
observations and that the workman is then requested to
c o ntru ct the ellip soid of revolution w hich w ill conform
most accurately to the bent sheet S uch a bent S heet
essentially includ es w ithi n it self t h e bent w ires re ferred to
in the first illustratio n and moreover the wires are now
held rigidly in the ir proper relative positions Th e sheet is
much more ho wever than this rigid sy stem of bent lines
for each are usually treat ed as a line is really a belt Of
con sid erable width which is n o w utiliz ed fully I t is o b
vions that the work m an would succ eed much bett er in con
stru c tin g accurat ely th e re quired ellip soid of revolution
from the o ne bent sheet than from the several bent wires
When this propositio n is exam ined analytically it will be
Given at th e I n te rnatio n al Geo grap h ic Co ngress 1904
are
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ON A
MERI DI AN
37
CI RCLE
n to be true to a much greater e xtent than appears
from this crude illustration
The area of irregular shape which is be ing treated as a
s ingle unit e xt end s from Maine to California and fro m
Lake S uperior to the Gulf of Mexico
I t covers a range of
°
°
57 in longitud e and 19 in latitud e and contai ns 4 77
as tronomic stations
This triangulation w ith its numerous
accompanying astronomical o bservations will even with
out combin ation with similar work in other countries
furn ish a remarkably strong d etermination of the figure
and siz e of th e earth
I t is possible that at some distant time in th e future the
dimensions and form of the geoid w ill be so accuratel y
known that instead of using an oblate spheroid of reference
that
i
s
a
ph
roid
of
uch
dim
n
s
ion
s
as
mo
s
t
clo
se
ly
s
e
s
e
(
corres pond to the earth treat ed as an oblat e spheroid such
as the Clarke S pheroid of
as is n o w done it w ill be
possible to treat any particular area of the earth as having
its own peculiar curvature and dim ensions
Con clu sio n
What is the form of the earth ? We went
to consid erable pai ns to prove that the earth is a sphere
That m ay be said to be its general form and in very many
calculation s it is always so treated For more exact cal
cu lat ions t he earth s d e partures from a sphere mu st be
born e in mind The regular geometric solid which the
e arth most nearly rese mbles is an oblat e spheroid
S trictly
s peaking however t he form of t he e arth ( not consid ering
such irregularities as mountains and valleys ) must be
c alled a geoid
see
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D I R E C TI ON S
On
a
Meridian Circl e
on a great circle of
.
t he
ON
TH E
E AR TH
Think
of yourself as standing
e arth passing through t he poles
.
THE FOR M OF THE E AR TH
38
P ointin g
from the northern horizon by way of your feet
to the southern horizon you have poin ted to all parts
of the meridian circle beneath you Your arm has
swrm g t hrough an an gle of
but you have pointed
°
through all poin ts of the meridian circle or 36 0 of it
Drop your arm
or from the horizon to the nad ir
an d you have pointed
through half of the meridian
°
circle for 180 of latitud e I t is apparent then that for
every d egree you drop your arm
you point through
a spac e of two degrees of latitude upon the earth
beneath
°
Drop
The north pole is let us say 4 5 from you
°
your arm 225 from the northern horizon and you will
point directly toward the north pole ( Fig
What
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,
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ever
the
r
ou
l
a
t
i
t
u
d
e
,
y
no rthern
drop you r
ho riz on
as
arm
r
ou
e
a
y
ha lf
degrees
will point di rectl y toward tha t pole
many degrees from
from the pole and you
as
,
.
accustomed to thinkin g of the north
po le as northward in a
horizontal line from you
that it does not seem
real to th ink of it as
below the horizon This
is because o ne is liable
to forget that he is
l
iving
on
a
b
T
o
all
Fi x 4
point to the horizon is
to point away from the earth
A P o in tin g E xercise
I t may not be eas y or even
essential to learn exactly to locate many plac es in re la
tion to the home region but the ability to locate read ily
Th e an gle in cl u ded be t wee n a tangen t an d a ch o rd is me as u red by
one half th e in te rce pted a rc
You may
be
so
.
.
.
1
.
.
,
.
A POI NTI NG E XE R CI S E
39
me salient points greatly clarifies one s sense of loca
tion and conception of the ea rth as a ball
The foll owing exer
Horiz o n Line
is design ed for
c ise
stud ents living not far
from the 4 5th parallel
S ince it is imposs ible
to point the arm or
pe ncil w ith accuracy
at any given angl e it
is roughly adapted for
th e north te mperate
latitudes (Fig
Persons l iving in the
s tates
may
southern
based
use Figure 16
Fig
s
on the 3oth parallel
The stud ent should make the nec essary re adjustment for
h is own latitude
Horiz on Li o
Drop the arm fro m
the n o rthern horizo n
quarter way do wn or
you are
and
pointin g to ward the
north pole ( Fig
Drop
it half way
°
do wn or 4 5 from the
horizon and you are
°
poin ting 4 5 the other
h
id
of
t
e north pole
s
e
Fig “
or half way to the
eq uator on th e same parallel but on t he oppo sit e S id e of
Were you to travel half
the earth in oppos it e longitud e
’
so
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THE F OR M OF TH E E AR TH
40
way around the earth in a d ue eas terly or west erly d irec
°
tion you would be at that point Drop the arm 225
°
°
more or 675 fro m the horizon and you are pointing 4 5
farther south o r to the equator on the opposite S id e of the
°
°
D rop the arm 22 5 more or 90 fro m the horizon
earth
to ward your feet and you are pointin g to ward our anti
°
pod es 4 5 south of the e quator on the meridian opposite
ours Find where on the ea rth this point is I S the
familiar statement digging through the earth to China
based upon a correct idea of positions and di rections on
the earth ?
Fro m the southern horizon drop the arm
and you
are pointing to a plac e having the sam e longi tud e but on
°
Drop the arm 225 more and you poin t to
th e equato r
a plac e having the same longitud e as ours but opposite
°
latit u d e being 4 5 south of t he equator on our meridian
°
Drop the arm 22 5 more and you point toward the south
pole Practice until you can point directly to ward any of
these seven point s w ithout referenc e to the diagram
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LATI TU D E
AN D
LO N GI TUD E
often have diff iculty in
remembering w hether it is latitud e that is measured east
and west or longitude When we recall the fact that
to the people w ho first used these terms the earth was
believed to be longer east and west than n orth and south
and n o w we kno w that o wing to the oblat eness of the
e arth this is actually t h e c ase w e can e asily re m e m ber that
longitud e ( f rom t he Latin lon gu s long ) is measured east
and west The word latitud e is f ro m the Latin la ti tu do
which is fro m latu s w ide and was originally u sed to
d esignate measure m ent of the w idth of the earth or
north and south
Origin
of
Term s
S tud ents
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42
TH E FOR M OF THE
E AR TH
French that o f the Paris Observatory the Greeks that of
the Athens Observatory t he R ussians that of the R oyal
Observatory at Pul k o wa near S t P etersburg
I n the maps of the United S tates the longitud e is often
,
,
.
,
.
koned both from Gree nwich and Washington The
°
latter c ity be ing a trifle more than 77 west of Greenwich
°
a meridian numbered at the top of the map as 90 west
°
from Greenwich is numbered at the bottom as 13 west
from Washington S inc e the United S tates Naval Obser
°
v atory t he point in Washington reckoned from is 77 3
”
81
wes t fro m Gree nwich this is slightly inaccurate
Among all E nglis h speaking people and I n most nations of
the world u nless otherwise d esignat ed t he longitud e of a
place is u nderstood to be reckoned from Greenwich
The lo ngitude of a place is the arc of the parall el inter
Longitud e
cept ed betwee n it and t he prime m eridian
may also be d efined as the arc of the equator intercepted
between the prime meridian and the meridian of the
place whose longitude is sou ght
S inc e longitud e is meas ured on parall el s and parallels
e
s
e
a
re
row
mall
r
toward
pol
d
e
r
e
of
longitud
s
e
h
es
t
e
g
g
shorter toward the poles be ing d egrees of small e r circles
Lati tu de is measured on a meridian and is reckoned
from the equator The number of d egrees in the arc of
a meridian circle , from the plac e whose latitude is sought
to the equator is its latitud e S tated more formally the
latitud e of a plac e is the arc of the meridian int erc ept ed
between the equator and that place (S ee Latitude in
Glossary ) What is the greatest n umber of d egrees of
latitud e any place may have ? What places have n o
latitud e ?
I f t he earth
Comparati ve Lengths of D egrees of Lati tude
were a perf ect sphere meridian c irc les wo uld be true mathe
rec
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43
LATI TUDE
matical
ircles S ince the earth is an oblate sphero id
meridian circles so called curve less rapidly toward the
poles S ince the curvature is greatest near the e quator
one would have to travel less distanc e on a meridian there
to cover a d egree of curvature and a d egree of latitu d e is
Conversely the meridian
thus shorter near the
bein g S lightly flat
tened to ward the
poles one would
travel farther there
to cover a degree
of latitude hence
degrees of latitude
are longer toward
the poles Perhaps
this may be seen
more clearly from
Figure 18
While all c ircles
have
the de
grees oi a small
circle are o f course
shorter than the d egrees of
No w
are of a meridian near t he e quator is obvious ly a part
of a smaller circle than an are taken near the poles and
conseq uently the degrees are shorter Near the poles
because of the flatness of a meridian there an arc of a
meridian is a part of a larger circle and the degrees are
l onger
As we travel northward the North star ( polestar )
rises from the horizon
I n travelin g from the equato r on
miles to see the polestar
a meridian on e wo u ld go
rise one d egree or in other word s to cover one d egree of
Near the pole where the earth
curvat u re of the meridian
c
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THE FORM OF THE EARTH
44
flattest one would have to travel
miles to cover one
degree of curvature of the meridian The average le ngth
of a degree of latitude throughout the Unite d S tates is
almost e xactly 69 miles
Table of Length s of D egrees
The f ollowing table
S hows th e le n gth of e ach de gree of the paralle l an d of the
meridian at every degree of latitude I t is bas ed upon
the Clarke s pheroid of 1866
is
,
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.
.
CHAPTE R I I I
THE ROTA TI ON OF
THE E AR TH
THE CE L E S TI AL S P H E R E
Apparent D om e
a clear night the stars
twinkling all over the sk y seem to be fixed in a dark dome
fitting do wn around the horizon This apparent concavity
studd ed w ith heave nly bodi es is called the c elestial s phere
Where the horizon is free from Obstructions o ne can see
half of the c elestial sphere at a given time from the same
place
A line from on e sid e of the horizon over the z enith point
to the opposite sid e of the horizon is half of a great circle
of the c elestial sphere The horizon line e xtend ed to the
c elestial sphere is a great circle Ow ing to its immense
of
th e Sk y
On
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,
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,
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.
.
I f thes e li nes met at a po ini 50,
dista nt , th e diff e re nce I n t h e ir d irec tio n
c o u ld n o t be m e as ur ed
S u c h is th e ratio
o f t h e d iam e te r o f t he e a rt h and th e dis
tance to the ve ry n eares t o f the s tars
o
.
.
distanc e a line from an obse rver at A ( Fig
pointing
to a star will make a line apparently parallel to o ne from
The most refined measurements at
B to the same st ar
No allo w an c e is h ere m ade f o th e ref rac tio n o f rays o f ligh t o r the
sligh t cu rvat u re o f th e glo b e in th e loc al ity
,
.
,
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r
.
45
46
THE R OTATI ON OF THE E AR TH
present poss ible fail to S how any angle whatever between
them
We may note the following in reference to th e celestial
h
t
e
T
se
e
s
e
e
arth
m
to
a
m
r
point
in
sphere
1
h
e
e
b
e
( )
center of this im mense hollow sphere (2 ) The stars
however distant are apparently fixed in this S phere
(3) An y plane from t he observer if extend ed will divide
es
4
C
t he c elestial sphere into two e qual parts
ircl
( )
may be proj ected on this sphere and positions on it indi
c ated by d egrees in d ist anc e from establish ed circles or
po int s
Cel estial Sph ere seem s to R o tate
The earth rotates on
its axis (the term rotation applied to the earth refers to
its daily or axial motion )
To u s however t he earth
see ms stationary and th e c elestial s phere seems to rotat e
S tanding in the c enter of a room and turning on e s body
around the obj ects in the room seem to rotate aroun d in
The point overhead w ill be th e
the opposite dire ction
only o ne that is stationary I magine a fly on a rotating
I f it were on on e of the poles that is at the end
s phere
of the axis of rotation the obj ect directly above it w ould
constantly remain above it while every other fixed obj ect
would seem to swing around in circles Were t he fl y to
walk to the equator the point directly away from the
globe w ould cut the largest ci rcle around him and the
stationary point s would be along the horizon
Cel estial P ol e
The point in t he c elestial s phere directly
above t he pole and in line with the axis has no motion
The star nearest the pol e
I t is called the c elest ial pole
of the c elestial sphere and directly above the north po le
of the earth is called the North star and the star nearest
I t may be of
t h e southern c elestial pole the S outh star
interest to note that as we located the North star by refer
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47
AT THE NOR TH P OLE
nce to the B ig D ipper the S outh star is located by refer
enc e to a group of stars known as t he S outhern Cross
Cel estial E q u a to r
A great circle is conc eived to e xtend
°
around the celestial sphere 90
from the poles ( Fig
This
is called t he celestial eq uato r
The axis of the earth if pro
longed would pierc e t he c eles
tial poles almost pierce the
North and S outh stars and
the equator of th e earth if ex
tended would coincide with the
celest ial equator
e
,
.
.
.
.
,
,
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.
At
th e
No rth
P ol e
An
.
Fig
.
no
observer at the north pole
will see the North star almost exactly overhead and
as t he earth turns around und er his fee t it w ill remain
°
Half way or 90 from
constantly overhead (Fig
is the c elestial equator aroun d the
t he North star
horizon As the earth
rotates
though it
see ms
to u s per
f ectly st ill
the stars
arou nd the sk y seem
to swin g in circles in
the opposite directi on
The planes of the star
paths are parallel to
m “
the h o r i z o n
The
same half of th e c el estial sphere can be seen all of t he
time and stars below the horizon al ways rema in so
All stars so uth of the c elestial equator be ing forever
in visible at the north pole S irius the bright est of the
,
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48
THE R OTATI ON OF THE E AR TH
tars and many of the beautiful constellations can never
be see n from that plac e
Ho w peculiar the view of the
heavens must be from the po le the B ig D ipper the
P le iad es the S quare of P egasu s and other star groups
sw ingin g
aroun d in courses parallel to the
et ernally
horizon Wh en the su n moon and planets are in t he
portion of their courses north of the c elestial equator
they of course w ill be seen throughout continued rotations
of the earth until t hey pass belo w the c elestial e quator
when they will remain invisible again for long period s
Th e direction of the daily apparent rotation of the stars
is from left to right ( west ward ) the dire ction of the
hand s of a clock looked at from above Lest t he direction
of rotation at the North pole be a matter of memory
rather than of insight we may notice that in the United
S tates and Canad a w hen we fac e so uthward we see the
sun s da ily course in the direction l e ft to right ( west ward )
and going poleward the direction remains the same though
t he su n approaches the horizon more and more as we
approach the North pole
At th e So u th Pol e
An observer at the S outh pol e at
th e other en d of the axis w ill see the S outh star dire ctly
overhead the c elestial equator on the horizon and the
plane of the star circles parallel with t he horizon The
direction of the apparent rotation of the c elestial sphere
is from right to le ft coun t er c lock w ise
I f a star is seen
’
at one s right on the horizon at six o clock in the morning
at noon it will be in front at about six o clock at night at
his left at midnight behind him and at about six O clock
in the morning at h is right again
At th e E q u ator An obse rver at th e e quator sees the
stars in the c el e stial sphere to be v ery diff erent in the ir
positions in relation to himself R e me mbering that he is
s
,
,
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,
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,
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,
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,
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THE R OTATI ON OF THE EARTH
50
l tial sphere is at right angles
apparent rotation of the
to the axis
ce es
.
Ph otographin g
th e
S ph ere
Cel estial
of
B ecause
.
the
.
rth s rotation the entire celestial sphere seems to rotate
Thus we see stars da ily circli ng aro u nd the polestar
always stationary When stars are photographed long
e xposu res are nec essary that the ir faint light may a ff e ct
the sensitive plate of th e camera and the photographic
instru ments mu st be constructed so that they will move
at th e s ame rate and in t he same direction as the stars
otherwise the stars will leave trails on the plate When
the photographi c instrument thus follo ws the stars in
their courses each is shown as a speck on the plate and
comet s meteors planets or as teroids moving at diff erent
rates and in diff erent directions S how as traces
R o tati o n of Cel estial Sph ere is Only Apparen t
Fo r a long
time it was believed that the heavenly bodies rotat ed
around the stationary earth as the c enter I t was only
about five hundred years ago that the astronomer Coper
n icu s established the fact that the motion of t he su n and
stars around the earth is only appare nt th e earth rotat ing
We may be interested in some proofs that this is the case
I t see ms hard to believe at first that this big earth
miles in circumference can turn aroun d onc e in a day
Wh y that would give u s a whirling motion of over a
thousand m iles an hour at the eq uator
Wh o could
stick to a m erry go ro u nd going at t he rate of a thousand
mil es an hour ? When we see however that the su n
miles away would have to swing around in a
course of over
miles per day and the stars at
the ir tremendous distan ces would have to move at unthin k
able rates of speed we see that it is far easier to believe
that it is th e earth and not the c elestial sphere that rotates
ea
’
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,
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-
”
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EASTWARD D E F LE CTI ON OF FALLI NG B OD I E S
51
d aily We kn ow by direct observatio n that other planets,
t he su n and t he m o on rotate upon their axis and may
.
,
,
onably infer that th e earth does too
S o far as th e whirling motion at th e equato r is conc erned
it does give bodies a slight tendency to fly off but the
amount of this forc e is only
as great as the attractive
in fluence of the earth ; that is an obj ect wh ich would
weigh 289 poun d s at th e equator were the earth at rest
weighs a po und less because of the centrifugal force of
rotation (see p
reas
.
,
,
,
,
,
.
P R OOF S
OF THE
E astward D eflectio n
of
E AR TH
’
S
R OTATI ON
Fal lin g B odies
P erhaps the
.
implest proof of the rotation of the earth is one po inted
out by Newt on although he had no means of demon
With h is clear vision be said that if the earth
stratin g it
rotates and an obj ect were dropped from a considerable
height instead of falling directly toward the center of
*
it would be
the earth in the direction of the plumb line
deflected to ward the east E xperiments have been mad e
in the shafts of min es where air currents have been shut off
and a slight but un mistakable eas tward tend ency has been
observed
D uring the summer of 1906 a number of newspapers
and magazin es in the United S tates gave accou nts of th e
eas tward falling of obj ect s dropped in th e d ee p min es of
n orthe rn Michigan one of which (S haft No 3 of th e Tam
arac k m in e ) is th e d eepest in th e world having a ve rtical
dept h of over one mile (and still digging l) I t was stated
t hat obj ec t s dropped in to such a shaft never reached the
1 Th e sli h t eocen t ric de viat io ns o f th e
m
x
l
b
l
i
u
l
i
n
e
r
e
e
a
a
g
g
p
p n ed
s
,
.
.
,
,
.
.
,
.
.
,
,
.
'
on
2
2
2
8
1
8
pp
-
.
.
THE R OTATI ON OF TH E E AR TH
52
bottom but al ways lodged among timbers on the east
sid e
S ome papers ad d ed a touch of the gre wsome by
implying that among t he obj ects found clinging to t he east
piec es of a di smembered human body w hich
S id e are
were not permitt ed to fall to the bottom be cause of t he rota
tion of the earth Follo w ing is a portion of an account
by F W Mc Nair P resid ent of t he Michigan College of
Mines
Obj ect s d roppin g into th e s haft
M c Nai r s E xperi men t
und er ordin ary condition s nearly al ways start w ith so m e
horizontal velocity ind eed it is usually d u e to such initial
velocity in the horizo ntal that they get into the shaft
at all Almost all common obj ects are irregular in S hape
and drop o n e of the m ever so carefully contact with the
air through w hich it is passing s oon d eviates it from
th e vertical giving it a horizontal velocity and this w hen
The Obj ect slid es o n e way or another
th e air is quite still
on t he air it compresses in front of it E ven if the body
is a sphere t he air w ill cau se it to d eviat e if it is rotating
about an axi s out of the vertic al Again t he air in the
and any obliquity of the
shaft is in c e asel e ss motion
curre nts would obviou sly d eviate the falling body from
I f t he falling
th e v ertic al no m att er wh at its shape
obj e ct is of steel the m ag netic in fl uenc e of the air mains
and st ea m mains w hich p ass do wn th e S haft and w hich
invariably become strongly magnetic may cause it to
swerve fro m a vertical course
A st ee l sphe re cho sen because it was the only con
w as su s pend ed about o ne foot
v en ient obj ect at hand
from t he timbers n ear the west ern corner of the compart
ment The compartment stand s diagonally with refer
Forty t wo hundred feet belo w
e nc e to t he cardinal point s
.
.
,
.
.
.
’
.
,
,
.
,
,
,
,
.
.
,
,
.
,
,
.
,
,
,
,
,
,
.
-
.
I n th e M i n i ng
a nd
S ci entific P ress, July 14 , 1906
.
‘
MONAI R S E XP E R I MENT
53
’
a clay bed was plac ed having its eastern edge S ome five
feet east of the point of su spen sion of the bal l Wh en
t he ball appeared to be st ill th e su spending thread w as
burned and the instant of the dropping of the ball was
indicated by a prearranged S ignal tran smitted by t ele
phone to the observers belo w who watch in hand waited
for the sphere to strike the bed of clay I t failed to
appear at all Another like sphere was hung in the c enter
of the compartment and the trial was re peated with the
same result
The shaft had to be cleared and no more
trials were feasible S ome months later o ne of the spheres
presumably the latter one was found by a timberman
where it had lodged in th e timbers 800 feet from the
surfac e
I t is not probable however that these ball s lodged
The matt er is
because of t he earth s rotation alone
really more complicat ed than the foregoing discussion
implies I t has rec eived mathematical treatment from
t he great Gauss
According to his results the d eviation
to the east for a fall of
feet at the Tamarack mine
B oth spheres had that
should be a little und er three feet
much to spare before striking the timbers I t is almost
c ertain therefore that others of the causes mentioned in
At any
t he beginning acted to prevent a vertical fall
rate these trials serve to emphasiz e the unlikelihood that
an obj ect which falls into a d eep vertical shaft like those
at the Tamarack min e will reach the bottom even when
some care is taken in sel ecting it and al so to st art it v erti
cally
I f the timbering permit s lodgm ent as is t he ca se in
most shaft s it may truthfully be said that if a shaft is
dee p in proportion to its cross section fe w ind eed will be
the obj ec ts falling into it w hich will reach the bottom
,
.
,
,
,
,
.
.
.
.
,
,
,
.
,
,
’
.
.
,
.
.
.
,
,
.
,
,
,
,
,
,
,
54
THE ROTATI ON OF THE E ARTH
uch obj ect s are more likely to lodge o n t he east erly
sid e than on any other
Th e Fou cau l t E xperim en t
Another s imple d emonstra
tion of t he earth s rotation is by t he celebrated Foucault
experime nt
I n 1851 the French phys icist M Leon Fou
c au lt su spend ed from t he dome of t he P antheon in P aris
A pin
iron ball by wire two hundred feet long
a
was fastened to t he lowest
sid e of t h e ball so that w hen
swin ging it trac ed a slight
mark in a layer of sand plac ed
beneath it Care fully the
long pendulum was set sw ing
ing
I t was fo u nd that t he
path grad ually moved aroun d
toward the right Now e ither
i
s
t
l
m
e
chang
d
the
u
u
e
d
p
plane or the building was
B
r
dually
turn
d
around
e
a
g
y
with a ball
e xperimenting
su spend ed from a rule r o n e
can read ily see that grad ually
turning the ruler will not
change the plane of the
sw in ging
pendulum I f the
pendulum swings back and forth in a north and south d irec
tion th e ru ler can be entirely turn ed arou nd w ithout chang
ing the direc tion of the pendulum s sw ing
I f at the north
pole a pendulum was se t sw inging to w ard a fixed star say
Arcturu s it would continue swinging to ward the sam e
star and th e earth w ould thu s be see n to turn around in
a day The earth would not seem to turn but the pendu
lum would seem to d eviate to ward the right or clockwise
an d s
”
.
.
’
.
.
,
,
,
,
,
.
.
.
.
.
.
,
’
.
,
,
.
.
THE FOUCAULT E XP E R I ME NT
Conditions for S uccess The Foucault experiment has
bee n mad e in many plac es at difl erent ti mes To be su c
c essf ul there should be a long sle nd er wire say forty f eet
or more in length down th e w ell of a stairway The weight
sus pend ed should be heavy and sph eri cal so that t h e
.
.
,
.
,
im pact against the air m ay not cause it to slide to on e
s i d e
a n d there
S
H
O
W
I
N
G TE E EARTHS MOTI ON
should
be protec
tion against drafts
I nterestinS h erm an in th e Dome
of air A good siz ed
circle marked off
0°
i
r
[11 d egrees
S hould
m n t u n d r th a usp lg
x
g
:
th e as tro
n om lc a! so cie ty o f F ran c
e too k p u c
y”
be plac ed un d er it
with t h e c enter
em tly un d er the
means o f a p end u l u m c on ist ing of a be ll
w ig h ing 6 0 p ou nds a ttach d by a w ire 3 0
ball W hen at rest
ya rd s i n le ng th to th e inte ri
o f th e d me
O
f
t
h
e
P an th e n
M r Ch num l e m i i s te r
r
h o n the rate of
of
who
p ub l ic i n tru c ti on
i d ed
p
,
’
.
,
e
,
e
e
:
e
,
.
‘
s
.
»
“
e
e
‘
or
.
'
t he
o
.
.
s
devI ati on the
o
.
n
res
,
.
b u rned a s tring t h a t tied th e we ig h t to a
p il la r a nd : th e imm en s e p e nd u l u m b e s t u
its Jo u rn e y 11= 8 an d h a d b e e n p lac e d o n
“
fl oo r au d ei ch t im e th e
nd ul u m p as sed
ove r i t a n ew tree]: w
n t ed i n reg u
lati tude m a y b e
a
,
.
demrm nl ed
or k no wmg t h e
latitude th e d evia
t i on m ay be cal
'
'
ly
easx
a
-
la r d e via ti o n . t h o ug h t h e
n e o r th e
p e n d u l u m s s w i ng re ai n
u n c h an g e d
Tl" “ N fl m w t V u
c om p l e t el y m oc c as
s o 3.
m
’
,
.
‘
,
Fix
.
To Calcu late Amou n t
D eviatio n
f
o
as
At first thought
.
it
might see m as though the floor would turn completely
around und er the pendulum in a day regardless of the
latitude I t will be read ily seen however that it is only
at th e pole that the earth would make o ne complete rota
tion un der the pendul um in one day or show a d eviation
°
of 15 in an ho ur At th e equator the pendulum w ill
show no d eviation and at int erm ediat e latitud es t h e rat e
S tric tly speak i n g in o ne side real day
,
.
,
,
.
,
,
.
56
of
TH E R OTATI ON OF THE E AR TH
varies Now th e ratio of variat io n from the
pole consid ered as one and th e equ ator as z ero is shown
in the table Of natu ral sines
p
n
I
b
e
t
c
a
(
demonstrated that th e number of degrees the plane of the
pendulum w ill d eviate in one hour at any latitud e is found
°
by multiplying 15 by th e sine of the latitude
d eviation
.
.
.
d
t
c
d
d eviation
latitud e
) X
sin e 4
Whether or not the student has a very clear conc eption of
what is meant by the sine Of t he latitud e h e may easily
calculate the d eviation or th e latitud e where such a pen
dulum e xperiment is mad e
°
E xamp le
S ine 4 0
S uppo se the latitud e is
The hourly d eviation at that latitud e then is
6428
°
15 or
S inc e t he pendulum d eviat es
6428
m on e hour for the entire circuit it will take as many
°
hours as that number Of d egrees is contained in 360 or
about 374 hours I t is just as simple to calculate one s
latitud e if the amount of d eviation for one hour is known
S uppose the plane of the pendulum is Observed to d eviate
°
9 in an hour
.
.
.
,
,
,
’
.
.
.
S ine
S in e
of
of
th e
th e
latitud e
latitud e
°
15
9
33
or
.
6000
.
this sine 6000 corre
tha n to the si ne
°
of any other whole d egree and hence 37 is the lati tud e
At that latitud e it would
where t he hourly d eviatio n is
take forty hours (360 9 40) for the pendulum to
mak e th e entire c irc u it
From the table of sines we find that
°
spond s more n e arly to that Of 37
,
.
,
.
,
58
THE R OTATI ON OF THE E AR TH
VE LO CI TY
The
veloc i
ty of
hour, in d ifierent
R OTATI ON
OF
rotation at the surfac e in miles
latitudes is as follows :
th e
,
r
e
p
,
V e loc ity
Latitu de
.
Unif orm R ate o f R otatio n
Ve lo c ity
.
Lat itu de
.
.
There are theo retical grou n ds
’
t he earth s rotation is get ting
.
believing that the rate of
s
e
A
s
r
e
a
dually
low
r
t
how
e
v
e
r
not
light
t
h
t
e
s
e
s
g
y
variation has been disc overed B e fore attacking the
so m ewhat comple x proble m of time t he stud e nt should
clearly bear in mind the fact that the earth rotates o n its
axis with such unerring regu larity t hat this is t he most
perfect standard for any time c alcul atio ns known to
sc ie nc e
f or
.
,
,
.
,
.
D E TE R M I N ATI O N
OF
LATI TUD E
Al titu d e of Cel estial P ol e E q u al s Latitu de
Le t u s return
in imagination to t he equ ator
Here we may see t he North
star on t h e horizon d u e north of u s, the S outh st ar on t he
.
,
.
,
59
To FI ND YOUR LATI TUD E
horizon du e
outh and halfway between these two points
exte nding from du e east th rough the z enith to d u e wes t
is t he c elestial e qu ator I f we travel northward we shall
be able to see Obj ects which were heretofore hidd en from
V i ew by the curvature of th e earth
We shall find that
the So uth star becomes hidde n from sight f or th e same
reason and the North star seems to rise in the sk y The
celestial e quator no longer extend s through the point
directly overhead but is som ewhat to the south Of the
zenith though it st ill intersect s the horizon at the east
and west po ints As we go farther north this rising Of
the northern sk y and sinking of the southern sk y bec omes
greater I f we go halfway to the north pole we shall find
the North star halfway bet ween the zenith and t he northern
°
horizon or at an altitude of 4 5 above the horiz on For
eve ry d egree Of curvature Of the earth we pass over
going northward the North star rises one degree fro m
°
the horizon
At New Orleans the North star is 30 from
°
At
the horizon for the city is 30 from th e e quator
°
°
P hilad elphia 40 north latitude the North sta r is 40
from the horizon S outh Of the equator the converse Of
this is true The North st ar sinks from the horiz o n and
the S outh star rises as o ne travels southward from the
The alti tu de of the North star i s the lati tude of
eq uator
a place n orth of the eq u ato r and the altitu de of the S ou th
I t is
star i s the lati tu de of a p lac e sou th of the eq u ato r
Obviou s the n that th e proble m of d et ermin ing latitud e is
t he proble m of d et ermin ing t he altitud e of th e c el estial
pole
B y means O f th e compas ses
To Find Yo u r Latitu de
This
and scale asc ertain t he altitud e Of t he North star
can be done by placing o n e sid e Of t he compas se s o n
a level window sill and sight ing the othe r sid e toward
s
,
,
,
.
.
.
,
.
.
,
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,
,
.
.
,
,
,
.
.
.
.
.
,
,
.
.
,
.
60
THE R OTATI ON OF THE E AR TH
t he Nor th
tar then measuring t he angle thus formed
i
s
e
s
noth
r
impl
proc
for
a
c
taining
latitud
to
s
s
s
r
e
e
e
e
A
d etermine the altitud e of a star not f ar fro m t he North
star when it is highest and when it is lowest ; th e average
Of th ese altitud es is th e altitud e Of t h e pole or t he latitud e
°
This may easily be done in latitud es north Of 38 during
t he winte r O bse rving say at 6 o clock in t h e morning
and at 6 O clock in t h e evening This is si m ple in that
it requires no tables Of course such measure ments are
very crud e w ith simple instrument s but with a little
c are o ne will usually be s urpri sed at t h e accuracy of h is
results
Ow ing to t he fact that t he North sta r is not exactly at
the north pole Of t h e c elestial sphere it has a slight rotary
m otion
I t will be more accurat e there fore if t he o bser
vat ion is mad e w hen t he B ig D ipper and Cassiopeia are
s
.
,
.
,
’
,
,
,
’
.
.
,
.
,
.
,
,
True Po l e
Tru e Po le
Tru e Pol e
positions ( A or B ) represented by Figure 26
I n case Of these positions th e altitude Of the North star
w ill give th e tru e latitud e it the n be ing t he sa m e altitud e
I n case Of po sition
as t he pole Of th e c e l estial sphe re
°
D th e North star is about l l; below th e true pol e he n c e
in
o ne
of
th e
.
,
.
,
,
TO FI ND Y OUR LATI TUD E
1
°
11
must be ad ded to the altitude Of the star I n case of
position C the North star is
above the true pole and
that amoun t must be subtracted from its altitud e I t is
obvious from the diagrams that a true north and south
line can be struck when the st ars are in posi tions C and D
by hanging two plumb lines so that they lie in t he same
plane as t he z enith meridian line through Mizar and D elta
Method s Of d etermining latitud e will be further
Cassiopeia
discussed on pp 172 174 The instrument commonly
used in Observations for d etermining latitude is the meri
dian circle or on shipboard the sext ant Read the de
scriptio n of these in strum ent s in any t ext on astrono m y
.
,
,
.
,
—
.
,
.
,
.
,
.
Q
UE R I E S
looking at the heavenly bodies at night do the stars;
m oon and planets all look as though th e y were equall y
distant or do some appear nearer than others ? The fact
that people of ancient ti mes believed the c elestial sphere
to be mad e of metal and all t he heavenly bodies fixed or
moving therein would indicat e that to the Observer who is
not biased by preconc eptions all seem equally distant
I f they did not see m equally distant they w ould not
assume the apparently spherical arrangement
The d eclination or di stanc e from the c el estial equator
Of the star ( B enetnasch ) at t he end Of t he handle of t he
B ig D ipper is
Ho w far is it from the c elestial pole ?
At what latitud e w ill it touch the horizon in its swin g
under the North star ? Ho w far south Of the equ ator co u ld
on e travel and still see that star at some time ?
In
,
,
,
,
.
,
,
CHAP TE R I V
LON GI TUD E AN D TI M E
S OLAR Tm n
Su n Tim e Varies
The
is th e
world s great tim e
kee per He is however a slightly erratic o ne At t he
equator t he l ength of day equals th e length Of night t he
year through At the poles there are six months day and
six months night and at int ermediat e latitud es th e tim e
of sunrise and of sun set varies wi th the seaso n Not only
does the t ime of sunrise vary but the time it takes the su n
apparently to swing onc e around the earth also varies
Thus from noon by the su n until noon by the su n again is
sometimes m ore than twenty four hours and sometim es
less than twenty four hours The reasons for this varia
tion will be taken up in the chapt er on the earth s revolution
Mean S olar D ay B y a mean solar day is meant the
average in te rval of time from sun noo n to su n n oon
While the apparent solar day varies the mean solar day
is exactly t wenty four hours long
A sundial does not
record the same time as a clock as a usual thing for t he
sundial record s apparent solar time w hil e t he clock re cord s
m ean solar time
R el atio n o f Lo ngitu de to Tim e
Th e sun s apparent daily
journ ey around the e arth w ith the other bodies of the
*
I t takes th e
celestial sphere giv es rise to day and night
su n on the av e rage twe nty f our ho u rs appare ntly to sw ing
Man y th o u gh tlessly as su m e that th e fac t of day an d n igh t is a
f
h
r
oo
o
f
t
h
t
t
e
e
a
s
a
i
r
t
r
o
o
n
p
.
.
su n
’
,
,
.
.
,
.
,
.
-
-
.
’
.
.
.
,
-
.
,
,
.
’
.
.
’
-
,
,
’
.
HOW LONGI TUD E I S D E TE R MI NE D
63
nce around the e arth I n this daily journey it crosses
°
°
360 of longitud e or 15 for each ho u r
I t thus takes
f our minutes for the sun s rays to sweep over on e d egree
o f longitud e
S uppo se it is noon by th e su n at the 90th
meridian in fo u r mi nutes th e su n will be over th e 91st
meridian in four more minutes it will be noon by the su n
on th e 92d merid ia n and so o n around th e globe
S tud ents are so metimes confused as to the tim e of day
in plac es eas t Of a given meridian as compared with the
time in places west Of it When t he sun is rising here it
has already risen for pl ac es east of u s hen c e their time is
after sunrise or later tha n ours I f it is noon by the
su n here at plac es eas t Of u s having alread y been noon
there it must be past noon or later in the day P laces
to the east ha ve later ti me becau se the su n reaches them first
I f the su n
To th e westward the co nverse of this is true
is ri sing here it has not yet ri sen for plac es west Of u s and
their time is before sunrise or earlier When it is noon by
the su n in Chicago the shad ow north it is pas t noon by
the su n in Detroit and other plac es eastward and be fore
noon by the su n in Min neapolis and other plac es west w ard
A man w hen in London
How Lo ngitu de is D eterm in ed
set h is w atch accord ing to mean so lar time
longitud e
there When he arrived at home he found the mean solar
time to be six hours earlier (or slower ) than his watch
which he had not changed S ince his w atch indicated
later time London must be east of h is home and sinc e the
su n appeared six hours earlier at London h is ho m e must
west of London
or
While on shipboard
be 6 x
at a c ertain plac e h e n otic ed that the sun s shad ow w as du e
north when his watch indicated
o clock P M Assum
ing that both th e w atch and the su n were o n time we
readily se e that sinc e Lo ndon time was two and o n e half
o
.
,
.
’
.
,
,
,
.
.
,
,
.
,
,
,
.
.
.
,
.
,
,
.
.
,
.
,
.
,
,
,
.
’
’
,
.
.
LONGI TUD E AND TI ME
64
hours later than the time at that place he must hav e been
°
west of London 2 5 x
or 37 30
S hi p s Chro n o m eter
E very oc ean vessel carries a very
accurate watch called a c hronometer This is regulated
to run as perfectly as possible and is set acco rding to the
mean solar time Of some well known meridian Vessel s
from English speaking nations all have the ir chronometers
B y Observing the time accord
set with Gree n w ich tim e
ing to the su n at the place w hose longitude is sought and
c omparing that time w ith the ti m e of t he prime m eridian
as indicat ed by the chronomet er t he longitud e is reck
Fo r example suppose the time according to the
oned
o clock A M and
su n is found by Observation to be
The prime
th e chronom eter indicates
O clock A M
meridian then m ust be east as it has later time S in ce
th e diff erenc e I n tim e is o ne hour and fifty minutes and
°
there are 15 diff erence in longitud e for an hour s diff er
enc e in tim e the di ff erenc e in longitud e mus t be 1 5 x
°
or 2 7
The re lation Of longitud e and time should be thoroughly
mastered From t he table at the close Of this chapter
giving the longitude Of t he principal cities Of the w orld
one c an d et ermine the ti me it is in tho se plac es w hen it is
noon at home Many other problems may also be su g
gested I t should be borne in mind that it is the mean
solar ti me that is thu s cons id ered which in mo st cities is
not the time indicated by the watches and clocks there
People all over Great B ritain set the ir ti m epiec es to agree
with Greenw ich time in I reland with D ublin in Franc e
Time used in Various Countries at
with P aris etc (see
the end Of this chapter )
Lo cal Tim e
The m ean solar time Of any plac e is Often
Thi s is the average time indicated
c alled its local time
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MOUNTAI N S TAND AR D TI ME
7
country und er the lead ership of William F Allen then sec
retary of the Gen eral Time Conve ntion Of R ailro ad Officials
As a result of h is un tiring eff orts th e railway associations
endorsed h is plan and at noon Of S un day Nove mber 18
1883 the prese nt syst em was inaugurated
E astern S tandard Tim e
Accordin g to the system all
°
c ities approximate ly within 75 Of t he 75th m eridian u se
the mean solar tim e Of tha t meridian t he clocks and
watches being thus just five hours earlier than those of
°
Greenwich This belt about 15 wid e is called the east ern
stand
time belt The 75th meridian passes through the
eas t ern portion of P hil ad elphia so the time u sed t hrough
out the eas tern portion Oi the United S tates corresponds
to P hilad elphia local mean solar time
Cen tral Standard Tim e
The tim e Of the next belt is th e
mean solar time of the 90th meridian or on e hour slo wer
than eas te rn standard time This meridian pas ses t hrough
or very near Mad i son Wisconsin S t Louis and New
Orleans where mean local time is the same as standard
time When it is noon at Was hington D C it is 1 1
at Chicago because the people Of the former
O clock A M
city u se eas tern standard time and those at th e latter u se
central standard time
Mou ntain S tandard Tim e To the west of the c entral
standard tim e be lt lies th e m ountain region where t he
time used is the mean solar time of the l o5th meridian
This meridian pas ses through D enver Colorad o and its
clocks as a conse quenc e indicate the same time that the
mean sun doe s the re As th e standard time map shows
all the belts are bounded by irregular lines d u e to the
fact that th e people Of a city usually u se the same time
s
e
i
t
th
ir
principal
railro
do
and
wh
r
tra
n s change
a
d
e
e
h
a
t
their time d e pend s in a large measure upon the c o n ven
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LONGI TUD E AND TI ME
68
ience
to be served This bel t shows the ano maly Of bein g
bound ed on the east by the c entral time belt on the west
by the P acific time belt and on the sou th by the same belts
The reaso ns w hy the mountain standard time belt t apers
to a point at the south and the peculiar conditions which
Four
c onse quently result are d is cu ssed und er the topi c
Kind s Of Time around E l P aso ( p
P eople living in th e states bor
Pacific S tandard Tim e
d ering or near the P acific Oc ean u se the mean solar time
th m eridian and thus have three hours earlier
o f th e l 20
time than the people Of the Atlantic coast states This
meridian forms a portio n of the eas tern bo undary Of
California
I n these great t ime belts all the clock s and other time
piec es diff er in time by w hol e hours I n ad dition to astro
no m ical Observatory clock s w hich are regulated according
to the mean local time of th e meridian passing through the
Georgia
o bservatory there are a f ew cities in Michigan
New Mexico and elsewhere in the United S tates where
mean local time is still u sed
I n many E u ropean countries
S tan dard Tim e in E u ro pe
standard ti me based upon Greenwich time or whole hour
c hanges from it is in gen e ral u se although there are m any
m ore cities which u se m ean local ti me than in th e United
S tates
Western E u ropean time or that Of the meridian
Of Greenwich is u sed in Great B ritain S pain B elgium and
Cen tral E u ropean time o ne hour later than that
Holland
Of Greenwich is u sed in Norw ay S wed en D enmark Luxe m
burg Germany S witz erland Au st ria Hungary S ervia and
E astern E u ropean ti me t wo hours later than that
I taly
of Greenwich is used in Turkey, B ulgaria and R oumania
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Fo r a d isc u ss io n o f th e t im e
Am e rica an d els ewh ere in th e w o rl d
,
in o th e r p o rtio ns
pp 8 1 8 7
u s ed
s ee
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of
No rth
GETTI NG THE TI ME
69
TE LE GRAP HI C TI M E S I GNALS
An ad mirable syste m of sendin g time
signals all over the coun try and eve n to Alaska Cuba and
Getting th e Tim e
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P anama
is
in vogue in t he Unit ed S tates havin g been
establis hed in August 186 5
The Naval Observatories at
Washington D C and Mare I sland California send out
the signal s during t he five m inut es prec eding noon each
day
I t is a common custom for as tronomical Observatories to
correct their own clocks by careful observations of the stars
The Washingto n Observatory send s t el e graphic signals to
all t he cities east of the R ocky Mountains and the Mare
I sland Observatory to P acific cities and Alaska
A few
railroads rec eive the ir ti me corrections fro m other Observ
ato ries
Good sell Observatory Carleto n College North
field Minnesota h as for many years furni shed ti me to the
Great Northern the Northern P acific the Great West ern
and the S ault S te Marie rail way syst ems Al legheny
Observatory send s out time to th e Pennsylvania syste m
and the Lick Observatory to the S outhern P acific syst em
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How Ti me i s D etermined
at
the
Uni ted S tate s Naval
Th e general plan Of correcting clocks at th e
United S tat es Naval Observatories by stellar Observation s
is as follows : A t elescope called a meridian transit is situ
Observatory
.
ated in a true north south directio n mounted on an east
west axis so that it can be rotated in the plane of the
meridian but not in the slightest d egree to the east or
w est
Other instrum ent s used are the chronograph and
The chronograph is an in strument
the si d ereal clock
which may be electrically connected with the clock and
which automatically makes a m ark for each second on a
The sid ereal clock
shee t of pape r f as te ned to a cylind er
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LONGI TUD E AND TI ME
70
n ot with the
regulated to kee p time with the stars
su n as are othe r cl oc k s
The re ason for thi s is be cause
t he stars make an apparent circui t with each rotation of
the earth and this we have Obse rved is une rring while
th e sun s apparent motion is quite irregular
TO correct the clock an equatorial or high z enith star
is sel ected
A well kno wn one is chose n s inc e t he exact
time it will c ross the meridian of t he Observer (that is be
at its highest point in its apparent daily rotation ) must be
calculated The chronograph is then started its pen and
ink ad juste d and its electrical wi res connected with the
clock The Observer now sights the telescope to th e point
where the expe cted st ar will cross his m eridian and with
h is han d on t he k e y he await s t he appe aranc e Of the star
As the star crosses each of t he e l even hair lines in the field
of the t elescope t he Observer presses the k ey which auto
matically marks upon t he ch ronographic cylind er
Then
by examinin g t he sheet he can tell at what time by the
clock t he star cro ssed t h e c enter line
He then calculates
just what time the clock shou ld indicat e and the difference
is the error Of t he clock
B y this means an error Of on e
tenth of a second can be discovered
Th e S idereal Cl o ck
The following fact s c onc erning t he
sid ere al clock may be Of in te rest
I t is m arked with
twenty four hour spaces instead of twelve Only one
moment in t he year does it indicate th e same time as
ordinary time piec es which are adjusted to the average su n
When the error of the clock is discovered t he cl ock is
not at onc e reset be cause an y tampering with th e clock
would involve a slight error The correction is simply
noted and th e rate of the clock s gaining or losing time is
calculated so that the true time c an be asc ertained very
precisely at any time by referring to the data showing the
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S E ND I NG TI ME S I GNALS
1
lock error when las t corrected and th e rate at which it
varies
A whil e before noon e ach day the exact sid ereal time is
calculated ; this is converted into local mean solar time and
this into standard time The Washin gton Naval Observ
atory convert s thi s into t h e standard time of t he 75th
meridian or E astern time and t he Mare I sland Observatory
into that Of the l 20t h meridian or P acific time
S en din g Tim e S ign al s
B y the co Operat ion of t elegraph
companies t he time signals which are se nt out daily from
th e Unit ed S tates Naval Observatorie s re ach practically
They are sent
every t el egraph station in t h e coun try
out at noon 75th meridian time from Washington which
is 1 1 O clock A M in cities u sing Central time and 10
O clock A M
where Mountain time prevails ; and at noon
l 20t h meridian time the y are sent to P acific coast cities
fro m the Mare I sland Observatory
three hours aft er
Washington has flashed the signal which makes correct
time acc essible to sixty million s of our population living
e ast Of t h e R ockies
No t only are the time signal s sent to t he t elegraph
stations and the nc e to rail w ay Of fic e s clock makers an d
re pairers schools cou rt hou ses etc but the same t ele
graphic signal that marks noon al so actually set s many
thousand s Of clocks their hand s whether fast or slo w auto
m atic ally flyin g to the true mark in res pon se to t he electric
current I n a number of cities Of the United S tates
n in eteen at pre sent huge ball s are plac ed upon to wers or
buildings and are automatically dropped by the electric
noon signal The time ball in Washington is co n spicu
o u sl y plac ed on t h e top Of th e S tat e War an d Navy build
ing and may be seen at con sid erabl e distanc es from man y
parts of the city
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LONGI TUD E AND TI ME
72
A f ew minute s before
oon each day o ne wire at each
telegraphic Offic e is cleared of all business and thousands
Of t ele graph operators sit in s il enc e waiting for t he click
master clock
Of t he k ey which sha ll t ell the m that t h e
At five minutes
in Washington has be gu n to s peak
before t welve the instru ment begins to click Off the second s
Figure 28 (adapted from a cut appe aring in Vol I V Appe n
dix I V United S tates Naval Observatory P ublications )
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20
Minut e b ef o re
noo n
Minute b e f ore
n o on
S S ec
o mitted
“
Minu te b ef ore
57
no on
S S ec
o mitted
“
Minu te b ef ore
58
noon
S S e c o mi tted
Min u te b e f o re
noon
IOS ee omitted
56
59
Fi g
.
28
graphically shows which second beats are sent along the
w ires d u ring e ach Of th e five minut es be fore noon by t he
transmitti n g clock at th e Naval Observatory
E xp lanati on of the S econ d B eats
I t will be notic ed
that the t wenty ninth second Of each minut e is omitt ed
Thi s is for th e purpose of permitting t h e Obse rv er to
disti n guish without countin g the beat s which is the o ne
d en oti n g the m iddle Of each minut e ; the five second s at
th e en d Of each of t he first four minut es are omitt ed to
m ark t he begi n ni n g of a n ew minute and the last ten
seco n d s Of t h e fift y ninth minut e are omitt ed to m ark
conspicuously th e moment Of noon The Omission Of the
Wh at s th e Time Y ou th s Comp a nio n Ma y 1 7 and J une
F ro m
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14 , 1 906
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74
out
LONGI TUD E AND TI ME
t he
country about seventeen years ago when stand
Fo r some reason which it
ard time was first adopt ed
is difficult to explain th e city fath ers Of D etroit have
refused to chan ge from th e Old local time to the standard
notwiths tanding t he fact that all Of t he neighboring cities
in
Cl eveland Toledo Columbus Cincinnati etc
practically the same longitud e had mad e the change years
ago and realiz ed t he benefits Of S O doing The business
m en Of Detroit and visitors to that city have been for a
long time laboring und er many disadvantages o wing to
t he confusion Of standard s and the y have at last taken
the matter into t he ir o wn hand s and a lively campaign
with t he c o Operation Of the newspapers has been
organized during the past two months
Many Of the
hot el s have adopted standard time regardless Of the
city and th e authorities Of Wayne County in which
Detroit is situated have al so d ecid ed to hold court on
Central S tandard time as that is t he Official standard of
The authoriti es Of t he city have
the st at e Of Michigan
I t is ann ounc ed in t he news
so far not taken action
papers that they probably will do so aft er t he election
and by that time if progre ss contin u es to be m ade the
Only clock in to wn k ee pi n g t h e local tim e w ill be on t h e
to wn hall All other matters will be reg u lat ed by standard
time and th e hours Of work will have been altered
accordingly in factories stores and school s S ome
but this as has been
Oppo sition h as be en enco u nt e red
t h e case in every city w here t he change h as been mad e
comes from peopl e who evid ently do not comprehen d the
One individual for i nstanc e writes
eff ect s Of t he change
to a newspaper that he will d ecli ne to pay pew rent in
any church w ho se clock to wer sho ws standard time ; he
refuses to have h is ho u rs Of rest curtailed Ho w these will
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FOUR
KI ND S
OF TI ME AROUND E L PASO
75
affe cted by t he change he does not e xplain E very
visitor to Detroit who has e ncountered the difficulties
which the confusion of standard s there gives rise to will
rejoice when the complet e c hange is eff ected
°
The longitude Of Detroit be ing 83 W it is seven d egrees
th meridian henc e t he local time used in the
east Of th e 90
city was twenty e ight minut es faster than Central time
and thirty two minutes slo wer than E astern time I n
Gainesville Georgia mean loc al su n time is u sed in the city
be
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the S outhern
railway passing throug h the city uses
E astern time and t he Georgia railway use s Central time
Fo u r Kin ds o f Tim e Aro u n d E l P aso
Another pl ac e Of
peculiar interest in connection w ith this subj ect is E l P as o
Texas from th e fact that four di ff ere nt systems are em
ployed The city the Atchison Topeka and S anta Fe
and the El P aso and S outhwest ern railways u se Mountain
tim e The Gal veston Harris burg and S an Antonio and
The
the Texas and P acific rail w ays u se Central time
S outhern P acific railway use s P acific time The Mexi can
Central railway u ses Mexican standard time
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LONGI TUDE AND TI ME
76
this it will be seen that when clocks in S trauss
N M a f ew miles from El P as o are strikin g twe lve the
c locks in E l P as o are striking one ; in Y sleta a f e w miles
east the y are striking two ; while across th e river in Juare z
Mexico the clocks indicat e
Tim e Co nf u sion f o r Travel ers
The confusion w hich
prevails where several diff erent standard s of time Obtain
is well illustrated in the follo wing e xtract from
The
I mpressions Of a Carel ess Traveler
by Lyman Abbott
in the Ou tlook Feb 28 1903
Th e changes in time are almost as inter estin g and
quit e as perplexin g as the c han ges in currency Of course
our steamer time changes every day ; a sha rp blast on th e
whistl e notifies u s when it is twelve O clock and c ertain
Of th e passengers set the ir w atch es accordingly e very
day I have tOO much respect for my faithful friend to
meddle w ith him to this extent and I keep my watch
unchan ged and make my calculations by a mental com
parison of my w atch with the ship s time B u t when we
ship s t im e
are in port w e gen erally have three times
local time and railroad time to w hich I must in my own
case add my own time which is quit e frequently ne ither
I n fact I ke pt New York time till w e re ached Genoa ;
have ke pt central E urope railroad time
sinc e the n I
Without changing my watch I am gettin g back to that
standard again and expe ct to find myself quit e accurat e
when we land in Naples
From
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THE LE GAL AS P E CT
OF
S TAN D AR D TI M E
Th e
l egal aspect of standard time presents many
int eresting features Laws have been enacted in many
di ff erent countries and several of t he stat es Of this country
legalizing some standard Of time Thus in Michigan
.
.
,
THE LE GAL AS P E CT OF S TAND AR D TI M E
77
Minn esota and other c entral states t he legal time is t he
°
mean solar time of longitud e 90 w est of Green w ich
When no other standard is explicitly re fe rred to t he
time Of the c entral belt is the legal time in force S imilarly
legal time in Germany w as d eclared by an imperial decree
dated March 12 1903 as follows :
We Wilh elm by th e grac e of Go d Ge rm an E mp e ro r King of
P ru ssia dec ree in th e n am e o f th e E m p i re th e B u n d es rath an d R eich
s t ag co n c u rring as fo llo w s :
Th e legal tim e in Ge rm any is th e m ean so lar tim e o f lo ngit u de 15
eas t fro m Greenwic h
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°
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Greenwich time for Great B ritain and D ublin time for
,
I reland
,
were legal ized by an act
A B I LL to re m o ve
to tim e occ u rrin g in
ments
Of
P arliame nt
follo ws :
do u bts as to th e m ean in g o f exp re ss io ns relative
ac ts o f P a rliam en t deeds an d o th e r legal ins tru
,
as
,
.
Wh e reas
t
do u b ts as to w h eth e r
exp re ssio ns
t
t o f P arliam en t, deeds , an d o the r
legal ins t ru m en ts relate in E nglan d an d S c o tlan d to Green w ic h tim e,
an d in I re lan d to D u blin t im e, o r to th e m ean as t ro n o m ical tim e in
each loc ali ty :
’
B e it th e re fo re en ac ted by th e Qu een s m o s t E x cellen t Maj es ty,
by and with th e ad vic e and c o nsen t o f th e Lo rds , sp i ritu al an d tem
n
P
r
l
i
n
i
n
a
a
m
e
a
s
s
m
l
d
t
t
r
a
l
a
n
d
C
o
mm
o
n
s
t
h
se
e
b
e
a
n
d
b
o
e
r
e
,
,
p
p
y
th e au th o rity o f th e sam e , as fo llo w s ( th at is to say ) :
1 Th at w h enever any exp re ss io n o f tim e o cc u rs in any ac t o f
P arliam en t, deed , o r o th er legal ins t ru m en t , th e tim e re fe rre d to
s h al l, u nl ess it is o t h e rwise sp ec ifically st ate d , h e h el d in th e c as e o f
Great B rit ain to be Gre e n wic h m ean tim e an d in th e c ase o f I re lan d ,
D u blin m ean tim e
2 This ac t may be cited as th e statu tes ( defini tio n o f tim e ) ac t, 1880
it is exp edie n to re m o v e
im e o cc u rrin g in ac s
of
t
c e r ain
.
.
.
.
S eventy fif th meridian time was l egaliz ed in th e D i strict
of Columbia by t h e following act of Congress :
AN ACT to est ablish a tan dard o f tim e in th e D is t ic t o f Co lu m bia
B e it enacted by th e S en ate an d Ho u se o f R ep re en tativ es o f th e
Seve ral o f th e fo llo wing q u o t at io ns a re t ak en f ro m th e P re sen t
S tatus of th e Use of S tan dard Time by E E Hayden
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78
LONGI TUD E AND TI ME
Uni ted S tates
Am e rica in Co ngress as sem bled , Tha t the legal
s tandard o f t im e in th e D is t ric t o f Co l u m b ia s ha ll h erea fte r be t h e
m ean tim e o f th e se ven ty fif th m e rid ian o f lo ngitu de w es t f ro m
Gre e n w ich
Th at this ac t shall n o t be so co ns tru ed as to afie c t
S E CTI ON 2
Of
-
.
.
e xis
ting con tracts
.
Ap pro ved , Marc h 13 , 1 884
I n New
se
ction
28
York
of the
.
a t rn standard time is legalized in
S ta tutory Con struc tion Law as follo ws :
e s e
Th e stan d ard tim e thro u gh o u t t h is S tate is t hat o f the 75th m e rid ian
o f l o ngit u d e w e st fro m Gree n wic h , an d all co u rts an d p u bl ic o ffi ces , an d
leg al an d Offi cial p ro cee d in gs , s h al l be regu lated t h ere by
An y act
re q u ire d by o r in p u rsu an c e o f l a w to be pe rfo rm ed at o r w it h in a p re
s cribed tim e , s h all be pe rfo rm e d a cc o rd in g to s u c h s t an d ard t im e
.
.
A New Jersey
tatute provid es that th e time Of the
same m eridian shall be that re cogniz ed in all t h e court s and
public Offic es Of the S tat e and also that the time named
in any notic e advertisement or contract shall be d eemed
and taken to be the said standard time unless it be other
I n P ennsylvania also it is provid ed
wise expressed
on and aft er July 1 1887 the mean solar time of
tha
th e seventy fifth meridian Of longitude west Of Gree nw ic h
commonly called east ern standard time shall be the
id ed that
standard in all public matt ers ; it is further prov
“
in any and all contract s d eed s w ills and
th e time
notic es and in the tran saction Of all matt ers Of business
public l egal commercial or other wise shall be construed
with referenc e to and in accordanc e w ith t he said standard
hereby adopted unl ess a diff erent standard is there in
e xpress ly provid ed for
Where there is no stand ard adopt ed by l egal authority
di fficulties may arise as t h e follo wing clipping from the
New York S u n November 25 1902 i llustrates
s
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THE LE GAL AS P ECT OF S TAND AR D TI ME
W HAT S
NOON I N A FI RE
POLI C Y
'
S o l a r N o o n o r S t a n d a r d Ti m e
No on
C o u r t s A s k e d t o Ba y
i n Lou i svi l l e a t 1 1 : 4 5
ard Ti me , Wh ic h Was 1 2
re
S ola r
fi me
P ol i c i es
m
.
.
,
-
.
s
.
in the po licies m e ans n oo n
by so lar tim e , o f co u rse the thir
teen com panies are absolved from
any res po n s ibility f o r the loss
I f it m eans n oo n by st andard
tim e, of cou rse t hey m us t pay
When the ins u ran ce peo ple got
th e claims o f th e co m panies they
declined to p ay, and wh en as k ed
f or an e lanatio n d eclare d that
n oo n in t e po lic ies m ean t n oo n
by so lar tim e
The bu rned o u t
an su it,
com panies imm ed iately
and in t he ir affid avits t ey say
that not o nly is standard tim e
th e o fficial ti m e o f th e S tate o f
Kentu ck y and th e city o f Lo u is
vill e , bu t it is al so th e tim e u po n
whi c h all bus in ess engagements
and all d om es tic and so c ial e n
h
m
n
a
k
o
n
T
e
a
e
t
s
c
e
r
e
r
e
e
d
g g
y
s tate fu rt he r th at th ey are pre
h
h
o
s
o
w
h
a
t
e
t
t
a
r
e
d
t
i
n
1
9
0
8
p
city o f Lou is vill e passed an o rd i
n an ce m ak ing s tan d ard time th e
o ffic ial tim e o f th e c ity, that all
legis la tio n is d ate d ac cord i ng to
s t and ard t im e , an d tha t th e go v
c ru o r Of th e s tate is in au gu rated
at noo n acco rd ing to th e same
meas u re me n t o f tim e
S olar tim e , s tate t h e com p anies ,
c an be fo u n d in u se in Lo u is ville
by o nly a f ew bank i ng ins titu
tio ns w hich got charte rs m an y
l
a
r
o
h
a
m
e
s
a
t
t
th em to
e
co
g
y
p
Mo st
use so l ar t im e to t his d ay
b ank s , t hey say, o perate o n stand
time, al th o u gh they k eep
ard
cl o ck s go ing at so lar t im e so as to
do bus in ess o n tha t bas is if
Ju
req u es te d
ng by stan dard
tim e the plain t s allege the ir fire
too k place fif tee n m in u tes before
the ir policies e xp ire d
The su its will soo n com e to trial ,
an d , o f co u rse , w ill be w atc hed with
n
i
n
s
l
s
e
b
ur
a
ce
a
t
t
t
e
o
i
n
r
e
r
e
e
p
p
g
y
n oo n
S tan d
: 02 1 2 p m
E xp i red a t
c
discovery it figured , o f
co u rse , b
s tan d ard tim e
S olar
tim e w o d m ak e it j ust two and
m in u te s afte r n oo n
a half
If
’
.
.
fi
the fire
79
.
.
.
Wh e th er
noo n ,
th e wo rd
winch m ark s th e beginning and
iratio n o f all fire insu ran ce
e
n
s
i
b
a
d
a
r
d
c
es
n
oo
n
o
m
e
a
n
s
,
y
p
time , or n oo n by so lar im e , is a
nes tio n
whi ch is soo n to be
h t o u t in th e co u rts o f Ken
0
h ir ee n su i s whi ch
tu y, in
have a rac ed th e a e n ion o f
fire ins
00 p eo le all o ve r the
p
wo rld
su r s
being
0
are
brou gh t by th e Peas lee Gau lbert
Co m an y and th e Lo u is v ill e Le ad
lo r Co m pany o f Lou is ville,
and
of
insu rance
and
mone y d e nds o n th e
h ou gh th e po licies in
No w ,
c om ani es all
p
were I n f o rce ro m n oo n o f
l , 1 901 , to n oo n o f Ap ril 1 ,
hem sa
wh a
n o t o ne o f
o f th e
kin d o f time ha pe ri
In
day is to be rec k o ned in
Lo u is vill e the solar n oo n is 17}
m inu es earlie r han th e s tand
°
o
t
lig
t t
t
tt
t
t
tt t
t
.
-
t
f
t
t t
t
.
t
t
t h at a
fire occu rring
in the ne hbo rhood o f n oo n o n
’
the day 0 a po licy s e x piratio n ,
ma eas il y be o pen to attack
re co rds o f th e Lou is ville
fire d artm e n t sh o w tha t th e fire
that estroyed th e bu ildings of
es w as dI sco v
th e two co m
’
o cloc k Lou is ville
ered at
standard tim c in th e fo re noo n o f
April 1 , las t
Th e fire began in
th e engine roo m o f the m a m f ac
to
and s p re ad to th e two o th er
b
whi ch we re u sed m ainly
as
Whe n the fire
ware h o uses
departmen t reco rd ed th e tim e o f
ard
n oo n , so
'
.
e
p
'
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.
-
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.
.
°
.
'
.
.
LONGI TUD E AND TI ME
80
An almost precisely
imilar case occurred
at Creston I o wa S e ptember 19 1897 I n this instanc e
th e insuranc e policies e xpired
at 12 o clock at noo n
and th e fire broke out at two and a half minutes past
noon according to standard time but at fifteen and o ne
half minutes before local mean solar noon I n each of
these cases the question of whether standard time or local
mean solar time was the acc ept ed meaning of the t erm
was submitt ed to a jury and in the first in stanc e th e ver
dict was in favor of standard time in the I owa cas e the
verdict was in favor of local time
E arly D ecisio n in E ngland
I n 1858 and thus prior to
th e formal adoption of standard time in Great B ritain it
was held that th e time appo inted for t he sitt in g of a court
must be und erstood as the mean solar time of the plac e
where th e court is held and not Greenwich time unl ess it be
so e xpressed and a n e w trial was grant ed to a d e fendant
who h ad arr i ved at the local time appointed by the court
but found the cou rt had m et by Greenwich time and the
case h ad been d ecid ed aga inst him
Co u rt D ecisio n in Geo rgia
I n a similar manner a court
in the st ate of Georgia rend ered the following opinion
I owa Case
.
,
,
s
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,
,
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.
Th e
t
o n ly s an da rd o f
tim e in co mp u tatio n o f
a
day,
or
h o u rs
of a
by th e law s o f Geo rgia is th e m e rid ian o f th e s u n ; an d
a l egal d ay b egin s an d e n ds at m id nigh t , th e m ean tim e be t w ee n m e ri
’
An arbit rary an d art i
d ian an d m e rid ian , o r 12 o c lo c k po st merid i em
fic ial s tan da rd o f t im e , fixed by p e rso ns in a c e rtain lin e o f bu s iness ,
c an n o t b e s u bs titu te d at w ill in a certain loc al ity f o r th e st an dard
day,
re c o g niz e d
.
reco g n iz ed
b y th e law
.
Need f o r Legal Tim e Ado ptio n
on a
S cien tific B asis
.
There
nothing in the foregoing d ecisions to d eterm ine whether
mean local time or the time as actually indicated by the
S inc e the latt er some
su n at a particular day is meant
is
,
,
.
LONGI TUD E AND TI ME
82
S tand ard tim e does n o t e xis t e xce p t f or
th e service o f railro ads w h ere it is in fo rce , n o t by law, bu t by o rd er
o f th e p ro per au th o ri ties
Austria Hu ngary, 1 h
-
fast
.
.
.
Official tim c is cal cu la ted from 0 to 24 h o u rs , z e ro corre
spo n di ng to mi dn igh t at Gree nw ic h
The R o yal Observ ato ry at
B ru ssels co mm u n icates d aily th e p rec ise h ou r by telegraph
B elg i u m
.
.
.
Great B ritai n
Th e me rid ian o f Greenw ich is th e s tand ard tim e
m e rid ian f o r En gland , I sle o f Man , Ork ne ys , S h e tlan d I slands ,
an d S c o tland
Th e m erid ian of Du a
is th e
I rela nd , 0 h 25 m
8
sl o w
s tandard t im e m e rid ian
Afric a (E nglis h Co l o n ies ) , 2 h fas t
S tan dard tim e f o r Cape Co lo n y,
Natal , Orange River Co lo ny, R h od esia an d Trans vaal
.
.
.
.
.
.
.
.
.
.
S outh Au stra li a
Canada
Alberta
a nd
N orthern Territo ry , 9 h 30m
.
.
fast
.
.
S as katc hewa n , 7 h slow
B riti sh Colu mbia , 8 h sl o w
Keewati n and M anito ba , 6 h slo w
Onta rio and Q u ebec , 5 h sl o w
N ew B ru nsw ic k, N o va S cotia , and P ri nce E dwa rd I s la nd , 4 h
an d
.
.
.
.
.
.
.
Chatham I sla nd , 1 1 h 30 m
.
fas t
fas t
Hongko ng, 8 h
M alta 1 h
,
.
.
.
fast
.
.
sl o w .
.
.
.
N ew Zeala nd, 1 1 h 3 0m fas t
I nd ia Lo c al m e an tim e o f th e Mad ras Observatory, 5 h 20m
s
is p ractically u sed as st an d ard t im e f o r I n d ia an d Ceyl on , be ing
telegraph ed daily all o ve r th e co u n try ; bu t f o r stric tly lo cal u se it
is generall y c o n ve rte d in to lo cal m ean tim e
I t is p ro po sed s oo n
to ad o p t th e s tan d ard tim e o f 5 h 30m fas t o f Green w ic h f o r I ndi a
and Ce yl o n , an d 6 h 30 m fas t o f Green wi ch f or B u rm ah
.
.
.
.
.
.
.
.
.
.
N ewfou nd la nd , 3 h
’
S t J oh n s )
.
.
30 m
.
.
8
.
sl o w
.
L
o
c
a
l
m
ean
(
tim e
of
.
.
8 sl o w
Th e o f ficial railro ad tim e is fu rnished b y
Chile, 4 h 4 2 m
I t is telegrap h ed o ver th e c o u n t ry daily
th e S an tiago Observato ry
’
Th e c ity o f V al p araiso u se s th e lo c al tim e , 4 h
at 7 o cl oc k , A M
m sl ow, o f th e o bservato ry at th e Nav al S ch oo l loc ated
46 h
.
.
.
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.
.
.
.
TI ME USE D I N VAR I OUS COUNTR I E S
83
An o bservato ry is m ain tained by th e J esu it mi ssion at
Zik awei n ear S hangh ai, and a tim e ball sus pen ded fro m a m as t o n
th e Fren ch B u nd in S ha n gh ai is d ro pped ele ct ricall y p re cisely at
Th is fu rnish es t h e lo cal tim e at th e po rt of
n oo n eac h d ay
8 fas t, w hi c h is ad o p ted by th e rail w ay and
S hangh ai 8 h 5 m
te legraph co m pan ies represe n ted th ere , as well as by the coas twise
s hi pp in g
Fro m S h an gh ai th e t im e is telegrap h ed to o th er po rts
Th e I m pe rial R ail w ays Of No rt h Chi n a u se th e sam e t im e , taking
it fro m th e B rit is h gu n at Tien tsin an d p as s ing it o n to th e s tat io ns
China
.
.
.
.
.
.
.
Of
th e
rail w ay
S t an d ard
e as
t co ast
tim e
twice eac h d ay
,
at
8
O cl o c k A
’
.
M
.
an d at
h
h
n
m
i
i
n
7
a
8
f
a
s
t
i
s
to
d
co
n
,
,
g
o f Chin a f ro m Ne w c h w ang to H o n gk o ng
8
u se all
.
.
o c lo c k P
’
al o ng
.
M
.
th e
.
Lo cal m e an tim e is u sed at B ogo t a, 4 h 56 m
s sl o w ,
tak en e ve ry d ay at n oo n in th e o bservato ry The lack of efiec tive
telegrap h ic se rvice m ak es it im po ssible to c o mm u ni cate the tim e
as c o rre c ted at B o go ta to o t h e r p arts o f th e co u n t ry , it fre q u e n tly
tak in g fo u r an d five d ays to sen d m essages a d istan ce o f fro m 50 to
100 m iles
Co lombia
.
.
.
.
.
.
8 sl o w
This is th e l o c al m ean tim e
Costa Rica , 5 h 36 m
Go v ern m e n t Obse rv ato ry at S an J o sé
.
.
.
.
of
th e
.
Cuba , 5 h 29 m 2 6 8 sl o w Th eOffic ial tim e o f th e R ep u bli c is the c ivil
me an t im e Of th e m e rid ian o f H av an a an d is u sed by th e railro ad s
Th e Ce n tral Me te o ro logi cal
and tel eg rap h l in es o f th e go ve rnm e n t
S tatio n gives th e t im e d a ily to th e p o rt an d c ity o f H av an a as w ell
as to all t h e telegrap h Offices o f th e R e pu blic
.
.
.
.
.
.
I n I cel an d , th e Faroe I sl an d s
D en ma rk , 1 h fas t
Wes t I n d ies , lo c al m e an t im e is u sed
.
.
th e D ani s h
an d
.
E gypt, 2 h fas t S tand ard t im e is sen t o u t ele c tricall y by the s tan d ard
c lo c k o f th e Obs e rv ato ry to th e c itadel at Cairo , to Ale xan d ria, P o rt
S aid and Wad y H al fa
.
.
-
.
8 slo w
Th e Offic ial tim e is th at o f th e m e rid ian
E q u ador, 5 h 14 m
u ito , co rre c ted d aily f ro m th e Natio n al Obse rv a to ry
of
.
.
.
.
Q
.
8 fas t
Le gal tim e in Fran ce , Al ge ria an d Tu n is is
F rance , 0h 9 m
Lo cal m ean tim e is
loc al m ean t im e o f th e P aris Obse rv ato ry
cons ide re d l egal in o t h e r Fre n ch coloni es
.
.
.
.
.
.
Germa ny, 1 h fas t
Kiaochau , 8 h fas t
S ou thwest Af rica , 1 h fas t
I t is p ropo sed to ad o p t s t an d ard t im e f o r th e fo ll o w in g
B ismarck Archip elago , Caro lin es , Marian e I s lan ds an d Ne w Gu in e a,
10 h u h
.
.
.
.
.
.
.
LONGI TUD E AND TI ME
84
fast o r 2 h
German East Africa, 2 h
Kameru n , 1 h fas t
.
.
.
30 m f ast
.
.
.
S amoa ( afte r an u nders tanding w ith th e U
Togo , Green wich tim e
12 h
.
.
fast
.
.
8 fast
B y ro yal dec ree o f S e p te m be r 1 4 , 1 895, th e
Greece, 1 h 34 m
tim e in comm on u s e is that of th e m ean tim e o f Athens , w h ich is
t ransm itte d fro m th e o bservato ry by telegraph to th e towns o f
th e k ingd o m
Th e lo c al tim e o f Am s te rd am , 0 h 1 9 m
8 fas t , is
Holla nd
n
h
i
m
s
b
u
w
i
c
i
l
u
u
s
e
d
t
G
r
ee
t
t
t
r
a
l
e
s
e
d
b
h
s
l
h
o
r
n
e
e
a
n
e
a
t
d
e
e
,
y
y
g
p
g p
ad m inist ratio n and th e rail w ays an d o th er t rans po rtat io n co m
T
h
e o bse rvato ry at Le yde n c o m m u ni c ates th e t im e t w ice
n ies
a
p
a wee k t o Am ste rd am , Th e H ag u e , R o tte rd am an d o th e r c ities ,
an d th e tel egrap h b u reau at Am s te rd am s ignals th e t im e to all
th e o t h e r telegraph bu re au s e ve ry m o rn in g
.
.
.
.
.
.
.
.
.
.
.
I n Ho ndu ras th e h al f h o u r n eare s t to th e m e rid ian o f
°
’
Tegu c igalp a, lo ngitu de 87 1 2 w es t fro m Gree nwic h , is gen eral ly
S aid h o u r, 6 h sl o w , is freq u e n tly de te rm ined at th e Na tio n al
u sed
I ns titu te by m e ans o f a so l ar c h ro po m ete r and co m m u n ic ated by
teleph o ne to th e I nd u st rial S c h oo l , w here in tu rn it is in d ic ated to
Th e ce n t ral telegraph Office co m
th e pu b l ic by a steam w h is tle
m u ni c ate s it to th e v ario u s s u b o ffi ces o f th e R epu blic , w h o se
c l o c k s ge n e rally se rve as a b as is f o r t h e t im e o f th e v ill ag e s , an d in
this m ann er an appro xim ately u nifo rm tim e is establish ed th ro u gh
o u t th e Re p u bl ic
Hondu ras
.
.
.
.
-
.
Ad o p ted by ro yal d ecre e o f Au gu s t 1 0, 1 893
This
I taly, 1 h fast
time is k ep t in all go vernm e n t es tab lishm en ts , s h ips o f th e I tal ian
Navy in th e p o rts o f I tal y, rai l ro ads , telegrap h o ffices , an d I tal ian
Th e h o u rs are nu m be red from 0 to 24 ,
s te am e rs
co as tin g
begin n in g w ith m id n igh t
.
.
.
.
.
“
I m pe rial o rd in an c e NO 51 , o f 1886 :
Th e m e rid ian th at
u gh th e o b se rvato ry a t Gree n wich , E n l an d , s hal l be
h
r
o
se
s
t
a
s
g
p
Lo n gitu d e s h all be co u n te d fro m th e abo ve
th e z e ro ( 0) m e rid ian
me rid ian e ast an d w es t u p to 1 80 degrees , th e e as t be in g po s itiv e
F ro m J an u ary 1 , 1888 , th e tim e o f th e
an d th e w es t n e gative
”
1 35th degree e as t lo ngitu d e s h al l be th e s t and ard tim e o f J ap an
This is 9 h fas t
“
I m perial o rd inan ce NO 16 7, o f 1895 : Th e s tand ard t im e hith e rto
Th e
u sed in J ap an sh all h e n ce fo rth be c al led cen t ral s tand ard t im e
tim e o f th e l 2oth degree eas t lo ngitu de s hall be th e s tan dard tim e
o f Fo rm osa , th e P es c ad o res , th e Y ae y am a, an d th e Miyak o gro u ps ,
This o rd in an ce shall
an d s h all be c alled w es te rn s t an d ard tim e
tak e efiect f rom the first of J an u ary,
This is 8 h fas t
J apa n
.
.
.
.
.
.
.
.
.
.
.
.
85
TI ME US E D I N V AR I OUS COUNTR I ES
Ce n tral s tandard t im e o f J apan is telegraph ed
daily to th e I m pe rial J ap an ese P os t and Telegraph Office at S eo ul
B e fo re Dece m be r, 1 904 , this w as co rre c te d by s u btrac ting 30 m ,
w hich nearly re p re se n ts th e d iffere n ce in lo ngitu de , an d w as th en
u sed by th e rail ro ad s , s t ree t rail w ays , a n d pos t an d te legrap h o ffices ,
and m os t o f th e be tte r c las se s
S in ce De cem be r 1 , 1 904 , th e J ap
anese pos t Offic es and rail ways in K o re a h av e begu n to u se cen t ra l
s tand ard tirn e o f J apan
I n th e c o u n try dis tricts th e peo p le u se
su n dials to s o m e e x te n t
Korea 8 h 30m
.
,
fas t
.
.
.
.
.
-
.
.
f
tim e
M exico 6 h 36 m
8 sl o w
Th e Natio n al As t ro nom ical Obse rvato ry
o f Tac u baya regu late s a c lo c k tw ice a d ay w hich m ark s th e lo c al
m ean tim e o f th e City o f Me xico an d a s ignal is raised tw ice a w ee k
at n oo n u po n th e roo f o f th e nat io n al p alace
su c h s ignal be ing
This s ign al th e clo c k at
u se d to regu l ate th e c ity s p u bl ic c loc k s
the cen t ral te legraph o ffice an d th e p u blic clo ck o n th e c ath ed ral
Th e
serve as a b as is f o r th e t im e u sed co mm o nl y by th e peo ple
l
h
h
i
l
l
f
n
n
r
a
l
t
l
ffi
t
r
t
t
i
s
t
i
a
t
o
a
o
i
t
s
b
r
a
c
h
r
a
e
e
e
O
a
n
s
m
i
s
m
d
e
ce
e
g
g p
y
o ffices
No t e v ery c ity in th e co u n t ry u s es th is t im e h o w e v e r
s in ce a lo c al t im e ve ry im perfe c tl y d e te rm in ed is m o re c o m m o n l y
Th e fo llo wi ng railro ad c o m pani es u se s tan dard City o f
o bs erved
Me xico tim e co rre c ted d aily by te legraph : Ce n t ral H idalgo Xico
Th e Ce n t ral an d Natio nal
and S an Ra fae l Natio n al and Me xi c an
rail ro ad s c o rre c t t h e ir c lo c k s to City o f Me xic o t im e d aily by m eans
o f th e n oo n s ignal se n t o u t fro m th e Nav al Obse rvato ry at Was h
ingto n (see p age 7 1 ) an d by a s im ilar s ign al fro m th e o bservato ry
Lu m
nbu rg,
,
l h
.
.
fas t
,
th e leg al
.
a n d u n i o rm
.
.
.
,
,
’
,
.
,
,
-
.
.
,
,
,
,
.
,
,
.
,
Th e Naco z ari, an d th e Can an ea, Y aq u i R ive r
S t Lo u is , Misso u ri
an d P ac ific rail ro ad s u s e Mo u n tain t im e , 7 h slo w , an d th e S on ora
rail ro ad u se s t h e l o cal t im e o f Gu aym as , 7 h 2 4 m slo w
at
.
.
.
N icaragu a , 5 h 4 5 m 10 8
.
o fi ces ,
.
.
sl o w
telegraph
rail w ays ,
.
.
.
Managu a tim e is issu ed
.
o ffices
all
u
l
i
b
c
p
in a z o ne tha t
N , to E l Oco tal ,
c h u rc h es
an d
to
t
fro m S an J u an del S u r lat itu de 1 1 15 44
latitu d e 12 4 6 N an d f ro m E l Cas t illo lo ngitu d e 84 22 3 7 W
W Th e t im e o f th e Atlan tic
to Co rin to lo ngitu d e 87 1 2 3 1
i
s u s u ally o btain ed fro m th e c ap tains o f ships
r
t
s
o
p
Ce n tral E u ro pean tim e is u sed e veryw h e re th ro u gh
Norwa y 1 h fas t
Telegrap h ic t im e s ign als are se n t o u t o n ce a
o u t th e co u n t ry
week to th e te legraph s tatio ns th rou gh o u t th e co u n try fro m th e
obse rvato ry o f th e Chris t ian ia Unive rsity
B o th th e lo cal m e an t im e o f Co lo n 5 h 19 m 39 8 slo w an d
P anama
Th e
e as te rn s t an d ard t im e o f th e Un ite d S t ate s 5 h sl o w are u sed
latte r tim e is cabled daily by th e Ce ntral and S o u th Am e rican Cable
°
e x e n ds
’
"
.
,
°
°
'
.
,
”
’
.
,
°
’
”
.
,
.
,
.
.
.
.
.
,
.
,
.
.
,
,
.
.
,
LONGI TUD E AND TI ME
86
Co m p an y f ro m the Naval Obse rvato ry
r
o
a
bl
so
o
n
s
n
t
t
r
b
b
e
a
d
o
a
s
a
e
d
d
a
d
p
y
p
at
Washi ngto n
will
and
,
.
P eru , 5 h 9 m 3 8 slo w
Th e re is n o Offic ial tim e
Th e rail ro ad from
Callao to Oro ya tak es its tim e by te legraph f ro m th e noo n s ignal at
th e naval s c h oo l at Cal lao , w h ic h m ay be s aid to be th e s tand ard
time f o r Callao , Lim a, and th e w h ole o f ce n t ral Peru Th e railro ad
fro m Mo llend o to Lak e Titic aca, in so u th ern Pe ru , tak es its tim e
from sh ips in th e B ay o f Mollend o
.
.
.
.
.
.
.
P ortu ga l , 0h 36 m
8 slo w
S tan dard t im e is in u s e th ro u gh o u t
P o rtu gal and is bas ed u po n th e m e rid ian o f Lisbo n
I t is es tab
lish ed by th e R o yal Obse rvato ry in th e R o yal P ark at Lisbo n ,
and fro m th ere se n t by tele graph to e v e ry rail w ay s t atio n th ro u gh
.
.
.
.
.
P o rtu gal h aving telegraph ic co m m u n ic at io n
Clo ck s
s tatio n platfo rm s are fiv e m in u tes be h ind and c loc k s
s tatio ns are t ru e
ou t
.
o n rail w ay
t
o u sid e
of
.
8 f as t
Ru ssia , 2 h 1 m
All telegraph s tatio ns u se th e tim e o f th e
At rail ro ad
R o yal Obse rvato ry at Pu l k o w a, n e ar S t P e te rs bu rg
s tat io ns bo th lo c al an d Pu l k o w a t im e are give n , fro m w hic h it is
to be inf e rred th at f o r all loc al p u rposes lo c al tim e is u sed
.
.
.
.
.
.
.
S a lvador, 5 h 56 m 32 8 slo w Th e go v e rn m e n t h as es tablish ed a n atio n al
Obse rvato ry at S an S al vad o r w h ic h iss u es t im e o n Wed n esd ays an d
S atu rd ays , at n oo n , to all p u blic Offices , te legrap h Offices , rail w ays ,
th ro u gh ou t th e R epu blic
e tc
.
.
.
.
.
.
S anto D om i ngo , 4 h 39 m 32 s slo w Lo cal m e an t im e is u se d , bu t th e re
is n o ce n tral o bse rvato ry and n o m e a ns o f co rre c t ing th e t im e : Th e
tim e d iff ers fro m that o f th e naval vessels in th es e w ate rs by abo u t
3 0 m in u tes
.
.
.
.
.
S ervia , l h fas t
Ce n t ral E u ro pean tim e is u sed by th e
h
n
o
k
s
co
m
a
n
i
a
l
n
r
a
ll
C
l
c
a
r
e
r
a
o
e
es
e
e
e
d
,
p
g p
g
y
p p
telegrap h fro m B u d apes t e very d ay at n oo n
.
.
.
t
rail ro ad , e le
re gu late d
by
.
Th is is th e Offi c ial tim e f o r u se in go ve rn
S pai n , Gree n w ich t im e
m en tal Offices in S p ain an d th e B alearic I slan d s , rail ro ad and
telegraph o ffices Th e h o u rs are n u m be red fro m 0 to 24 , begin ning
I n so m e po rtio ns lo cal t im e is s till u sed f o r p rivate
with midn igh t
m atters
.
.
.
.
S weden , 1 h fas t
Cen tral E u ro pe an t im e is th e
I t is se n t o u t e v e ry w ee k by te legraph
use
Obse rvato ry
.
.
.
t
s and ard
fro m
th e
in gene ral
S to ckh o lm
.
Ce n tral E u ro pean tim e is th e o n ly legal t im e
o u t d ail y by teleg raph fro m th e Can to n al Obse rvato ry at
S w itz erla nd , 1 h
I t is
se n
t
.
fas t
.
.
TI ME USE D I N V AR I OUS COUNTR I E S
87
Two kinds o f t im e are u sed Tu rkis h and E as te rn E u ro pe an
time , th e fo rmer f o r th e natives an d th e latter f o r E u ro pean s Th e
rail roads ge n e rall y u se bo th , th e latte r f o r th e ac tu al ru n n ing o f
trains and Tu rk ish tim e tables f o r th e benefit of the na tives
S tand ard Tu rkish tim e is u se d gen erally by th e peo ple , su nse t be ing
Tu rkey
.
,
.
-
.
h o u rs being add ed f or a th eo re t ical s u n ris e
’
Th e o ffic ial cloc k s are se t d aily s o as to read 1 2 o cloc k at th e t h eo
re tical s u n rise , fro m tables s h o w i ng th e t im es o f s u ns e t , b u t th e
tower clo c k s are set o nly two o r th ree t im es a week Th e go v ern
m en t telegraph lines u se Tu rk is h tim e th ro u gh o u t th e e m p ire , an d
S t S o phia t ime , 1 h 56 m 53 8 fas t , f o r telegram s se n t o u t o f th e
the bas e,
and
twelve
.
.
.
.
t
cou n ry
.
.
.
S tand ard t im e b ased u po n the m e rid ian o f Gre e n wi ch ,
United S tates
v arying by w h ole h o u rs f ro m Gree n w ich t im e , is alm os t u ni ve rs ally
u sed, an d is se n t ou t d aily by te legrap h to m os t o f th e co u n try, an d
to Havana an d P an am a fro m th e Na val Obse rvato ry at Was h in gto n ,
an d to th e P ac ific co as t fro m th e o bse rvato ry at Mare I sl an d Navy
Fo r fu rth e r d is cu ss io ns of s tandard tim e be l ts in
Y ard , Cal i fo rnia
th e United S tate s , see pp 66 6 8 an d th e U S stand ard th e belt
I ns u l ar po ssessio ns h ave tim e as fo llo ws :
m ap
P orto Ric o , 4 h slo w , Atlan tic s tan d ard tim e
Alas ka , 9 h S lo w , Alas k a s tan d ard tim e
Hawaiia n I sla nd s , 10 h 30 m slo w, Haw ai i an s tan dard time
Gu am, 9 h 30 m fas t , Gu am s tan d ard time
P hil ip p i ne I slands , 8 h fas t, P hilip pin e s tand ard tim e
Tutu ila , S amoa, 1 1 h 30 m slo w , S am o an s tand ard t im e
.
.
—
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
8 s lo w
Th e t im e in com m o n u se is th e m e an
Urugu ay, 3 h 44 m
time o f th e m erid ian o f th e do m e o f th e Me tro po litan Ch u rch o f
Mo n te video Th e co rre c t tim e is ind ic ated by a s triking c loc k in
An as tro n o mical geo de t ic Obse rvato ry ,
the to we r o f th at Ch u rc h
with m e rid ian teles co pe a n d c h ro no m ete rs , h as n o w been es t ab
I t is p ro po sed to
lish ed an d w ill in th e fu tu re fu rn ish th e tim e
ins tall a tim e bal l f o r th e be n e fit o f n avigato rs at th e po rt o f Mo n te
An elec tric tim e se rvice w ill be e xtended th ro u gh o u t th e
video
co u n t ry, u s in g at firs t th e m e ridian o f th e ch u rch an d afte rw ard s
th at o f th e natio nal obse rvato ry, w hen co ns tru cted
s
Th e tim e is co m pu ted d aily a t th e Caracas
Venez uela , 4 h 27 m
Observato ry fro m o bse rvatio ns o f th e su n an d is oc cas io nally te le
e z u el a
h
a
f
n
T
h
h
r
r
t
s
h
t
o
r
o
V
e
l
o
t
t
e
d
o
e
e
c
a
e
d
r
a
l
a
c
c
k
a
t Caracas
p
g p
is co rre c te d by m ea ns o f th ese o bse rvatio ns
R ail w ay t im e is at
leas t five m in u tes l ate r th an th at in d icated by th e c ath ed ral clo ck ,
whi c h is acce pted as s tand ard by th e peo ple
S o m e peo ple tak e
tim e fro m th e o bservato ry flag, which al ways fal ls at n oo n
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
88
LONGI TUD E AND TI ME
LATI TUD E
LON GI TUD E
AN D
The latitud e and lo n gitud e
OF
CI TI E S
cities in the following
table was compiled from various sourc es Where possible
the e xac t plac e 13 given the abbreviation
O
stand ing
C
for Observatory
for cathedral etc
Of
.
,
,
,
,
.
Lo n gl t u d e f ro m
Gre e n w l c h
'
L ati tu d e
Adelaide , S Au s t ral ia , S nap
r P o in t
A en , Arab ia , Tel S tati o n
t , E u n os P t
Al e xan d ria , E
Am s te rd am , o aiI d , Ch
An twerp , B e lg iu m , 0
’
Ap ia, S am o a, R u ge s Wh a rf
Ath ens , Greece , 0
B angk o k , S iam , Old B r Fac t
B arcelo na , S pain , Old Mo le
Ligh t
l t av ia l av a, O
a
i
n fi
l o rw ay C
I e
n y, O
Be
, Ge rm
a
B o m bay , I n d i a, 0
B o rd eau x , Fran ce , 0
B ru sse ls ,
B u eno s Aire s , Cu s to m Ho use
Cadi z , S p ain , 0
t, 0
Cairo , E
Cal c u tta , t W m S e m aph o re
Can to n , Chin a , D u tch Li gh t
Cape Ho rn , S o u th S u m mi t
Cape To w n , S Afric a , 0
Caye n n e , Fr Gu ian a, Lan d in g
Ch ris tian ia, No rw ay , 0
Co ns tan tin o ple , Tu rk ey , C
k
w
0
a
r
N
e
n
n
m
Co pe n h ag
e
D
e
,
,
8
D u bl in I re lan d , 0
E d in bu rgh , S c o tl an d 0
Flo re n ce , I t aly , 0
Gib ral t ar, S pain , D o c k Fl
Glas go w , S co tl an d , 0
Hag u e , Th e , Ho llan d , Ch
Ham bu rg , Germ any, 0
Hav an a , Cu ba , Mo rro Lt
Hongk o ng, China, C
.
.
.
.
.
.
g
.
.
ifiii
,
.
.
.
.
.
.
.
.
.
.
.
?
.
.
.
.
.
.
.
.
LONGI TUD E AND TI ME
90
Latitud e
B u fi al o , N Y
Charlesto n , S C , Lt Ho use
Ch eyenne , Wyo , Ast S ta
Chi cago , m , 0
Cin cinn ati, Ohio
Cl e velan d , Ohi o , Lt H
Colu m bia, S C
Co l u m b u s , Ohio
Co n co rd , N H
D ead w oo d , S D , P 0
D e n ver, Co l , 0
D es Mo ines , I o wa
D e t ro it , Mi ch
D u lu th , Min n
E rie , P a Waterwo rk s
'
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Gu th rie , Okla
Hartfo rd , Co n n
.
.
Helen a Mo n t
Ho n ol u lu , S an d w ich I slan ds
.
,
I nd ian ap o lis , I n d
J ac k so n , Mis s
J ac k so n vill e , Fla , M E Ch
Kans as Cit , Mo
Key Wes t , a , Li
Lans ing , Mich , Cap ito l
Le xi
o n , Ky , Un iv
Lin co
Ne b
Little R o c k , Ark
Lo s A eles , Cal , Ct Ho u se
Lo u is v e , Ky
Lo well , Mas s
Mad iso n , W is , O
Manila , Lu z o n , C
Mem p his , Te n n
Mil wau k ee , W is , Ct Ho use
Min nea Olis , Minn
Mitch el S D
Mo bile , Ala , E I S Chu rc
Mo n tgo m e ry, A
Nas h ville , enn , (
Newark , N J M E Oh
New Haven , Co n n " Y al e
Ne w Orleans , La , Min t
Ne w Y o rk , N Y City Hall
No rth field , Min n , O
.
.
.
.
.
.
.
.
.
.
.
.
.
.
”
.
.
.
.
.
E
.
.
.
i
r
.
.
.
.
.
.
.
.
.
.
.
.
.
.
LATI TUD E AND LONGI TUD E OF CI TI ES
91
L ati tu d e
’
am o a
Pa , S
.
tate Hou se
Pitts bu , P a
P o in t
h
rro w
h
t
t
i
i
es
l
a
( g
tu de I n the United S tates )
P ortland , Ore
Prin ceto n , N J O
Pro viden ce , R I , Unit Ch
R al eI gb , N C
Ric hm o nd , Va , Capito l
Ro ch es ter, N Y O
S ac rame nto , Cal
S t Lo u is , Mo
S t P aul , Minn
S an Fran cisco , Cal , C S S ta
P o rto R I co , Mo rro
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
'
o use
N M
S avann ah Ga , E x change
S eattle , Was h ” C S As t S ta
S itk a A
las k a P arad e Gro u nd
Tall ahassee , Fla
Tren ton , N J Capito l
V irgin ia City, Nev
.
.
,
.
.
.
,
.
.
,
.
.
.
.
Was h ingto n D C O
Wheeling W Va
Wilmingto n Del To wn Hall
Wino na Minn
.
,
.
,
.
,
,
.
.
.
,
,
.
13
'
03
'
16
'
18
’
56
’
22
'
26
08 N
”
06 S
”
53 N
”
34 N
”
°
1 11
°
122
°
95
°
1 70
°
75
°
100
°
80
’
59
’
57
'
57
’
42
'
09
’
20
'
02
”
45
”
00
”
33
”
31
”
03
”
26
”
38
W
W
W
W
W
W
W
CHAPTE R
V
CI R C UM N A V I GATI ON AN D
Magell an
TI M E
When the sole survivin g S hip Of
Magellan s fleet returned to S pain in 1522 after having
circumn avigated the globe it is said that th e crew were
h
e
e
t
r
atly
a
toni
h
d
that
th
ir
cal
ndar
and
that
of
e
s
s
e
e
g
S paniard s did not correspond
They land ed according to
their own reckoning on S e ptember 6 but were told it was
S e ptember 7 At first they tho u ght they had mad e a m is
take and some time elapsed be fore they realiz ed that they
h ad lost a day by going around th e world with t he su n
Had they travel ed toward the east they would have
gained a day and would have record ed the same date as
S e ptember 8
Fleet
’
s
.
’
,
.
,
,
,
.
,
.
,
,
.
My p ilo t is de ad o f
m ay
I as k th e lo ngitu de , tim e an d day ?
Th e fi rs t tw o given an d c o mp ared ;
Th e third ,
th e c o mm an d an te s ta re d !
s c u rvy :
The firs t o f J u n e ? I m ak e it s ec o n d ,
’
S aid th e s tran ge r, Th en yo u ve w ro ngly rec k o n e d !
B R E T HA R TE in The Lo st Ga lleo n
.
,
xplanation Of this phe nomenon is S impl e I n
traveling westward in the same way with the su n one s
days are len g thened as compared wit h the day at any
°
fixed plac e Wh en o ne has traveled 15 west ward at what
e ver rat e Of spe ed h e find s h is watch is o n e hour behind
the time at h is starting po int if h e changes it according
to th e su n He has thus lost an hour as compared with
Th e
e
.
’
,
,
,
.
,
,
.
92
WE S TWAR D
TR AVE L
D AYS ARE LE NGTHE NE D
93
time at his starting point After he has traveled 15
farther he will set h is watch back two hours and thus
record a loss of two hours And S O it continues through
°
out th e twenty four belts Of 15 e ach los in g one hour in
each belt ; by t he time h e arrives at his starting point
°
t he
.
,
.
-
,
Fig 30
.
again he has set h is hour hand back twenty four hours
and has lost a day
D ays are Len gth en ed
W estward Travel
TO make this
clearer let u s suppose a travele r starts from Lo ndon Mon
°
day noon January l st traveling westward 15 e ach day
°
On Tuesday when h e find s h e is 1 5 west Of London h e
I t is then noon by th e su n
set s h is watch back an hour
He says
I left Monday noon it is now
where he is
-
,
.
.
,
.
,
,
,
,
.
.
,
,
94
CI R CUMNAV I GATI ON AND TI ME
Tuesday n oon ; therefore I have been out
one
day
The
.
tower clock at London and his chronometer set with it
however indicate a d ifierent view They say it is Tuesday
1 O clock P M and he has been out a day and an hour
The n ext day th e proc ess is re peated
The traveler hav
°
ing covered another space of 15 westward sets h is watch
back a second hour and says I t is Wednesday noon and
I have been out just two days
The Lo ndon clock how
e v er
says Wedn esday
2 O clock P M
two days and
two hours S inc e he left The third day this Occurs again
t h e traveler lo sing a third hour ; and what to him see ms
three days Monday noon to Thursday noon is in reality
by London time three days and three hours E ach of his
days is really a little more than twenty four hours long
for he is going with the su n B y the time he arrives at
London again he finds what to him was twenty four days
is in reality twenty five days for h e has set h is watch
back an hour e ach day for twenty four days or an entire
day TO have h is calendar correct he must omit a day
that is move th e date ahead on e day to make up the date
lost from his reckoning I t is Obvious that this will be
tru e whatever the rate Of travel and the day can be omitted
from his calendar anywhere in the journey and th e error
corrected
E astward Travel
D ays are S h o rten ed
Had our trav
°
e ler gon e eastward wh en h e h ad covered 15 Of longitud e
he would set h is watch ahead o ne hour and then say
I t is now Tuesday noon
I have be en out o n e day
The London clock would in dicate 1 1 O clock A M of
Tuesday and thus say h is day had but twenty three
hou rs in it the traveler having moved the hour hand
ahead o ne spac e He has gain ed o ne hour The second
day he would gain another hour and by the time he arrived
,
,
.
,
’
,
.
.
.
,
.
,
,
,
.
’
—
,
,
.
,
.
,
.
,
,
.
-
,
.
-
-
,
,
,
-
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THE I NTE R NATI ONAL D ATE LI NE
at London again h e would
have set h is hour han d ahead
twenty f our hours or one
full day To correct his cal
end ar so m ewh ere on his voy
age h e would have to repe at
a day
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Th e
I n ternational
I t is
D ate
bvious from
th e forego ing explanation
that somewhere and so me
time in circumnavigation a
day must be omitted in trav
eling westward a
n d a day
repeated in traveling east
ward
Where and when the
change is made is a mere
matt er of convenienc e The
theoretical location of the
date line commonly used is
the l 80th meridian
This
line where a traveler s cal
endar n eed s c ha ng ing varies
as do th e boundaries Of th e
st andard time belt s and for
the same reas on
While
t he change could be mad e
at any particular point on
a parallel it would make a
serious inconvenie nce were
t he change mad e in some
I magine for ex
places
ample the 90th meridian
Lin e
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CI R CUMNAVI GATI ON AND TI ME
96
Greenwich , to be th e line used Whe n it was
S un day in Chi cago , New York , and o ther ea stern points,
it would be Monday in S t Pau l , Kansas Ci ty , and western
poin ts A traveler leavin g Minneapoli s on S u nday nigh t
west
of
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.
.
arri ve in Chi cago on S un day morning and thus
have two S undays on su ccessive days Our nationa l holi
days and elec tions wou ld then occur on diff ere nt days
To reduce to the
in di ff erent parts Of the coun try
minimum su ch inconveniences as nec essarily a ttend chang
ing one s calendar th e change is made where there is a
rela tively small amount of travel away o u t in th e P acific
Ocean
Going westward across thi s line one must set his
cale ndar ahea d a day ; going ea stward back a day
As shown in Figures 3 1 and 32 this line be gins on th e
180th meridian far to the north sweeps to the ea stward
around Cape Deshn ef R ussia then westward be yond th e
180th m eridian seve n de grees tha t the Al eu tian i slands
may be to the east of it and have the same day as
c ontinental Uni ted S ta tes ; then the li ne e xtend s to th e
180th m eridian whi ch it follows so u thward swee ping
so me wha t eas tward to give th e Fiji and Chatham i slands
Th e fOllOW
th e same day as Australia and New Zeala nd
ing is a l ette r by C B T Moore comm ander U S N
Go vernor of Tu tuila rela tive to th e ac curac y of the map
in this book :
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P ogo P o go , S amoa, D ecem ber 1 , 1906
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The map of yo u r Mathem atical Geograph y is
D E AR S I R :
corre c t in placing S am o a to th e eas t o f th e in te rna tio nal d ate lin e
The older geographies were als o righ t in pl ac ing t h ese islan ds wes t
of the in terna tio nal d ate lin e , becau se th ey u se d to k eep th e sam e d a te
as Aus tralia and New Ze aland , w hich are wes t of th e inte rnational
.
The
S ociety
f o r this m is tak e is that w he n the Lo nd o n Miss io nary
sen t its missionaries to S amo a they w ere n o t ac q u ain ted with
re aso n
CI R CUMNAVI GATI ON AND TI ME
98
Wh ere D ays B egi n Wh en it is
O clock P M
on
O clock A M
S atu rday at De nver it is
S unday at
New York I t is thu s evid ent that parts of two days
exist at the same time on th e e arth
Were one to travel
around the earth with the su n and as rapidly it would be
perpetually noon When he has gone around once o ne
day has passed Where did that day begin ? Or su p
pose we wished to be the first on earth to hail the new
year where could we go to do so ? The midnight line
just Oppos ite the su n is constantly bringing a ne w day
Midnight ushers in the new year at Chicago
so mewhere
S till east
Previous to this it was beg u n at New York
of this New Year s Day began some time before I f we
kee p going around eastward we mu st su rely come to
some plac e where New Ye ar s Day was first co u nted o r we
shall get entirely aro u nd to New York and find that the
New Year s Day began the day before and this midnight
As previously stated the date
would commenc e it again
l ine commonly acce pted nearly coincides with the 180th
merid ian Here it is that New Year s Day first dawns
an d each n ew day beg ins
Th e Total D u ratio n of a D ay
While a day at any
particular place is twenty four hours long each day las ts
An y given day say
on e arth at least fo rty e ight hours
Christ mas is first counted as that day just west of the
°
date line An hour later Christmas begins 15 west of
°
that line two hours later it begins 30 west of it and S O on
around the globe The people j u st west of the date line
wh o first ha iled Christ mas have enjoyed twelve hours of
it when it begins in E ngland eighteen hours of it when
it begins in c entral United S tates and twenty four hou rs
Of it or the whole day when it begins in west e rn Alas ka
just eas t of the d ate line Christmas then has existed
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CONFUS I ON OF TR AVE LE R S
99
twenty four hours on the globe but hav ing just begun in
western Alaska it will tarry twenty f our hours longer
among mankind making forty e ight hours that the day
blesses the e arth
°
I f t he date line followed the meridian 180 without
any variation the total duration Of a day would be exactly
forty e ight hours as j ust explained B ut that line is q uite
irregular as previously described and as S hown on th e
map Be ca use Of this irregularity Of t he date line the
same day lasts some where o n e arth over forty nine hou rs
°
S uppose we start at Cape Deshn e f S iberia lon gitud e 169
West a moment after midnight Of the 3d Of July The
4th of July h as begun and as midnight swee ps around
west ward s ucc ess ive plac e s see the beginning of thi s day
When it is the 4th in Lo ndon it has been the 4th at
Wh en
Cape Deshnc f t we l ve hours and forty four minutes
th e glorious day arrives at Ne w York it has been seven
teen hours and forty four minutes sinc e it began at Cape
When it reaches our most western point on this
De shn ef
°
continent Attu I sland 1 73 E it has been twenty five
hours and twelve minutes S inc e I t began at Cape Deshnef
S inc e it will las t twenty four hours at Attu I sland forty
nine hours and twelve minutes will have elapsed S inc e the
beginning Of the day until the moment when all plac es
on earth cease to count it that day
Wh en Three D ays Co exist P ortions Of three days
and
exist at t he same time betwee n
O clock A M
o clock P M London time When it I S Monday
noon at London Tuesday h as begun at Cape Deshn ef
but Monday morning has not yet dawned at Attu I sland ;
nearly half an hour Of S unday still re mains there
Co nf u sio n o f Travel ers
Many stories are told Of the
co nfu sion to trave le rs w h o pas s from pl ac es reckoning
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CI R CUMNAVI GATI ON AND TI ME
100
day across this line to places ha vin g a diff erent day
I f it is such a d ead ly S in to w ork 011 S u nday on e or th e
other of Mr A and Mr B coming o ne from the eas t
the other from the west Of the 180t h m eridian must if
he continues his daily vocations be in a bad way
S ome
Of our people in t he Fiji are in thi s unenviable po sition
°
as the line 180 passe s through Loma Loma
I went
from Fiji to Tonga in Her Maj esty s S hip Nymp h and
arrived at our destination on S unday according to our
reckoning from Fiji but on S aturday according to the
proper computation west from Greenwich We how
one
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v r found the natives all keeping S u nday On my ask
ing the missionaries about it they told me that the m is
sion aries to that group and S amoa having come fro m
e e
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CI R CUMNAVI GATI ON AND TI ME
102
modification that as all events on a S hip must be regu
lated by a common timepiec e changed according to
longitud e S O the community on board in order to adjust
to a common calendar must acc ept the change whe n mad e
by the captain
Origin an d Ch ange of D ate Lin e
Th e origin of this
line is of con sid erable int erest The day ad opted in any
region d epended upo n the direction from which the
people came who settled the country For exampl e
people who went to Australia Hongkong and other E ng
lish possessions in the Orient traveled around Africa or
across the Mediterranean They thus set their watches
ahead an hour for every
For two c enturies after
th e S pan i sh settle ment the trad e of Manila with the
west ern world was carried on via Acapulco and Me xico
E
ncy
B
ri
hu
h
tim
which
O
btain
d
in
h
e
T
s
e
e
e
t
t
t
(
)
P hilippines was found by setti n g watches backward s an
hour for every
and S O it came about that the cal endar
of the P hilippines was a day earlier than that of Australia
Hongkong etc Th e date line at that tim e was very ind efi
nite and irregular I n 184 5 by a d ecree of th e B ishop Of
Manila w ho w as also Governor General Tuesday Dec em
ber 3 1 was stricken from th e calendar ; th e day after
Monday D ec ember 30 w as Wednesday January 1 1846
This cutting t he year to 364 days and th e week to 6 days
gave the P hilippines the same day as oth er Asiati c plac es
and S hifted the date l ine to the east Of that archipelago
Had this chang e n ever been mad e all of th e possessions
of the Unit ed Stat es w ould have th e same day
For some time aft er th e ac quisition of Alaska th e people
living there formerly citiz ens of R ussia used the day lat er
than ours and also used the R ussian or Julian cal endar
twelve days later tha n ours As peopl e moved there from
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103
P R OB LE M
United S tates our system grad ually was e xtend ed bu t
for a time both systems were in vogue This mad e aff airs
confusin g so me keepin g S u nday when others reckoned the
same day as S aturday and counted it as twelve days later
in the c alendar New Year s Day Christmas etc coming
at diff erent times S oon however the American syste m
h
e R uss ian
h
s
t
r
vail
d
to
ntir
e
xclu
ion
of
t
h
e
e
e
t
e
e
e
p
in habitants re peatin g a day and thus having eight days
in one wee k While the R ussians in their churches in
Alas ka are c ele bratin g the Holy Mass on o u r S unday
their brethren in S iberia n o t far away an d in other parts
of R ussia are busy with Monday s duties
the
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Fij i, No X I V , 1879 : An o rd i
nance e nac ted by th e go verno r o f th e c o lo n y o f F ij i, w ith th e ad v ice
and c o nsen t o f th e legisla t ive co u n c il th e reo f, to p ro v id e f o r a u niv er
sal d ay th ro u gh o u t th e c o lo n y
Whereas , acco rd ing to th e o rd inary ru le o f no ting tim e, an y given
time wo u ld in that part o f the co lony lying to th e eas t o f th e m eridian
°
o f 180 f ro m Gre en w ic h be n o ted as o f a day of th e w ee k an d m o n th
d ifi e re nt f ro m th e d ay b y w h ich th e sam e tim e w o ul d be n o te d in th e
h
n
ar
o
f
t
l
n
l
r
i
d
n
t
o
i
s
t
f
u
m
di
a
n
a
t
o
s
e
co
t
o
h
w
c
h
e
e
e
;
p
y y g
Whereas , by c u sto m th e o rd in ary ru le h as been set as ide a nd tim e
h as bee n no ted th ro u gh o u t th e c o lo ny as th o u gh th e wh o le w e re situ
ated to t h e w es t o f s u ch m e rid ia n ; an d
Whereas , in o rd er to p rec l u de u n ce rtain ty f o r th e f u tu re it is e xpe
d ien t th at th e abo ve c us to m s h o ul d be legaliz ed ; th e refo re
B e it enac ted by the governor, with the ad vice a nd co n sent o/ the
legislati ve co u nci l, as fo llo ws
Tim e in this c o lo ny sh all b e n o ted as if th e w h o le c o lo ny w e re
°
s itu ated to the w es t o f th e m e rid ian o f 180 f ro m Gre e nw ich
E
r
m
l
i
a
t
i
a
T
i
n
r
o
d
a
i
t
o
r
d
i
ru
l
h
h
a
c
h
a
c
o
r
d
n
t
o
e
w
c
e
,
(
p g
g
y
y
f o r n o ting tim e is o n th e is lan d o f Ov alau th e 5th day o f J u n e, and
on th e is lan d o f V an u a B ale vu th e 4 th d ay o f J u n e, w o u l d by th is
o rdin anc e be dee m ed as th e 5th day o f J u ne , 1 879, in th e w h o le
co lo ny )
Pro blem
Assu ming it w as 5 A M , S u nd ay, May 1 , 1898, w h en th e
naval b attle o f Mani la began , w hat t im e w as it in Milw au k ee , th e c ity
°
using s tandard time and D ewey using th e loc al t im e o f 120 eas t ?
D ate
Li ne
E ast
of
Fiji Islands
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CHAPTER VI
THE E AR TH S R E VOL UTI ON
’
P R OOF S
R E V OL UTI ON
OF
at least 24 00 years the theory Of th e revolution
of th e earth around th e su n h as been advocated but only
in mod ern times has th e fact been d emo nstrated beyond
succ essful contradiction
Th e proofs rest upon three set s
Of astronomical Observation s all of w hich are Of a d elicat e
and abstruse character although the und erlying principles
are easily und erstood
Aberratio n of Ligh t
When rain is falling on a calm day
th e drops w ill strike t h e top of on e s head if he is stand
ing still in the rain ; but if o ne moves th e dire ction of the
drops will see m to have changed st riking o ne in th e face
more and more as the speed is increased ( Fig
No w
l ight rays from the su n a star or other heavenly body
strike th e earth somewhat slantingly be cau se th e e arth is
moving around the su n at the rate of over a thousand
miles per minute B e cause of this fact the astronome r
must tip h is t elescope S lightly to th e east of a star in ord er
to see it when the earth is in on e S id e of its orbit an d to
th e west Of it w hen in th e opposite S id e Of th e orbit
Th e
n ec essity of this tipping Of the t elescope w ill be apparent
if we imagin e th e rays passing through th e t elescope are
like raindrops falling through a tube I f the tube is car
ried forward swiftly enough the drops w ill strike the S ides
Of th e tube
and in ord er that th ey may pass directly
through it the tube must be tilted forward somewhat
FOR
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104
THE E AR TH S R E VOL UTI ON
106
’
revolves around the su n th e precise form of this aberra
tion al orbit of any star can be calc u lated and Observation
invariably confirms the calculation R ational mind s can
not conc eive that the millions o i stars at varying dis
tances can all actually have these peculiar annual motions
in
S ix mo nths toward t h e e arth and six months from it
addition to the other motions which many Of them (and
probably all of them see pp 265 26 7) have The dis
co very and exp lanation of these fact s in 1 72 7 by James
B radley (see p
t he E nglish Astronomer R oyal forever
put at rest all disputes as to the revolution of the earth
Motion in th e Lin e of S igh t I f you have stood near by
when a swiftly moving train passed with its bell ringing
you may have notic ed a sudd en change in the tone of the
bell ; it rings a lower note immed iately upon passing The
pitch of a note d epends upon the rate at which the sound
waves strike th e car ; the more rapid they are the higher
*
is the pitch
I magine a boy throwing c hips into a river
at a uniform rate whil e walking do wn stream toward a
bridge and then while walking upstream away from the
bridge Th e chips wi ll be close r together as they pass
und er the bridge when the boy is walking toward it than
when he is walking away from it I n a S imilar way the
sound waves from t he bell of th e rapidly approach ing
locomotive accumulate upon the ear of the list ener and
th e pitch is higher than it would be if th e train were sta
t io nary and aft er th e train passes th e sound waves will be
farther apart as Observed by th e same person who w il l
hear a lower note in conse quenc e
No w in a prec isely
Color varies wi th Rate of Vibration
S imil ar mann er th e colors in a ray Of light vary in t h e rat e
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This
432
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il lu s tra t ion
is
t
ad ap e d
fro m
Todd
’
s
Ne w As t ro nomy, p
.
MOTI ON I N THE LI NE OF SI GHT
107
of vibra tion The violet is the most rapid indigo abou t
one tenth par t slower blue sligh tly slower still the n gre e n
yellow orange and red The spec trosc ope is an astro
nomical instrumen t whi ch spread s ou t the line Of ligh t
from a celestial body into a band and breaks it up into
its several colors
I f a ringing bell rapidly approaches us
or if we approach it the to ne of th e bell sounds hi gh er
than if it recedes from us or if we recede from it I f we
rapidl y approach a star or a star approach es us its color
shi f ts toward th e viol e t end of th e spectrosc ope ; and if we
rapidl y re c ede from it or it rec e des from u s its color shif ts
toward th e red end
Now year af ter year th e thousands
of stars in the vicinity of the plane Of the earth s pathway
show in the spectrosc ope thi s cha nge toward V iol et at one
The f ar
season and to ward red at the oppo site season
ther from the plane of th e earth s orbit a star is locate d
the l ess is thi s annual change in color since the earth
neither approaches nor rece des from stars toward the
poles Ei ther the stars near the plane of the earth s
orbi t move rapidl y toward the earth at one season gradu
ally sto p and Six month s late r as rapidly recede and stars
away f rom thi s plane approach and recede at ra tes dimi n
ishin g exac tly in proportion to their dista nc e from thi s
plane or the earth itself swiftl y moves about the su n
P roof of the Rotati on of the Earth
The same set Of
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Th e rate o f vibratio n per
of ligh t is as fo ll o ws :
seco n d
“
x 10
“
x 10
Gre en
x
"
10
x
"
10
for
each of
th e
colo rs
in
a ray
Y ello w
Orange
Re d
Thus th e v io le t colo r has 756 0 m illio ns o f m illio ns
second ; ind igo , 6 98 8 millio ns of millio ns , etc
.
o f vibratio ns each
THE EAR TH S RE VOLUTI ON
108
’
and
reasoning applies to the rotation of the earth
I n t he evening a star in the e ast S hows a color approaching
th e violet S id e o f t he spectroscope an d this gradual ly S hift s
tow ard the red during the night as the star is seen higher
in t he S k y then nearly overhead then in the west Now
either th e star swiftly approaches th e earth early in th e
e vening th e n grad ually pauses and at midnight begins to
go away from th e earth faster and faster as it approac hes
t he west ern horizon or th e earth rotates on its axis
toward a star seen in the eas t neither toward nor from it
when nearly overhead and away from it when seen near
S in c e the same star rises at diff erent hours
the west
throughout the year it would have to fly back and forth
toward and from th e earth two trips every day varyin g
its period s ac cording to the time of its rising and setting
B esid es this when a st ar is ris ing at Cal c utta it S hows the
V iolet t e nd ency to Observers there (Calcutta is rotating
toward the star when the star is rising ) and at the same
moment the same st ar is setting at New Orleans and thus
Now the
S ho ws a S hift toward t he red to Observ ers th ere
dist ant st ar cannot possibly be actually rapidly approach
in g Calcutta and at the same time be as rapidly rec eding
from New Orleans Th e spectroscope that wonderful
in strument w hich h as multiplied astronomical knowledge
during the las t half cent u ry d emonstrates with mathe
m at ical c e rtainty th e rotation Of th e earth and multiplies
mill ionfold the c ertainty Of the earth s revolution
B efore l eaving this topi c we
Actu al M otion s of S tars
shoul d notic e that other changes in t h e colors of stars S ho w
that some are actually approaching th e earth at a uniform
rate and some are recedin g from it Careful Observa
tions at long int ervals S how other chan ges in the posi
tions Of stars The latter motion of a star is called its
facts
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1 10
THE E AR TH S RE V OLUTI ON
’
paral laxes thus mul tiplying th e proofs of the mo tion of
th e ear th around the su n
D isplacement of a S tar Vari es wi th its D i stance Figu re 34
shows that the amoun t of
the di splace men t of a star
in th e background of the
heavens owin g to a cha nge
in th e position of th e earth
varies with th e distance Of
th e sta r
The nearer the
star th e grea ter th e di splace
ment ; in every in stance h ow
e ver thi s apparent shifti ng of
a star is exceedingly minute
owing to the great di stance
see
2
h
pp
v
ry
4
5
4
6
O
f
e
t
e
(
)
nearest of the stars
S ince stu dents Ofte n con
se th e apparent orbi t Oi a
fu
Fi g 34
star desc ribe d u n d er abe rra
tion of ligh t with tha t du e to the parallax we may make
th e f ollowing comparisons :
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AB E RR ATI ON AL OR B I T
1
Th e
.
th s
ear
’
rap id
PAR ALLACTI C OR B I T
m o t io n
to slan t
ligh t
o
o
s
e
h
l
n
e
esc
t
t
t
l
i
o
t
e
n
e
ar
a
p
( pp
y)
th at, as th e earth ch anges its
d ire c t io n in going aro u n d th e s u n ,
th e s tar seems to sh ift s ligh tly
c auses
abo ?
t
th e
rays o f
in its
m o ve
u
n
d
r
o
g
t
th e
o rb i
abo u
of
th e
all
.
me
ga
t
s ars ,
m o ves
e ar
.
t
th e
.
Th is o rbit h as
m axim u m width f o r
h owe ve r n ear o r distant
2
th
1 As th e
t
s ars
u po n
celes
t
abo u
se em
t
to
bac k
th e
tial sph ere
.
t
2 This o rb i varies in Wi d h
w i h th e dis an ce o f th e s a r ; th e
n e are r th e s ar, th e gre a e r th e
.
t
t
t
t
t
WI NTER
CONSTE LLATI ONS I NVI S I B LE I N S UMME R
E FFE CTS
OF
B AR TII
’
S
111
R E V OLUTI ON
Win ter Constellations I nvisible in Su mmer You have
dou btless Observed that some const ellations which are
V is ibl e on a wint er s night can not be seen on a su mm er s
night I n January the beautiful constellation Orion may
be see n early in t he even ing and the whole night through ;
in July not at all That this is du e to the revolution of
the earth arou nd the su n may read ily be mad e apparent
I n the daytime we cannot easily see the stars around the
.
’
’
,
.
'
.
,
.
MS “?
Pic
-
as
th e
peculiar
of the atmosphere ; six mont hs from now the earth will
have moved halfway arou nd the su n and we S hall be
between the su n and the stars he no w hi des from view
and at night the stars now invisible will be V isible
I f you have mad e a record of th e observations suggested
in Chapter I you will now find that E xhibit I ( Fig
sho ws that the B ig D ipper and other star groups have
slightly chan ged the ir relative positions for the sam e time
of night mak ing a littl e more than one complet e rotation
during each twenty f our hours I n ot her word s the stars
e
r
at
g
su n ,
,
,
.
.
,
,
-
.
,
112
THE E AR TH S R E VOL UTI ON
’
have been gaining a little on the su n in the apparent daily
swing of t h e c elestial s phere around th e ea rth
Th e reasons for this may be und erstood fro m a careful
.
Fi g
.
36
udy of Figure 36 Th e outer circl e which S hould be
ind efinitely great re present s the c elestial sphere ; the inner
No w the su n
ellipse th e path of th e e arth around th e su n
does not see m to be as it really is relatively near the
earth but is proj e cted into the c el est ial S phere among the
st
.
,
,
.
,
,
,
,
THE E AR TH S R E VOLUTI ON
114
’
not then be on the horizon but the earth having moved
upward
it wo u ld be somewhat below the horizon
The same star howeve r would be on t he horizon for the
e arth doe s not change its position in relation to t he stars
After another rotation the earth w ould be relative to the
stars V ie wed in that dire ction highe r up I n its orbit and
the su n farther below the hori zon whe n the star w as just
rising I n three months w hen the star ro se the su n would
be nearly beneath o ne S feet or it w ould be midnight ; in
S ix month s we S hould be on the other S id e Of the su n
and it would be settin g when the star was risin g ; in nine
months the earth would have covered the down ward
quad rant of its journey around the su n and the star
w ould ri se at noon ; t welve m O
nthS later th e su n and
I f the su n and a star
star would ri se together again
on the next evening the star
se t together o ne evening
would se t a little before th e su n the next night earlier
still
S ince the su n passes around its orbit
in a year
36 5 days it passes o ver a space of nearly o ne d egree e ach
day Th e diameter of the su n as see n fro m the earth
covers about half a d egree of the c elestial sphere During
o ne rotation of t he earth then t he su n cree ps eas tward
among th e stars about t w ic e its o wn w idth A star risin g
with t he su n w ill gain on the su n nearly s i n of a day
during each rotation or a little less than four minutes
The su n sets n e arly four minutes later than the st ar with
which it set th e day before
S ide real D ay
S olar D ay
The time from star rise to
is called a
o r an e xact rotatio n Of t h e e ar th
star ri se
si dereal day
I ts exact l e ngth is 23 h 56 m
S
Th e
time between t wo succ e ssive passages of the su n o ver a
given meridian or from noon by the su n until the ne xt
.
,
.
,
,
,
,
.
.
.
’
,
,
,
.
,
,
.
,
,
,
.
.
,
,
.
.
,
.
.
-
.
-
,
,
.
.
,
.
.
CAUS E S OF AP P AR E NT MOTI ONS OF THE S UN
115
noon by the su n is called a solar day
I ts length vari es
some w hat
for reasons to be explained later but aver
“
ages twenty four hours Wh en we say day if it is n ot
otherwi se qualified we usually mean an average solar
day divided into twenty four hours from midnight to
“
midnight The te rm hour tOO w hen not otherwise
qualified refers to o ne t wenty fourth of a mean solar
day
Cau ses o f Apparen t M o ti o n s of th e S u n
The apparent
motions of the sun are du e to the real motions of th e
*
.
,
,
,
-
.
,
,
-
,
”
.
,
,
-
,
.
.
Pie 3 7
a th moved S lowly arou nd the su n the
Just
su n w ould appe ar to move S lo wly among the stars
as we kno w th e di re ction and rate Of th e e arth s rotation
by Observing the direction and rate of the apparent rota
th
ear
.
I f th e
e r
,
.
’
d ay is so m etim es defin ed as th e in te rval f ro m su n rise to
s u n rise again
Th is is t ru e o nly at th e eq u ato r Th e le ngth o f th e
so la r d ay co rresp o n din g t o F eb ru a ry 1 2 , May 1 5, J u ly 2 7, o r No v e m be r
3 , is alm o s t e xac t ly t w e n ty fo u r h o u rs
Th e t im e in te rve nin g b e t w ee n
su n rise an d s u n ris e ag ain v a ries g re at ly w ith th e latit u de an d s e as o n
On th e da te s n am ed a so la r d ay at th e p o le is t w e n ty fo u r h o u rs lo ng,
as it is e v e ryw h e re e lse o n e arth
Th e tim e f ro m su n ris e to su n rise
agai n , h ow ever, is alm os t six m o n th s at eith e r p ole
A
so lar
.
.
-
.
.
-
.
.
1 16
THE E ARTH S R E VOLUTI ON
’
of the celest ial sphere we kno w the direction and
rate Of the earth s revolution by Observing th e dire ction
an d rate of the su n s appare nt annual motion
Th e E cliptic
The path which the center of the sun
to trace around the celestial S phere in its ann u al
tion
,
’
’
.
.
Fig
is
.
38
.
Cel est i al sph ere, sh ow ing
z odiac
called
The line trac ed by the c ent er
Of th e earth in its revolutio n about the su n is its orbit
S ince t he sun s apparent annual revolutio n around the S k y
is du e to the earth s actual motion about the su n t h e path
Of th e su n the e cliptic must lie in the same plan e with the
orbit
*
the ecli ptic
.
.
’
’
,
,
,
the
S o c alled bec ause eclipses
l
o
f
li
i
a
h
t
t
c
e
e
ec
n
p
p
.
can o ccu r onl y
wh en th e m oo n
cro sses
THE EARTH S RE VOLUTI ON
18
’
journey to Canterbury
Chaucer says it was
about
was
Wh en
t
middle of April
the
,
Zep h iru s eek wi h h is swee te b re e th
E ns p ired h a h in ev e ry b o lt an d h ea h
Th e e n d re c ro pp es , and th e yo u nge so nne
Ha h in th e R am h is h al e co u rse y ro nn e
t
t
t
t
f
.
E ve n if clothed in mod ern E ngli sh such a d escription
would be unintelligible to a large proportion of the stu
d ents o f to day and would need some such tran slation as
—
,
follow ing
When the west w ind of S pring w ith its sweet breath
hath inspired or given n e w life in every field and heath
to th e tend er crops and the young su n (young because it
had got only half way through the sign Aries t he R am
which marked the beginning of the n ew year in Chaucer s
day ) hath run h alf h is course through the S ign the R am
Obliq u ity of th e E cliptic
The orbi t of the earth is
I f it were the ecliptic
n ot at right angles to t h e axi s
would coincid e with the c elestial equator The plane Of
th e ecliptic and t he plane of th e c elestial e quator form an
*
This is called the Obliquity of t he
angle of nearly
We sometimes speak of this as the inclination Of
ecliptic
the earth s axi s from a perpendicular to the plane of its
orbit
°
S inc e t he plane Of the ecliptic form s an a ngle of 2 35 with
the pla ne of t he e quator th e su n in its apparent a nnual
course around in t he ecliptic crosses the c elestial e quator
th e
.
,
,
,
’
”
.
.
,
.
.
.
’
.
,
Th e
in g
e xac
t
am o u n
t
tab le is tak en fro m th e Nau t
1903
1 904
1905
23
°
23
°
°
23
'
27
’
27
’
27
tly fro m
f
Th e o llo w
year to ye ar
’
ic al Alm an ac , Ne wc o m b s Calc u la io ns
v a ries s ligh
1906
1907
1908
.
23
°
23
°
23
°
’
27
’
27
’
27
t
VAR Y I NG S P E E D OF THE E AR TH
19
twic e each year and at one season gets 235 north of it
°
an d at t he oppo site se ason 235 south of it
The su n thus
never gets nearer the pole of the celest ial sphere than
On March 2 1 and S eptember 23 the sun is on the c eles
tial equator On June 2 1
and De cember 22 the su n
°
is 235 from the c el estial
equ ator
E arth s Orbit
We have
learned that the earth s orbit
is an e llipse and the su n is
at a focus Of it While the
ecc entricity is not g reat and
when redu ced in scal e the
orbit does not d ifier materi
F ig 39
ally from a circle the diff er
enc e is suf ficient to make an appreciable dif ferenc e in th e
rate of the earth s motion in diff erent parts Of its orbit
Figure 113 p 285 represent s the orbit of th e earth greatly
e xaggerating t h e elliptici ty
The point in th e orbit nearest
th e su n is called perihelion (from peri around or near and
Thi s po int is about 91 5millio n miles from
helio s the su n )
the su n and th e earth re aches it about Dec ember 31st
Th e point in the earth s orbit farthest fro m the su n is
called aphelion (from a away from and helios su n ) I ts
di stan c e is about 94 5 million miles and the ea rth reache s
it about July l st
Varyin g S peed of th e E arth
According to t he law of
r
i
s
n
s
t
ravitation
h
a
th
mov
e
s
fa
t
e
r
in
orbit
wh
n
ar
e
e
e
t
e
g
perihelion and S lo wer when n ear aphelio n I n Dec e mber
and
an d January th e earth moves fas test in its orbit
during that period the su n moves f as test in the eclipti c
an d falls farther wh ind th e stars in the ir rotation in the
°
,
,
.
.
.
’
.
’
,
.
,
.
,
’
.
,
.
,
,
.
,
,
.
,
,
.
’
,
,
,
.
,
.
.
,
,
.
,
THE E ARTH S RE VOLUTI ON
120
’
l ial sphere S olar days are thus longer then t han
they are in mid su m m er when the ear th moves m ore S lowly
in its orbit an d more nearly keeps up with the stars
I magine the su n and a star are rising together January
After o ne exact rotatio n of the earth a sid erea l day
l st
th e star w ill be rising again but S inc e the earth has moved
rapidly in its course around the su n the sun is so m ewhat
fart her behi nd the star t ha n it would be in su m mer whe n
At star
th e earth moved more S low ly around th e su n
rise January 3d the su n is behind still farther and in
the course of a f e w weeks the su n will be several minutes
behind the point where it would be if the earth s orbital
motion were uniform The su n is then said to be S low of
I n July the su n cree ps back less rapidly
th e average su n
in the ecliptic and thus a solar day is more nearly the
same l ength as a sid ereal day and henc e short er than the
av erage
Another factor modifies the foregoing statements The
daily courses Of the stars sw in ging aroun d with the celes
t ial sphere are parallel and are at right angles to th e axis
The su n in its an nual
s di agonally
path
cr
p
e
e
26
a
ro
th
cour
ss
c
eir
ses
25
Wh en farthest fro m the
24
celestral e quator I n June
o
23
and in December the
°
22
sun s movem ent in the
21
ecliptic is nearly parallel
to the courses of the
i
4
F
i
t
stars
0
a
s
( g
)
g et s nearer th e c el estial equator in March and in S e p
tember th e course is more Oblique Henc e in the latter
i
n
e
e
h
c
t
e
s
u
e
of
J
n
of
mb
r
r
p
ng
back
in
D
e
e
c
n
d
r
e
u
a
a
t
p
ce est
.
.
,
.
,
,
,
.
,
,
’
.
.
,
,
.
.
.
o
.
0
,
,
’
.
,
.
,
,
,
E E AR TH S R E V OLUTI O N
TH
122
’
xt evening The Gree k dramatist E uripides (480 407
in his traged y R hesus makes the Chorus say :
ne
-
.
”
,
is th e gu ard ? Wh o tak es m y tu rn ? The firs t s igns
are s e tting , an d the se ve n Ple iad es are in th e sk y, an d th e E agle
h
b
r
illi
a
n
c
o
t
e
m
i
w
h
h
A
w
n
t
s
t
h
k
a
s
a
k
!
S
ee
e
lid
e
d
r
ou
t
e
e
y
g
y
g
y
y
o f the m oo n ? Morn , m o m ,ind eed is app roac hi ng, and hi t he r is o ne
o f the fo re warning s tars
Whose
.
.
No te
f
care u lly
these p ro positio ns
th s o rbit is an e llipse
Th e e arth s o rbital dire c tio n is the sam e as the di re c tio n o f its
axial m o tio n
The rat e of th e earth s ro tatio n is u ni fo rm he n ce s ide real days
are o f e q u al le n gt h
Th e o rb it o f the earth is in nearly th e same plane as that o f the
eq u at o r
Th e e arth s re volu tio n aro u n d th e s u n m ak es the s u n see m to
falling
cree p b ac k w ard am o n g th e s t ars f ro m w es t to e as t
The s tars see m to s w in g
behin d t h em abo u t a d egree a d ay
aro u n d th e eart h d aily gain in g abo u t fo u r m in u te s u po n the
Th e
’
ear
.
’
.
’
,
.
.
’
.
,
,
.
,
su n
Th e
.
t
of
ra e
th e
s u n s app are n
t
ra e
of
Th e
e ar
t
t
o rb i al
Of
’
ear
,
,
the
t
t he
.
th s o rb ital m o tio n v aries be ing fas tes t
n e are st th e s u n o r in p e rih elio n an d s lo w es t
th e
th is
farth est fro m
th e
m o tio n de te rm ines th e rate
ann u al b ac k w ard m o tio n a m o n g th e s tars
ear
’
Th e
th s
’
w he n
w he n
s u n o r in ap h el io n .
t
su n s app are n
t
t
an n u al
t
t
m o io n , b ack w ard or e as w ard am o ng
the s ars , is gre a e r w h e n in o r n ear pe rih elio n ( De ce m be r 3 1 )
h an at an y o h e r im e
’
t
t
.
'
Th e len gt h o f so lar ( l ays v aries , ave raging 24 h o u rs in le ngt h
The re are tw o reaso ns f o r this v ariat io n
’
B e cau se th e e arth s o rb ital m o tio n is n o t u n ifo rm , it be in g fas te r
a
w h e n n e are r th e su n , an d s lo w e r w h en fart he r fro m it
b B e c au se w h en n ear th e eq u ino xes th e appare n t ann u al m o tio n
o f t h e s u n in the celes tial sph er
e is mo re d iago nal t h an w h e n
near th e t ropics
9
.
.
.
.
.
.
.
S UN FAS T OR S UN SLOW
123
10 B ecause o f th ese two se ts o f cau ses , so lar days are more th an 24
ho u rs in length fro m D e cem be r 2 5 to Ap ril 15 an d fro m J u n e
1 5 to Se p tem be r 1 , an d less th an 24 h o u rs in length fro m Ap ril
1 5 to J un e 1 5 and fro m Sep tem ber 1 to D ecember 2 5
.
.
E Q UATI ON
OF
TI M E
The
relation of the apparent
so lar time to me an solar time is called t he eq u ation of
time As just sho wn the apparent east ward motion of
the su n in the ecliptic is faster t han the averag e twic e a
year and slower than the averag e twice a year A ficti
tious su n is imagined to move at a u niform rate eastward
in the c elestial e quator starting with the appare nt su n at
the vernal e q uin ox (see E quinox in Glossary ) and com
l
e
i
n
t
s
h
e
e
s
t
i
annual
cou
around
c
l
s
tial
s
ph
e
r
in
r
e
t
e
e
g
p
t he same time in whi ch th e su n apparently makes its cir
cuit Of the ecliptic Whi le e xce pting four times a year
the appare nt su n is fast or S low as compared w ith t h is
fictitious su n which indicates mean sola r time the ir d iff er
e nc e at any mome nt
or the eq uation Of time may be
ac curate ly calculate d
The eq uation of time is indicated in variou s ways
The
usual method is to indicate the time by w hich the appar
e n t su n is fas t e r than t he average by a minus S ign and the
time by whi ch it is S lo wer than the average by a plus S ign
The apparent time and the eq uation of time thus in dicated
when combined will give the mean time Thus if the sun
indicates noon (apparent time ) and we know the equation
to be
we know it is 1 1 h 53 m A M
7 In (su n fast 7
by mean solar time
Any almanac shows th e e quation of time for any day of
the year
I t is indicate d in a variety Of ways
a
I n the World Al manac it is give n und er the title
S u n Fast
or
S u n Sl ow
.
.
,
.
,
,
.
,
,
'
,
,
,
.
.
,
.
,
,
.
,
,
.
,
.
.
.
.
.
.
,
.
.
THE E AR TH S R E VOL UTI ON
124
’
on Meridian
The local mea n solar time of the
sun s cross ing a meridian is give n to the nearest second
Thus Jan 1 1908 it is given as 12 h 3 m 16 S
We know
from this t hat the apparent su n is 3 m 16 S S lo w Of the
average on that dat e
b I n t he Old Farmer s Almanac t he e quation Of time is
given in a column head ed S u n Fast or S u n S low
c
I n some plac es the equation of time is indicat ed by
clock ahead of su n and clock behind su n
th e word s
Of course the stud ent know s from this that if the clock is
ahead of the su n the su n is S lower than t he average and
conversely if the clock is behind the su n the latter must
be faster than the average
d Most al man ac s give times of sunrise and of sunset
No w half way bet ween sun rise and sunset it is apparent
noon S uppose the su n ri ses at
AM
O clock
and
Half way bet ween those times
sets at 4 : 43 o clock P M
O clock
is
the time when the su n is on the
meridian and thus the su n is 35 minutes S low (Jan 1 at
New York )
The Nau tic al Almanac h as the most d etailed and
e
accurate date obtainable Table I I for each month gives
in the column E quation of Time the number of min
utes and second s to be add ed to or subtracted f ro m 12
The
O clock noon at Gree n w ich for th e apparent s u n ti m e
adjoining column gives the diff erenc e for o ne hour to be
added when the su n is gaining or subtracted when the su n
is losing for plac es east Of Green w ich and vi ce versa for
plac es west
Whether or not the stud ent has acc ess to a copy of th e
Sun
.
’
.
.
,
.
,
.
.
.
.
.
’
.
”
”
.
,
.
”
,
.
,
,
,
,
,
,
.
.
.
’
,
.
.
.
,
’
,
.
.
’
,
.
,
,
.
.
.
’
.
,
,
,
.
by th e P ro fesso r o f
Math e m atics, Uni ted S tates Navy , Was h in gton , D C I t is so ld by
th e B u reau o f E q u ip m en t at ac tu al c os t o f p u b lic atio n , on e do l lar
P rep are d
ann u al ly
th ree
r
s
e
a
y
in
ad v an ce ,
.
.
.
1 26
THE E AR TH S R E VOLUTI ON
’
ard time ; five hours aft er Greenwich noon it is Obvious
S or 6 S S lo we r t ha n it was at
that the su n is 5 x
The e quation of time at Ne w
Greenwich mean noon
York would then be 3 m
S
6 S or 3 m
S
A
h
m
a
n
a
l
e
m
graphically
indicat
es
e
approx
i
mat
h
e
t
e
T
f
e quation of ti m e for any day Of t he year and also indicate s
the d eclination of the su n (or its di stanc e from t he c el estial
S in ce our year ha s 36 51 days the equation of
e quator )
time for a given dat e of o ne year w ill not be quit e the
sa m e as t ha t of t he same dat e in a succ eeding ye ar
That
for 1910 will be approximately o ne fourth of a day or S ix
hours lat er in each day than for 1909 ; that is the table
for Greenwich in 1910 will be very nearly correct for Cen
tral Unit ed Stat es in 1909 S inc e for the ordi n ary pur
poses Of the stud ent using thi s book an error Of a f ew
t h e anal e mma w ill an swer for
se cond s is inappreciable
most Of h is calculat ions
The vertical lin es of th e anale mma re present t he n u m
ber Of minut es the appare nt su n is S lo w or fast as com
h
n
e
ar
d
w
ith
t
e
m
an
S
u
r
e
xampl
e
h
e
dot
r
e
F
o
t
re
e
p
p
senting Fe bruary 2 5 is a littl e over half way bet wee n t he
lines r e presenting su n S lo w 12 m and 14 m The su n is then
I t w ill be Observed that April 15
S lo w about 13 m 18 S
June 15 S e pt ember 1 and Dece mber 2 5 are on t he c entral
line The equatio n Of time is t hen z ero and the su n may
P ersons living in t he Unit ed
on time
be said to be
S tat es on th e 90th meridian w ill see t h e S hadow d u e north
at 12 O clock on those days ; if west Of a standard time
meridian o n e w ill note the north S hado w w hen it is past
12 O clock four minutes for every d egree ; and if e ast Of
a standard time meridian be fore 12 O c lock four mi nutes
for each d egre e S inc e t h e anale mma S ho w s ho w fast or
slo w the su n is e ach day it is obvious that kno wing o ne S
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128
THE E AR TH S R E VOLUTI ON
’
e
e
e
e
h
e
s
n
u
lon
i
ud
can
h
i
s
w
atch
by
t
by
r
f
r
nc
n
se
t
e
e
t
o
g
to this diag ram or having cor rect clock time on e c an
asc ertain his longitude
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US E S
Yo u r
To Ascertain
ANALE MMA
O F THE
Lo ngitu d e
.
To do this
Y o u must
your w atch
also have a
must S how correct standard time
true north south line
1 Care fully Observe the time when t he S hadow is north
Asc ertain from the analemma t he number Of minutes and
second s the su n is fast or S low
2 I f fast add that amount to the time by your watch ;
if S low subtract This gives you r mean local time
3 Divide the minutes and se cond s past or before twe lve
by four This gives you th e number of d egrees and
minutes you are from th e standard time meridian I f
the correct ed time is be fore twelve you are c ast of it ; if
after you are west of it
4 S ubtract (or add ) the number of d egrees you are
east (or west ) of t h e standard ti me m eridia n and this is
your longitude
1 Your
For example say the dat e is October 5th
watch says 12 h 10m 30S P M when t he S hadow is north
2 The
The an alemma S hows the su n to be 11 m 30S fast
sun be i ng fast you add these and get
O clock P M
3 D ivid ing
This is the mean local time of your plac e
This is
the minut es past twelve by four you get 5 m 30S
th e number Of d egrees and minut es you are west from the
meridian I f you live in the Central standard
st and
°
ti m e belt of the United States your longitud e is 90 plus
°
°
I f you are in the E ast ern time belt
or 95
5
°
°
°
I f you are in S pain it is 0 plus
it is 75 plus 5
°
and so on
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THE E AR TH S R E VOLUTI ON
130
’
To
do t his you must
kno w your longitude and have correct time
St eps 1 2 and 3 are exactly as in t he foregoing explana
tion how to set y u r watch by t he sun At the time you
Obtain in ste p 3 you know t he shadow is north ; then draw
th e line of th e shad ow or if out of doors drive st akes or
otherwise indicat e the line Of the shadow
To Ascertai n You r Latitu de
This use of t he analemma
is reserved for lat er discussion
Civil an d Astro n om ical D ays
The mean solar day of
t wenty four hours reckoned from mid n ight is called a civil
day and among all Christian nations has t he sanction of
S inc e astronomers work at night they
law and u sage
Thus th e civil forenoon is
rec kon a day from noon
dated a day ahead of the as trono mical day t he aft ernoon
being the las t half of t he civil day but th e beginning of
B e fore the invention of clocks and
the astrono mical day
wat ches the sundial was the common standard for t h e
time during each day and this as we have seen is a con
When clocks were invented it was
s tantly varying one
found impossible to have the m S O adj usted as to gain or
Until 1815 a civil day in Franc e was a
low with the su n
day according to the actual position of the su n and hence
was a very un c ertain aff air
To Strik e
a
North Sou th Line
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A FE W FACT8 : DO Y OU UN D E RS TAN D THEM
A day of twenty four hours
commonl y use the
term is not one rotation of the earth A solar day is a
little more than one complete rota tion and averages
Thi s is a civil or
e xactly twenty four hours in l ength
legal day
2 A sid ereal day is t he time of on e rotation of th e
earth on its axis
1
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.
as
we
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.
131
CI VI L AND ASTR ONOMI CAL D AYS
rotations of t he earth (sidereal
in one year of 365 days (solar days )
4 A sundial record s appare nt or actual su n time
is t he same as mean su n ti me only four times a year
5 A c loc k record s mean su n time and thus correspo nd s
to su ndial time only four times a year
6 I n man y cities using standard time t he S had ow of the
sun is never in a north south line when t he clock strikes
°
This is true of all citi es more than 4 east or
twelve
west of t h e meridian on which their standard time is based
°
7 An y city within 4 of its standard time meridian will
have north south shad ow lines at twelve O cloc k no more
than four times a year at th e most S trictly speaking
practically n o city ever has a shad ow exact ly n orth so uth
at twelve o c lock
3
.
There
are
366
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CHAPTER VI I
TI M E AN D THE CAL EN D AR
I N th e
arly days of mankind it is not probable that
there was any conc ern at all about dates or season s or
years Herodotu s is called the father of history and his
history does not contain a S ingle date S ubstantially
th e sam e may be said of Thucydid es who wrote only a
little later somewhat over 400 B C I f Geography and
Chronology are th e two eyes of history then some histories
are blind of the on e eye and can see but little out of th e
other
Tropical Year
S idereal Year
As there are two kind s
of days solar and sidereal there are two kind s of years
so lar or tropical years and sid ereal years but for v ery
diff erent reasons The sid ereal year is the time elapsing
between the passage of th e eart h s c ent er over a given
point in it s orbit unt il it crosses it again For reasons
not properly discussed here (see P rec ession of the E qui
noxes p
th e point in th e orbit where th e e arth is
w hen th e vertical ray is on th e equator S hift s S lightly
west ward S O that we reach th e point of t he vernal e quinox
a second time a f ew minutes be fore a sid ereal year has
The time elapsing from th e sun s crossing of th e
elap sed
c elestial equator in the S pring until the cro ssing the next
S pring is a tropic al ye ar and is what we me an when we
a year 1 S inc e it is the tropical year that we
say
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R W Farlan d in P o pu lar Astro nomy f o r Fe b ruary , 1895
1 A third kin d o f yea r is c o ns ide red in as t ro no m y, th e an o m alis tic
i
i
b
h
i
n
c
cu
e
d
t
h
a
r
t
r
l
i
n
r
o
m
li
t
t
v
f
h
m
o
e
e
a
r
i
h
n
r
t
e
e
e
e
e
o
e
t
o
a
,
p
y
g
p
y
i
1
l
h
h
s
li
n agai n
I
e
s
3
5
d
n
t
h
6
6
e
r
i
h
o
t
3
m
s
T
e
l
u
n
a
r
ear,
e
g
p
y
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132
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134
TI ME AND THE CALE ND AR
xact length of the solar year in t he possession of the
ancient E gyptians see ms to have been little regard ed
Early R oman Cal endar
S inc e our calendar is t h e same
as that w orked out by th e R om an s a brie f S ketch of the ir
syst e m may be he lpful
The anci ent R omans seem to
have had ten months th e first be ing March We can see
that this was t he case from t he fact that S e pte mber means
se venth ; October e ighth ; Novembe r ninth ; and Dece m
ber t enth
I t was possibly during th e reign of Numa
that two months were add ed Janu ary and February
There are about 295 days in a lunar month or from on e
n ew moon to t h e n e xt so to have the ir months conform
to the moon s they were given 29 and 30 days alter
n ately beginning with Januar
e
hi
s
gav
e
th
e
m
tw
e
lv
T
y
lunar months in a year of 354 days I t was thought
unlucky to have t he number even S O a day was ad ded for
luck
This year having but 355 days was over t en days too
S hort S O festival s that cam e in t h e summ e r season would
Appear t en days earli er e ach year until those d edicat ed
to B acchus t h e god of wine came when th e grapes were
still green and tho se Of Ceres t h e godd ess of t h e harvest
before t he head s of the wheat had appeared To correct
thi s an ext ra month was add ed call ed Merc edonius every
S inc e t h e length of this month was not fixed
se cond year
by law but was d etermi n ed by t h e pontiff s it gave rise
to seriou s corruption and fraud int erferin g with the collec
tion of d ebts by t h e dropping out Of c ertain expected
dates len gthening t h e t erm s Of Offic e of favorites etc
Th e Ju l ian an d th e Au gu stan Cal en dars
I n the year
4 6 B C Juliu s Caesar aid ed by th e E gyptian astronomer
He d ecreed that begin
S o sigen es refor m ed t h e calendar
ning with January the months S hould have alt ernat ely 31
e
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135
THE GRE GOR I AN CALE ND AR
days save Fe bruary to w hi ch was assigned 29
days and every fourth year an additional day This
mad e a year of exactly 365} days S ince the true year has
se c
and th e Jul ian year
365 days 5 hours 48 min
had 36 5 days 6 hours it was 1 1
J UL I AN AUG U S TAN
min 14 4 9 sec too long
l
5
D uring th e reign of Augu st us
23 35
al) : 293
M”
another day w as taken from Fe b
36
ru ary and add ed to Augu st in ord er
31
31
that
that
month
th e name of w hich
2?
3?
30
31
had bee n changed from S e xtilis to
ugu
A
st in h is honor might ha ve as
g},
3?
many days in it as the month
if)
3? uintilis whose name had been
Q
changed to Jul y in honor of Julius Caesar To prevent the
three months July August and S e ptember from having 31
days each such an arrange ment be ing considered un lucky
Augustus ord e red that o n e day be taken from S e pte mber
and ad d ed to October o ne from Nove mber and add ed to
Thus we find t he easy plan of rememberin g
De c e mber
the months having 3 1 days every other o n e w as d is
arranged and we m u st n o w count our knuckles or learn :
Th irt y d ays h ath S ep te m be Ap ri l J u n e an d No v m be
All th e re s t h ave th i ty o n e av e t h e ec o n d o n e alo n e
Whic h h as fo u an d tw e n ty f u till leap yea r giv e it o n e d ay m o re
and
30
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e
s
s
o
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r,
s
.
Th e Grego rian Cal en dar
Thi s Julian cale ndar as it
is called w as adopted by E uro pe an countries just as they
.
,
,
adopted other R oman customs I ts length was
days w hereas t he true length of the year is
days Wh ile t he error was only 0078 of a day in the
cou rse Of c enturies thi s addition to the true year began
to amount to days B y 1582 t he diff erenc e had amounted
to abo ut 13 days so that t he time of the spring e quinox
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TI ME AND TH E CALE ND AR
1 36
w hen th e
crosses the celest ial eq uator occurred the
11th of March
I n that year P ope Gregory XI I I reformed
th e calendar S O that th e March equinox might occur on
March 2 l st th e same date as it did in t he year 325 A D
when t he great Council Of Nic aea w as held w hich finally
decided t he method Of re ckoning E ast er One thousa nd
two hundred and fifty seven years had elapsed e ach being
1 1 min 14 sec too long
The error of 10 days was
corrected by having the date follo w ing October 4th Of that
year record ed as October 15 TO prevent a recurrenc e of
t he e rror t h e P ope furt her d ecreed that t hereafter t he
c enturial years not divisible by 4 00 S hould not be coun ted
Thus t he ye ars 16 00 2000 24 00 etc are
as l eap years
leap years but t he years 1700 1900 2 100 etc are not
leap years Thi s calculation reduc es the error to a very
low point as according to the Gregorian calendar nearly
4 000 years mu st elapse be fore t he error amount s to a
single day
The Gregorian calendar was soon adopt ed in all R oman
Catholic countries Franc e recording t he dat e aft er Dec e m
I t w as adopted by P oland in
ber 9th as D ec e mbe r 20th
1 786 an d by Hungary in 1 787
P rot estant Germany
Denmark and Holland adopt ed it in 1 700 and P rotestant
Th e Greek Cat h olic countries have
S witz erland in 1 701
not yet adopted thi s cal endar and are now thirteen days
be hind our d at es No n Chri stian countries have calendars
of their o wn
I n E ngland and h er colonies the change to t he Gre
gorian syst em was eff ect ed in 1752 by having t he date
follo w in g S e ptember 2d read S ept ember 14 The change
was viol ently oppo sed by some wh o see med to think that
c h anging the numbe r assigned to a particular day modi
fied time it self and the m em bers of the Government are
su n
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TI ME AND TH E CALE ND AR
138
historian s often write s uch dat es October
12
-
th e upper dat e
—
21
refe rring to old style and the lo wer to n ew style
A historian u sually follo ws the dates in the calendar used
by h is country at the time of the event I f however t he
e vent re f ers to two nation s having diff erent calendars both
dates are given Thus throughou t Macaulay s History
o n e sees such date s as the following : Avaux
Of E nglan d
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A
ii 5
l
—
2
L
—
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g
Vol
(
1689
.
.
III
.
A few
)
dates in American
his
tory prior to S e ptember 1 752 have been changed to agree
with the ne w style Thus Washington was born Feb 11
but we al ways write it Feb 22 1 732 The
1 731 O S
reason why all such dates are not tran slate d into n ew
styl e is be cau se great confu s ion w ould re
sult and besid es
Thus the principal S hip
som e incong ruiti es would obtain
of Columbu s was wrec ked D ec 25 1492 and S ir I saac
Newton w as born Dec 25 1 64 2 and S inc e in each c ase
this was Christmas it w ould hardly do to record them as
Christmas Jan 3 1493 in t h e form er in stance or as
Christ m as Jan 4 1643 in th e latt er case as we should
have to do to write the m in n ew style
Th e B egin n in g o f th e Year
With t he ancient R om ans
the year had commenc ed w ith the March e quinox as
w e notic e in the name s of th e last months S e pt e mber
October November Dec e mber meaning 7th 8th 9th
l oth w hich could only have tho se names by co u n tin g
back to March as th e first month B y t he time of Julius
Caesar t h e Dec e mber sol stice was commonly regard ed as
th e beginning of th e year and h e confirmed t he change
making h is n ew year begin January first The later
Teuton ic n ation s for a long time continued counting the
beginning Of th e year from March 25t h I n 1563 by an
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139
OLD STYLE I S S TI LL US E D I N E NGLAND
dict of Charles I X Franc e changed the time of the begin
ning of the year to January first I n 1600 S cotland mad e
the same change and England did t he same in 1 752 w hen
t he Gregorian syste m was adopt ed there
Dates between
t he first of January and t he twenty fifth of March from
1600 to 1752 are in o ne year in S cotland and another year
in England I n Macaulay s History of E ngland (Vol
“
III p
Act P ar]
he gives t he foll ow ing referenc e :
S cot Mar 19 1689
The dat e be ing between Jan
uary l st and March 25t h in the interval between 1600 and
1 752 it w as record ed as t he year 1689 in E ngland and a
year later or 1690 in S cotland
S cotland datin g th e n ew
year from January 1st E ngland from March 25th This
explains also why Was hin gton s birthday was in 1 731 0S
and 1 732 N S sinc e E nglish coloni es used th e same
syst e m of dating as t he mother country
Old S tyl e is still u sed in E n glan d s Treasu ry D epart
“
m en t
The old style is still retain ed in the accounts
of Her Maj esty s Treasury Thi s is why the Christmas
divid ends are not consid ered d u e until Twelfth Day and
t he mid summer divid e nd s not till t he 5th of July and in
just the same way it is not u n til th e 5th of April that
There is another piec e
Lad y D ay is suppo sed to arrive
of antiquity in the public accounts I n the old times the
year was held to begin on t he 25th of March and this
change is also still observed in th e computations over
whi ch the Chanc ellor of t he E xchequer presid es The
consequence is that the first day of t he financial y ear is
the 5th of April being old Lady D ay and with that day
the reckonin gs of our annual budgets begin and end
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London
*
Ti mes,
Feb 16 , 186 1
.
.
Un de r th e d ate o f S ep te m be r 10 1906 , th e sam e au t h o rity
th e fac ts abo v e q u o te d o b tai n in E n gl and at th e p rese n t t im e
,
t h at
.
S ays
140
TI ME AND THE CALEND AR
Greek
Cath oli c
Catholic
Cou n tries Use Ol d S tyl e
Th e Gree k
R ussia , some of t he B alkan state s and
.
countries
Greec e still e mploy t he old Julian calendar whi ch no w
w ith their counting 1900 as a l eap year and our not
counting it so makes their dates 13 days beh ind ours
D ates in these countries record ed by P rotestants or R oman
Catholic s or writt en for general circulation are commonly
recorded in both styles by placing t he Gregorian date
und er the Julian date For example the date we cele
brat e as our national holiday would be written by an
June 2 1
American in R ussia as
The day we comme m
July 4
,
,
,
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,
,
,
.
orate
as
t he
ann iversary of the birth of Christ
day they commemorate
D ec
25
.
,
1906
,
D ec
.
25
hould be
It
,
12
s
Jan 7 1907
remembered t hat if t he dat e is before 1900 the diff er
S te ps are be ing
enc e w ill be less than thirt een days
taken in R ussia looking to an early rev ision of the
calendar
Mo h amm edan and Jew ish Cal endars The old syst em
employed be fore t h e tim e of t he Cae sars is still used by
The year of the forme r
the Mohamm edan s and the Jews
is t he lunar y ear of 354 311} day s and be ing about 03 of
a year too S ho rt to correspond w ith t he solar year t he
sam e dat e pa sses through all season s of t h e year in th e
course of 33 years Their calendar dates from the year
of the Hegira or the fl ight of Mohammed which occurred
I f their year was a full solar year the ir
July 622 A D
dat e corresponding to 1900 w ould be 622 years less than
that number or 12 78 but being short er in length there are
more of them and they writ e t he date 1318 that year
begin nin g w ith w hat to u s was May 1 That is to say
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TI ME AND THE CALE ND AR
142
°
paces of 30 e ach giving u s the plan of t welve months
in th e year Their divisions of the day led to our 24
hours each havin g 60 minutes with 60 se cond s each
They used th e w eek of seVen d ays o ne for each of th e
heavenly bodies that were seen to move in the zodiac
This origin is suggested in the names of the days of th e
week
DAYS OF TH E WE E K
s
,
.
.
,
,
,
.
.
R o m an
1
.
S u n d ay
D i es S o l is
D i m an c h e
S u n n a n —d ao g
S o n n tag
M o n a n d a og
M o n tag
M o n d ay
M oo n
D i es L u n a
Lu n di
3 Tu e sd ay
M ars
D i es M ar t i s
M a rd i
2
.
.
4
.
W ed n es d a y M e rc u ry
5 Th u rsday
.
6 F ri day
.
7 S a t u rd ay
.
J
D i es
u p i te r
-
7
9 363312
11
41
M e rc u rii M e rc redi
D i e s J o v is
J e nd i
em r)
Tl
fif g
g fgg
o
D i e s V e n e ri s V e n d redi
V en u s
S a t u rn
D i e s S at u rn i
S am e d i
F re i tag
32 33123;
111
S ae t e r d a og
Com pl ex Cal endar Co n ditio n s in Tu rk ey
-
11
1
it is in
Turkey that th e time probl e m be comes really complicated
very irritating to him w ho takes it seriously very funny
to him who enjoys a joke To begin with there are four
years in Turkey
a Mohammedan civil year a Moham
medan religiou s year a Greek or E ast ern year and a E uro
pean or Western year Then in the year the re are both
lun ar months d epending on the chan ges of th e moon and
months w hich like ours are c ertain artificial propo rtions
Then the varieties of language in
of the solar year
B ut
.
,
,
.
,
,
,
,
.
,
,
,
.
COMP LE X CALE ND AR COND I TI ONS I N TUR KE Y
Tu rkey
1 43
till further complicate the c alendars in custom
I brought away with me a page fro m the diary
m y use
which stood on m y friend s library table an d which is
c u stomarily sold in Turkish shops to serve th e purpo se of
a calendar ; and I got from my fri end t he m eaning of th e
hieroglyphi c s which I record here as well as I can remem
Numbering the
ber them
This page represent s one day
compart ments in it from left to right it read s as follows :
s
.
’
,
,
.
.
,
1
.
2
.
March ,
March ,
1 3 1 8 ( Civil Y ear )
1 3 20 ( R eligio us
.
Y ear)
.
Y ear)
4 Wed nes d ay
5 Thirty d ays
.
.
.
.
6
.
27
li
R
e
(
gio us
a
a
rc
h
i
M
il
Y
e
r)
v
C
:
(
.
u
s
l
i
i
Y
h
R
e
o
e
a
r
M
a
r
c
:
)
(
g
8 Marc h Wed nes d ay ( Ar
7
.
.
.
,
9 April ,Wedn esd ay ( Fnen c h )
10 March ,Wed nesd ay (Greek )
.
.
E c clesias tical D ay ( Fnen ch
R C Ch u rc h )
1l
.
s ian
13
.
.
.
)
.
Mo n th D ay
Month D ay
Mon th D ay
w
H
b
r
e
e
)
(
.
l
d
t
O
l
S
e
(
y )
15
( New S tyle )
16 E ccl es ias tical D ay ( Ar
14
.
.
.
.
.
t
17 E c cl es ias ical D ay ( Gree k )
18 Midd ay, 5 : 35, 1 902 ; Mid
.
.
d ay, 5: 2 1
mg
.
I am not quite
t he las t se ction ,
.
44
clear in my min d now as to the meaning
of
but I think it is that n oon according to
European reckon ing is twenty o ne m inutes past five accord
-
,
TI ME AND THE CAL E ND AR
144
ing to Turkish reckoning For there is in Turkey ad ded
to the complication of year month and day a further
complication as to hours The Turks reckon not from an
artificial or conventional hour but from sunrise and their
reckonin g runs for twenty four hours Thus when the
Turkish time The
su n rises at 6 : 30 our noon w ill be
Turkish hours there fore change every day The steam
ers on t he B o sphoru s run accordin g to Turki s h time and
o ne must fi rst look in t he time table to see the hour and
then calculate from sunrise of the day what time by h is
My friend s in Turkey
E uropean clock the boat will start
h ad apparently gotten used to thi s complicated calendar
with its variable ye ars and months and the constantly
changing hours and took it as a matter of course
Modern Jewish Cal endar The mod ern Jewish c alendar
e mploys also a lunar year but h as alt e rnat e ye ars length
ened by adding e xtra days to make up the diff erenc e
between such year and the solar year Thus o ne year
will have 354 days and another 22 or 23 days more
S ept 23 1900 according to our calendar was the begin
n ing of the ir y ear 566 1
Many remedies have bee n suggest ed for readjusting
our calendar so that th e sa m e date S hall always recur on
th e same day of the week
While it is interesting for the
stud ent to s peculate on the problem and d evise ways of
meeting th e difficulties non e can be suggest ed that does
not involve S O many changes from our present syste m that
it will be impo ssible for a long long time to overco me
social ine rtia sufficie ntly to accompli sh a reform
I f the stud ent becomes impatient with t he complexity
of the problem he may recall with profi t these words of
,
.
,
,
,
.
,
,
,
-
.
,
.
.
,
,
,
-
,
.
,
”
.
,
.
,
.
.
,
.
,
,
,
.
.
,
,
.
,
The I m p re ss ions o f
Ou tloo k , Fe b 28 , 1903
.
.
a
Carele ss Travele r, by Lyman Ab bo tt
.
Th e
CHAPTE R
V erti cal
an d
Slantin g R ays
of
VI I I
th e S u n
.
He would be
uno bservant ind eed who did not know from first hand
e xperienc e that the mo rning and e vening ray s of t h e su n
do not feel so warm as those of midday and if living out
sid e th e torrid zone that rays from the low wint er su n in
some way la ck the heating po wer of tho se from t he high
summ er su n
The reason for this di ff erenc e may not be
The vertical rays are not warmer than the
so apparent
slanting ones but t he more n early ve rtical th e su n the
more heat rays are interc epted by a given surface I f
you plac e a tub in the rain and tip it so that the rain falls
in slantingly it is obvious that less wat er will be caught
than if the tub stood at right angles to the course of the
raindrops B u t before we take up in detail the eff ects of
the shifting rays of th e su n let u s care fully e xamine the
conditions an d causes of th e S hi ftin g
M otio ns of th e E arth
The direc tion an d rate of the
earth s rotation are asc e rtain ed f rom the direction and
rat e of th e apparent rotation of th e c elestial sphere The
direc tion and rate of the earth s revolu tion are asc ertained
from the apparent revolution of the su n among the stars
of th e c el est ial sphere Just as any change in the ro tation
of the earth would produc e a corresponding change in th e
apparent rotation of the c el estial sphere so any change
in the revolution of t he earth w ould produc e a correspond
ing change in the apparen t revolution of the su n
Were t he su n to pass am ong the st ars at right angles to
-
,
,
,
,
,
.
.
,
,
.
,
.
,
.
.
’
.
’
.
,
.
14 6
E QUI NOXE S
the
147
c elestial equator passing through the c elestial poles
we S hould know that t he earth went a round th e sun in a
path whose plane was perpendicular to the plane of the
I n such an
equator and was in the plane of the axis
event th e su n at som e time during the year would S hine
vertically on each point on the earth s surfac e S eas ons
would be nearly the same in o n e portion of the earth
The su n would sometimes cast a north
as in another
shad ow at any giv en plac e and sometim es a south shad o w
Were th e su n al ways in the c elestial equator the ecliptic
c oinciding with it we should k now that th e earth travel ed
around the su n at right angles to t he axis The ve rtical
ray of the su n would then al ways be overhead at noon on
Were
the equator and no change in season woul d occur
°
th e plane of the earth s orbit at an angle of 4 5 from the
e quator t he ecliptic would e xt end half way between th e
poles and the equator and the su n would at o n e time get
°
°
within 4 5 of the North star and S ix months later 4 5
from the S outh star The vertical ray on the earth wou ld
°
°
then travel from 4 5 south latitud e to 4 5 no rth latitude
°
and the torrid zone would be 90 wide
B u t we know that the vertical
Obliq u ity o f th e E clipti c
ray neve r get s farther north or south of the equator than
about
or nearer the poles than about
The
plane of the ecliptic or of the earth s orbit is then inclin ed
°
°
at an angle of 66 i to the axis or at an angle of 235 to
This obli quity of the ecliptic
th e plane of th e e quator
varies slightly from year to year as is shown on
pp 1 18 288
E q u in o xes
The su n c rosses the celestial equator t wic e
a year March 20 or 2 1 and S e pte m ber 22 or
varying
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,
The re as o n w h y th e date sh ifts lies in th e co nst ru c tio n o f o u r
Th e tim e
s
c ale n dar, w h ic h m ust fit a ye ar o f 36 5 days, 5 h 4 8 m
.
.
.
148
S E AS ONS
from year to year the exact date for any year be ing easily
found by referring to any al manac These dates are
called equinoxes (equinox ; (Pqu u s equal ; n ox night ) for
th e reason that t he days and night s are the n t welve
hours long every where on e arth March 2 1 is called
t he vernal (spring ) equinox and S epte mber 2 3 is called
for reasons obvious to those
the a utu m nal e quinox
wh o live in t he northern hem i sphere (see E quinox in
Glossary )
S ol stic es
About t h e time when t he su n reaches its most
i
distant point from t he c elest al e quator for several days it
see m s n e ith er to re c ed e from it nor to approach it
The
dates when t he su n is at these two point s are called the
sol stic es ( from sol su n ; and stare to stand )
June 21 is
th e summer solstic e and D ec e mber 22 is the wint er solstic e ;
vice versa for t h e south ern hem i sph ere
The same terms
are al so applied to th e t wo point s in t h e ecliptic farthest
from t he equator ; that is t he po sition of the su n on those
dates
At th e E q u ator
I magin e you are at t he
M arch 2 1
B ear in mind t he fact that th e No rth
e quator March 2 1
s
t
h
h
s
trictly
p
aking
north
pol
of
c
l
tial
e
e
e
t
e
e
s
star
e
(
sphere ) is on th e northern horizon th e S outh star on th e
and the c elestial equator extend s from
southe rn horizon
I t is sunrise of
d u e e ast through th e z enith to d u e west
The su n is seen on the east ern hori
th e vernal equinox
zon ; t he S hado w it casts is d u e west and re mains d ue west
until noon getting shorter an d S horter as the su n rises
higher
E aste rn
6 w as Ma rch 2 1 7 : 46 A M
o f t h e v e rn al e q u in o x in 190
tan da d t im e I n 1907 it o cc u red 36 5 d ays 5 h 48 m
or
s late
,
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,
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,
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,
,
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,
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,
r
s
at
1 : 35 P M
.
5 h 48 m
.
are
r
.
.
,
Ma rch
.
t ru e o f
.
.
,
r,
.
I n 1908 , b e ing le ap ye ar, it w ill oc c u r 36 6 d ays ,
s l a e r, o r at ab o u
7 : 24 P M , Ma rc h 20 Th e s am e ac s
so ls ice s ; h ey o c c u r J u n e 2 1 22 an d D ec em be r 22 23
.
th e
,
.
t
21
t
.
t
t
.
.
—
f t
.
—
.
150
S E AS ONS
xtend s at this time fro m pole to pole coincid es with a
meridian circle and bisect s each parallel Half of each
parallel be ing in the light and half in the dark during
o n e rotation eve ry point w ill be in t h e light half a day and
away from the su n the othe r half and day and night are
e qual e ve rywhere on t h e globe
After M arch 2 1 t he su n cree ps b ack in its orbit gradu
ally away from t he c elestial equator toward the North
star
At t he e quator the su n thu s rise s more and more
toward the north of the du e east point on the horizon
and at noon cast s a shado w to ward the south As the
su n get s farther from t h e c ele stial e quator t he south noon
shad ow len gthens
and the su n ri ses and sets farther
toward the north of e as t and west
On J u ne 2 1 the su n h as re ached the point in th e eclip
°
tic farthest from the c elestial equator about 235 north
The vertical ray on t he earth is at a corres ponding distanc e
from t he equator The su n is n ear the conste llation
Canc er and the paralle l marking t h e turning of the su n
from h is course to w ard the polestar is called the Tro pic
t
a
m
i
n
fr
m
a
r
k
ord
m
aning
of
anc
r
o
ee
w
C
e
O
r
e
u
G
(
g)
t errestrial parallel marking t he southward turn in g of the
v ertical ray is al so call ed t he Tropic of Canc er
At this
°
date t he circle of illumination extend s 235 beyond the
°
north pole and all of the parallels north of 66 5 from the
equ ator are e ntirely w ithin this circle of illumination and
have daylight during t he e ntire rot ation of the earth At
this time the circle of illumination c ut s unequally parallels
n orth of t h e e quator S O that more than half of th em are in
the lighted portion and henc e days are longer than nights
in the northern hemisphere
S outh of t he eq uator the
condition s are reversed The circle of illumination does
not extend so far south as the south pole but falls short
'
e
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,
AT THE E Q UATOR
151
°
Of
it
and consequently all parallels sou th of 66 5 are
entirely in t he dark portion of th e e arth and it is con
t in u al night
Other circl es south of th e eq uator are so
interse cted by the circle of illumination that less than
half of them are in the lighted sid e of t he earth and the
days are shorter than the night s I t is mid w inter there
Afuer J u ne 2 1 gradually th e su n creeps along in its
orbit aw ay from this northern po int in the celestial sphere
to w ard t he celestial equator The circle of illumination
ag ain draws to w ard th e poles the days are more n early
of the same len gth as the nights t he noon su n is m
ore
nearly overhe ad at the equator again until by S epte mber
23 t he autumnal eq uino x the su n is again on the c elest ial
eq uator and conditions are exactly as they were at t he
March e quinox
After S ep tember 2 3 the su n passin g to w ard the S outh
star from th e c elestial e quator ri ses to t he south of a d u e
e ast line on the e quator and at noon is to t he south of t he
zenith c as ting a north sh ad ow The circle of illumina
tion withdraws from the north pole l eaving it in darkness
and ext ends beyond the south pole spre ading there the
glad sunshine D ays grow shorter north of the equator less
than half of their parallels be ing in the lighted half and
south of th e eq uator th e days leng then and summer com es
On D ecem ber 2 2 t he su n h as re ached t h e most distant
point in t he ecliptic from the c elestial e quator to w ard the
°
°
S outh star 235 from t he c elestial e quator and 66 5 from
the S outh star th e ve rtical ray on the e arth be ing at co rre
spo n d in g distanc es from the e quator and th e south pol e
The su n is n o w ne ar the con stellation Caprico rn and every
where within t he tropic s the shadow is to ward the north ;
o n t he tropic of Capricorn th e su n is overhe ad at noon
and south of it the shad ow is to w ard the south Here
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152
S E AS ONS
the
vertical ray turn s to ward the equator again as th e su n
cree ps in the ecliptic toward the c elestial equator
Just as the tropic s are t he parallels which mark the
farthest limit of the vertical ray from th e equator the
polar circles are the parallel s marking the farthest extent
of the circle of illumination beyond the pol es and are the
same di stanc e from t he poles that the tropic s are fro m th e
e q uator
Th e W idth o f th e Z o n es is thus d eterm ined by the d is
tanc e t he vertical ray travel s on the earth and w ith the
moving of the vertical ray the shifting of the day circle
This di stanc e is in turn d et ermined by th e angle which
The
th e earth s orbit form s w ith t h e plane of th e equator
planes of t he equator and t he orbit forming an angle of
the vertical ray travel s that m any d egree s each side
°
of the e quator and t he torrid zone is 4 7 wid e The circle
°
of illumination never extend s more than 2 35 beyond each
°
pole and the frigid zones are thus 235 w ide The remain
ing or temperate zones bet ween the torrid and t he f rigid
°
zones must each be 4 3 wid e
I magine you are at th e north pole
At th e No rth P ol e
B ear in mind th e fact that t he North star is al ways almo st
e xactly overhead and t h e c el estial e quator al ways on the
horizon On March 2 1 the su n is on the c elest ial e qua
*
The su n n o w swings
tor and henc e on the horizon
around the horizon onc e each rotation of t he earth casting
lo n g shado w s in every direction though be ing at the
north pole they are al ways to ward the so u th r After the
S p eak in g e x ac t ly th e u n is e n th e b e fo re th e sp ri n g eq u in o x
f rac tio n an d th e dip o f th e
an d afte th e au t u m n al eq u in o x o w in g to
.
,
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,
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’
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,
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’
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,
,
r
s
s
e
er
re
,
S ee p 16 0
1 Th e s u de n S h o u l d b e ar in m in d th e ac h a d irec io ns o n th e
ru e geo g rap h ic al
e a r h a re d e e rm in e d s o le ly b y re e ren c e to th e
’
i
A
h
m
f
n
m
h
n
n
i
l
n
a
e
l
o
t
r
s
c
o
e
r
o
o
t
t
e
c
o
e
h
e
m
ar
e
a
ss
t
t
e
o
h
,
g
p
p
p
h o riz
‘
t
on
.
.
t
t
.
t
t
f
f tt t
t
t
.
t
154
S E AS ONS
Another cbnd ition o f
th e e arth in its revolution shou ld be bo rne in mind in
The earth might rotate on
e xplaining change of se asons
an axis and revolve around the su n with the axis inclined
°
235 an d still give u s no change in seaso ns
This can
eas ily be d e mon strat ed by carrying a globe around a cen
P arall elism
of
th e E arth
’
Axis
s
.
.
.
tral obj ect representing t he su n and by rotating the axis
o n e can maintain t he same inclination but k ee p th e verti
c al ray continually at t he e quator or at any other circl e
within the tropic s I n ord er to get the shifting of the
v ertical ray and change of se asons which now O btain th e
axis must constantly point in the same direc tion and its
position at o ne time be parall el to its position at any other
time This is called the paralle lism of the e arth s axis
That t he earth s axis has a very slow rotary motion a
w hich varies its inclination
nodding
slight periodic
toward t he plane of t he eclip tic and also irregular motions
of diverse charact er need n o t confuse u s here as they are
e ither so min ut e as to re quire v ery d elicat e obse rvatio ns
to d etermine them or so slo w as to require many years to
These three motions of the axis are dis
S how a change
cussed in the Appendix under P rec ession of the E q ui
noxes
Nutation of th e P oles and Wand ering of the
p
P oles
(
E xperim en ts w ith th e Gyro sc o pe
The gyroscope pro b
ably fam iliar to most person s admirably illustrates the
cause s of the parallelism of the earth s axis A disk su p
ported ln a ring is rapidly w hirl ed and the rotation tend s
to kee p th e axis of the disk al w ays pointing in th e same
dire ction I f the ring be held in the hand s and carried
about t he disk rapidly rotating it will be discovered that
any att e mpt to change th e direction of the axis will meet
with resistance This is sho wn in the simple fact that a
,
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’
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’
,
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”
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”
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’
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,
D AY S LE NGTH AT THE E QUI NOXE S
155
’
rapidly rotat ing top remain s upright and is not eas ily
tipped over ; and similarly a bicycle running at a rapid
rate rema ins erect the rapid motion of the whee l (or
top ) gi ving the axis a tendency to re main in the same
,
,
,
The gyroscope shown in Figure 4 6
is o ne u sed by
P rofessor R S Holway of t he University of California
.
.
.
I t was
on
mad e by mounting a six inch sewing machine wheel
ball bearings in the fork of an old bicycle I ts ad van
-
.
tages over those commonly used are its simplicity the
ball bearings and its greater weight
Fou cau l t E xperim ent
I n 1852 the year after h is
famous pe ndulum e xperiment d emonstrating the rotation
of the earth M Leon Foucault d e monstrat ed the same
facts by means of a gyroscope so mounted that although
the earth tu rned t h e axis of t h e rotating wheel re main ed
constantly in the same direction
,
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,
.
CO MP AR ATI V E LE NGTH
D AY
OF
AN D
NI GHT
half of the earth
being al ways in the sunlight the circle of illumination is a
h
t
e
h
e
s
h
e
r
at
circl
v
rtical
ray
mark
c
nt
r
of
e
T
e
t
e
e
e
g
lighted half of the surfac e of t he earth At t h e e quinoxes
Tak en by pe rm issio n fro m th e J o r na l of Geography f o r Feb ru ary
D ay s Length
’
at
th e E q u in o xes
.
On e
,
.
.
,
1904
.
,
u
,
,
156
SE AS ONS
the
vertical ray is at the equator and the circle of illu mi
nation extend s from pole to pole bise cting every parallel
S inc e at this time any given parall el is cut into t wo e qual
parts by the circl e of ill umination o ne half of it is in t he
sunligh t and o ne half of it is in darkn ess and during o ne
ro tation a po int on a parallel w ill have had t welve hours
N
i
w
o
e
s
day and twelve hours night
allo
anc
mad
for
e
(
refraction or t w ilight )
D ay s Len gth af ter th e E q u in o xes
Aft er t he vernal
e quino x th e vertical ray mov es north w ard and t he circl e
of illumination e xtend s beyond the north pole but falls
S hort of the south pole
Then all parallel s save th e
e quator are un e qually divid ed by t h e circle of illumination
for more than half of each parallel north of the equator
is in t he light and more than half of each parallel south
of the e quator is in darkness Con se quently while the
vertical ray is nort h of the equator or from March 2 1 to
S e pte mber 23 th e days are longer than t h e night s north
of t he e quator but are S horter than t he nights south of
t he e qua tor
During t h e o ther half of t he year w hen t h e vertical ray
is south of t h e equator these conditions are e xactly
reversed The farther t he vertical ray is from t he e quator
the farther is t he circle of illumination extend ed be yond
and the more
o n e pol e and a way fro m t h e oth er pol e
unevenly are t he parallel s divid ed by it ; henc e t he days
are proportionally long er in t h e hemi s phere where th e
vertical ray is and t he night s longer in the opposite hemi
The farther from the equator too t he greater
s phere
is t he diff erenc e as may be observed from Figure 50
page 16 2 P arallels near the equator are al ways nearly
bise cted by th e circle of illumination and henc e day
nearly equals night there th e ye ar aro u nd
,
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,
,
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.
’
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,
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,
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,
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,
.
158
SE ASONS
longest day that is from sunrise to sunset in
l atitudes is as follows
,
°
0
°
5
°
10
°
15
°
20
12
12
12
12
13
h
h
h
h
h
.
.
.
.
17 m
35 m
53 m
13 m
,
,
°
.
.
.
.
25
°
30
°
35
°
40
°
45
difierent
13 h
13 h
14 h
14 h
15 h
.
.
.
.
.
34
56
22
51
26
m
m
m
m
m
16 h
17 h
18 h
21 h
24 h
°
.
.
.
.
.
50
°
55
°
60
°
65
°
'
66 33
.
.
.
.
.
9m
7m
30m
09 m
oo m
°
.
.
.
.
.
65 days
103
1 34
16 1
6 m os
70
°
75
°
80
°
85
°
90
.
Th e foregoing table makes no allowance f or the fact
that the vertical ray is north of t he e quator for a longer
time than it is south of the e quator owing to the fact that
we are farther from th e su n then and conseq u ently the
No allo wance is
e arth re volves more slow ly in its orbit
mad e for refraction which lifts up the rays o f the su n
,
,
.
,
when it
where
is
near
th e
horiz on thus le ngthening days
,
y
ever
.
Th e
rays of l ight
on e
ntering
the
out of straight courses Whenever a ray of light enters
obliquely a medium of greater or of less d ensity the ray
S uch a change in
is bent out of its course ( Fig
.
,
.
AMOUNT OF RE F R ACTI ON V AR I E S
9
c alled re fraction Wh en a ray of light enters
obliquely a med ium of great er d ensity as in pas sing
through from the upper rarer atmosphere to the lower
d enser layers or from air into water the rays are bent in
the direction toward a pe rpe ndicular to th e surfac e or less
obli quely This is called the first law of refract ion The
se cond law of re fraction is th e conve rse of this ; that is on
e nt er ing a rarer m ed ium t he ray is bent more oblique ly
or away from a perpendicular to th e surfac e Wh en a
d irect ion
Is
.
,
,
,
.
.
,
.
Fil
e
d
ray of light from
obj ect strikes the eye we see the
obj ect in the direction taken by the ray as it enters the
eye and if t h e ray is re fract ed thi s will n o t be t h e real
position of the obj ect Thus a fish in th e water ( Fig 48 )
would see the adjac ent bo y as though the boy were nearly
above it for the ray from the boy to t he fish is be nt
downward s and t he ray as it enters the eye of the fish
seems to be comin g from a plac e higher up
Am o u n t of R ef raction V aries
Th e amount of refrac
tion d e pend s upon the diff erenc e in t he density of the
,
,
.
.
,
,
.
.
16 0
S E ASONS
media and th e obli queness with which th e rays enter
R ays enterin g perpendicularly are not refract ed at all
The atmosphere diff ers very greatly in d ensity at diff erent
altitudes o wing to its weight and elasticity About one
half of it is compressed within three miles of t he surface
of the earth and at a he ight of ten miles it is so rare that
A ray of
sound can scarc ely be transmitt ed through it
light entering the atmosphere obliquely is thus obliged to
traverse layers of air of increasing d en sity and is re fract ed
more and more as it approaches the earth
E fi ect o f R ef ractio n o n Cel estial Al titu d es
Thu s refrac
tion in creas es the apparent altitud es of all c elestial obj ects
e xc epti n g those at th e
z enith ( Fig
The
amount of refraction at
the horizon is ordinarily
'
36
that is to say
a star seen on the hori
zon is in reality over
o ne half a d e gree below
t he horizon
The ao
tual amount of ref rac
tion varies with the t emperature humidity and pressure
of the air all of which aff ect its d ensity and which must
be taken into consid eration in accurate calculations
S inc e t he w idth of the su n as seen fro m th e earth is about
when t he su n is seen just above the horizon it actually
is just below it and sinc e t h e su n pas ses o n e d egree in
about four minut es th e day is thus lengthened about four
minut es in th e latitud es of th e United S tates and more in
higher latitud es This accoun t s for the st atement in alma
nac s as to the exact length of t he day at the equin oxes
Theoretically the day is t welve hou rs long then but prac
.
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16 2
S E AS ONS
broken up and re flected to the lower air Thi s in
brief is t he explanation of t wilight There be ing practi
cally no atmosphere on the moon there is no t wilight
there These and other conse quenc es resulting from the
lack of an atmospheric envelope on t he moon are d escribed
on pp 263 264
Length o f Tw iligh t
Tw ilight is consid ered to last while
°
t he su n is l ess than about 18 belo w t he horizon though
th e exact distanc e vari es some w hat w ith t he condition of
t he atmosphere the latitud e and t he se ason of th e year
The re is thus a
t w ilight zone im
med iately beyond
th e circl e of illu m i
nation and out side
of this zone is the
true n ight Figure
50 represe nt s these
three portions : ( 1 )
P ig s
t he hemi sphere t e
ce iv in g direct ray s (slightly more than a he mi sphere o w in g
°
to refraction ) (2 ) the belt 18 from the circle of ill umina
tion and (3 ) the seg m ent in darkness
total save for
The height of the atmosphere is
starlight or moon light
of course greatly ex aggerat ed Th e atmo sphere above
th e lin e AB rec e iv es direct rays of light and re flect s
and di ff uses the m to th e lo wer layers of atmosphere
I t will be see n from
Tw iligh t P eriod V aries w ith S easo n
Figure 50 that t h e fraction of a parallel in t h e t w ilight
zone vari es greatly w ith t he latitud e and t he season At
t h e e quator th e su n drop s do wn at right an gl es to th e
8
°
l
horizon henc e covers the 18 t w ilight zone in
are
.
,
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o
‘
,
—
,
,
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,
'
.
.
.
,
360
TWI LI GHT NE AR TH E E QUATOR
63
day or one hour and twelve minutes This remain s prae
tically the same the year aroun d there I n latitudes of
the United S tat es the twilight averages o n e and o n e half
hours long being greater in mid summer At the poles
twilight lasts about t wo and one half months
Tw iligh t Lo ng in High Latitu d es
The reason w hy t he
twilight lasts so long in high latitud es in the summer will
be apparent if w e reme mber that the su n ri sing north of
east sw inging slantingly around and setting to t he north
of west passes t hrough the t wilight zone at t he same
°
oblique angle At latitud e 48 33 the su n passes around
°
so obliquely at t he summe r solstic e that it does not sink 18
below the horizon at midnight and stays within t h e twi
light zone fro m sunset to sunrise At higher latitudes on
that dat e the su n S inks even less distanc e below t he
°
horizon For example at St P et ersburg latitud e 59 56
°
the su n is only 6 36 2 5 belo w t h e horizon at mid
night June 2 1 and it is light enough to read w ithout
°
artificial light From 66 to the pole the su n st ays
e ntire ly abov e t h e horizon throughout t h e e ntire summe r
land of the mid
so lstic e that be ing t he boun dary of t h e
n ight su n
Twiligh t Near th e E q u ato r
Here comes scie nc e now
taking from u s another of our cherished belie fs t he wid e
super stition that in th e tropic s there is almost no t w ilight
and that t he su n goes down like thun d er out 0 China
cro sst t h e bay
E very boy s book of ad ve nture tell s of
travelers overtaken by the sudd en desc ent of night and
men of S cienc e u sed to bear out t h ese tales
Young in
h is Gen eral Astronomy point s out that at Q uito t h e
twilight is said to be at best only t wenty minut es
In
a monograph upo n The D uration of Twilight in th e
Tropic s S I B ailey points out by care fully verifi ed
.
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-
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’
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’
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,
,
”
'
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,
”
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,
’
’
’
’
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,
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’
,
‘
,
’
.
’
,
.
.
,
16 4
S E ASONS
observation and experiment s that th e tropic s have their
fair S hare of twilights He says : Twilight may be said
to last until t he las t bit of illumin at ed sk y disappears from
I n general it has been found that
the west ern horizon
this occurs w hen th e su n has sunk about eighteen d egree s
below t he horizon
Arequipa P eru lies within the
tropic s and has an elevation of
feet and the air is
and conditions appear to be
es pecially pure and dry
exc e ptionally favorabl e for an ext rem ely short t w ilight
On S un day Jun e 2 5 1899 the follo w ing observation s
were mad e at the Harvard Astro nomical S tation which is
The su n di sappeared at 5: 30 P M local
situat ed here :
mean tim e At 6 P M thirty minutes after sunset I
could read ordinary print with perfect eas e At 6 : 30 P M
I could see th e tim e read ily by an ordinary watch
At
6 : 40 P M seventy minut es aft er sun set th e illuminat ed
west ern sk y w as still bright e nough to ca st a faint shad ow
of an opaque body on a white surfac e At
P M
it had d is
o n e hour and t wenty minut es aft er sunset
appe ared On August 2 7 1899 t he follo w ing o bserva
tions were mad e at Vincocaya The latitud e of this place
is about sixt een d egrees south and t he altitud e
feet Here it was po ssible to read coarse print forty
seve n minut es aft er sun set and t w ilight could be seen for
an hour and t welve min ut es afte r the sun s di sappe arance
S o t he common superstition about no twilight in th e
tropic s goes to join th e William Tell myth
Harper s
Weeekly April 5 1902
Twiligh t Near th e P ol e
I t may be int e resting to re
late the exact amount o i light and darkn ess expe rienced
during a winter passed by m e in th e Arctic regions wit hi n
four hundred and S ixty mil es of the P ole
From th e time of crossin g the Arctic c ircle until we
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’
’
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”
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’
16 6
S EAS ONS
tical ray is any warmer but because more rays fall over
a given area I n Figure 51 we notice that more perpen
d icu lar rays extend over a given area than slanting ones
,
.
.
F ig
.
51
We obse rve the morn ing and evenin g rays of the su n
say
e ven w hen falling pe rpe ndicularly upo n an
through a convex len s or burning glass are not so
warm as those at midday The reas on is apparent
from Figure 52 the
rays tra
slanting
verse through more
of the atmosphere
At t he summer
sun s
sol stic e
t he
rays are more nearly
vertical over E urope
and the United
S tat es than at other
times I n addition to t h e greater amount of heat received
because of th e less oblique rays th e d ays are longer than
,
,
.
,
.
’
.
,
MAXI MUM HEAT F OLLOWS S UMME R S OLS TI CE
16 7
nights and conse quently more heat is rec eived d uring t he
day than is rad iated off at night Thi s in creasing length
of day time greatly modifies the climate of regio ns far to
Here the long summ er days accum u late enough
th e north
heat to mature grain crops and forage plants I t is inter
est ing to not e that in ma ny northern cities of t he Un it ed
S tates the maximum te mperatures are as great as in so me
southern cities
How th e Atm osph ere is Heated
To und erstan d ho w
the atmosphere get s its heat we may u se as an il lustratio n
th e peculiar heat re c e iving and heat transmitting pro per
ties o f glass We all know that glass permit s heat rays
from the su n to pass read ily through it and that the dark
rays of heat from the stove or radiator do not readily pass
through t he glass Were it not for this fact it would be
no warmer in a room in the sunshine than in t he shad e
and if glass permitted heat to escape from a roo m as
readily as it lets the sun shine in we S hould have to d is
pense with windo ws in cold weather S tating this in
more techn ical language transparent glass is d iatherma
nous to luminous heat rays but athermanous to dark rays
Dry air possesses this same peculiar prope rty and perm its
the luminous rays from th e su n to pass read ily through to
th e earth only about o n e fourth being absorbed as the y
pass through About three fourths of the heat th e at m os
i
i
s
w
s
es
a
d
r
c
iv
that
hich
r
iat
d
back
dark
r
y
h
r
e
e
e
e
e
a
s
s
a
p
from the earth B ein g athermanous to these rays th e heat
is retained a consid erable length of ti m e before it at l ength
I t is for this reason that high alti
e scapes into spac e
tudes are cold the atmosphere being heate d from the
bottom upward s ;
Maxim u m Heat Foll o w s S u m m er So lstice
B e cau se of
these conditions and of the convecting currents of air and
.
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168
S E AS O NS
a very limited exte nt of wate r the heat is so d istrib
u ted and ac cumulated that the hotte st weather is in t he
mo nth follo wing the summer so lstice (July in the northern
he misphere and January in the so uthern ) ; conversely the
co ldest month is t he o ne follo wing the winter solstice
This se asonal variation is prec ise ly parallel to the diurnal
change At noon t he su n is highest in the sk y and po urs
in heat most rapidly but the po int of maximum heat is
not usually reac he d until the middle of the afternoon when
t he accumu late d he at in the atmos phere begins grad ually
to disappear
Astro n om ical and Clim atic S easo ns
Astronomically
there are four se aso ns eac h year : s pring from the vernal
eq uinox to the summer so lstic e ; s ummer
from the su m
mer so lstic e to the autumnal eq uinox ; autumn from t he
autu mnal eq uinox to the winte r solstice ; winter from t he
As treate d in phy
winte r sol stic e to the s pring eq uinox
s eason s vary gre atly in number and
sleaf geography
length with di ff ering conditions of topo graphy and posi
tion in relation to wind s mountains and bo dies of water
I n most parts of contine ntal United S tate s and E urope
there are four fairly marked seaso ns : March April and
May are c alled s pring months ; June July and August
October and Novem ber
s ummer months ; S e pte mbe r
autumn months ; and De ce mber Janua ry and Fe bruary
I n th e southern state s and in western
wint er months
E uro pe the se as o ns j u st name d begin earlier
I n Cali
fornis and in most tropical regions there are two seasons
I n nort hern S o u th America there
o ne wet and o ne dry
t wo wet and t wo dry
are four s easo ns
From the po mt of view of mathematical ge ography
there are four se as ons having the follo w ing lengths in the
northern hemisphere
to
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1 70
S E AS ONS
D E TE R MI NATI ON
LATI TUD E
OF
F R OM
ALTI TU D E
S uN
’
s
ME R I D I AN
.
learned how latitude is d ete rmined by
ascertaining the altitude of the c elestial pole We are now
in a po sitio n to see how this is com monl y d etermined by
referenc e to th e noo n su n
I n Chapter I I we
.
.
R elative P o sitio ns
Cel estial E q u ato r and Celestial P o l e
of the c elestial equator at a given
of
.
Th e
meridian altitude
plac e and the altitude of the c elestial pole at that plac e are
co m ple mentary angles that is together they equal
Though w hen understood this propo sition is exc eedi ngly
simple stud ent s sometimes only partially compre hend it
and the later conclusions are conse quently hazy
°
1 The c e lest ial equator is always 90 from the c elestial
pole
2 An arc of th e c elestial sphere from th e northern hori
,
,
,
,
.
.
.
.
Ze n i t h
H o ri z
on
Li n e
a t La t i t u d e 4
O H
‘
Fi g 53
.
through
z on
z enith to
the
s
outhe rn horizon compri ses
°
there are 90 from the pole to the e quator
from the northern horizon to the pole and from the
southe rn horizon to th e e quator must together e qual
3
.
S inc e
th e
,
D E CLI NATI ON o r THE S UN
One
of
the
following
is
tatements
s
171
incorrect
.
Find
it is
°
a
I n la titud e 30 the altitud e of the celestial pole is
°
30 and that of the c elestial e quator is
°
b I n latitud e 36 the altitud e of th e celestial e quator
w hich
o ne
.
.
.
c
In
.
4 8 20 t he
’
the
altitud e of
celestial e qua
°
tor is
d
latitude
°
41
°
I f the
celestial e quator is 51 above the southe rn
°
horizon the c elestial pole is 39 above the northern horizon
°
e
I f the altitud e of the c elestial equator is 4 9
th e
°
latitude must be 4 0 29
°
I
h
f
h
t
e
a
l
titud
e
of
t
c
e
l
tial
e
quator
2
h
es
e
i
s
1
t
e
f
°
latitude is 69
*
On March 2 1 the su n is on t he c elest ial e quator
I f on
this day the sun s noon S hadow indicates an altitude of
we know that is th e altitud e of the c elestial e quator
°
and this subtracted from 90 equals
t he latitud e of
the plac e
On S e ptember 23 th e su n is again on th e c eles
°
tial e quator and its noon altitude subtracted from 90
e q uals t h e latitud e of t he plac e where t he observation is
mad e
De clin atio n o f th e S u n
Th e d ecl ination of th e s u n or of
any other heavenly body is its distance north or south of
The analemma shown on page 12 7
t he c e lestial equator
gives the approximate d eclination of the su n for every day
in the year The Nautical Almanac Table 1 f or any
.
,
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"
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,
Of co u rse , th e c e n te r o f th e s u n is n o t o n th e ce les tial eq u ato r al l
Th e v e rn al eq u in o x
day, it is th e re b u t th e m o m e n t o f its c rossing
is th e p o in t o f c ross ing , bu t w e co mm o nl y ap p ly th e te rm to th e day
’
w h en th e p ass age o f th e s u n s c e n te r ac ross th e c eles tial eq u ato r
D u rin g t h is day th e su n t rave ls n o rth w ard less th an
oc c u rs
’
an d s in ce its diam e te r is so m e w h at m o re th an 33 so m e p o rtio n o f th e
’
su n s dis k is o n th e c e les tial eq u ato r th e e n tire day
.
.
.
172
S E ASONS
month gives the dec lination very exact ly (to the tenth of
a se cond ) at apparent su n noon at the meridian of Green
wich and the diff erence in d eclination for every hour so
t he st ud ent can get th e d eclination at h is o wn longitude
for any given day very e xactly from this table With
out good instruments ho wever t he proportion o f error of
observation is so great that the analemma will answer
ordinary purposes
,
,
.
,
,
.
Ho w to D etermi n e th e Lati tu de
An y Plac e
of
By
.
ascer
and re ferring to the
anale mma or a d eclination
table o ne can easily comput e
the latitud e of a plac e
1 First d et ermine when
the su n will be on your m e
rid ian and its shadow strike
a north south line This is
discussed on pp 128 129
2 B y some d evic e meas
u re t h e altitud e of th e su n at
apparent noo n ; i e when the
A card
shadow is north
board placed level un der a
window S had e as illustrated
in Figure 54 will give su r
prisin gly accurate results ; a
car
e fully moun t ed quad rant
Fi g 54
e
e
i
how
v
r
will
see
F
g
(
give more uni formly successful measurements Angle A
i
F
the shadow on t he q uadrant is t he altitud e of
( g
the su n
This is appare nt from Figure 56 sinc e my is the
lin e to the su n and angle B
angle A
3 Consult the analemma and as c ertain the d eclination
taining
th e
noo n altitud e of
t he
su n ,
,
.
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,
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,
.
,
,
.
.
,
.
.
,
,
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,
.
.
174
S EASONS
declination is 1 1 S Adding we get
the
altitude of the c elestial equator
°
°
4 90
52 equals
latitude of place of Observer
Converse ly know ing t he latitude of a plac e on e can
ascertain the noon altitude of the su n at any given day
From t he analemma and the table of latitud es many inter
esting proble ms will suggest the mse lves as t he following
e xamples illustrate
Pro bl em 1 Ho w high above th e horizon does the su n
P
22
?
e
e
rs
D
at
t
burg
on
c
mb
r
t
S
e
e
e
t
e
g
°
S o l u tio n
The latitud e of S t P etersburg is 59 56 N
°
The
henc e the altitud e of t he celest ial equator is 30
°
d eclination of the su n December 22 is 23 27 S S ince
south is below t he c e lestial eq u ator
at St P et ersburg the altitude of the
°
°
°
su n is 30 4 l ess 2 3
or 6
Pro bl em
2 At which city is th e
noon su n higher o n June 2 1 Chicago
?
or Q uito
S o lu tio n
Th e latitud e of Chic ago
°
and t he altitude of t he
is 4 1
°
The dec
c elestial equator 4 8
°
linat io n of th e su n June 2 1 is 23
27 N
North ben higher than the
c elestial equator at Chic ago t he
°
noon altitude of t he su n is 48 10
°
°
or 71
plus 23
The latitud e of Q uito be ing
the
altitud e of the c elestial equator is
mm
m"
s
h
h
t
e
i
d
clination
of
b
ng
T
e
e
u
n
e
213
°
2 3 2 7 from this t he sun s noo n alti
°
°
°
The su n is thus
or 6 6
tude must be 90 less 23
°
5 4 higher at Chicago than at t he e quator on J une 2 1
3
.
°
The
.
.
—
.
.
,
,
.
,
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.
.
.
'
.
.
.
,
'
.
'
.
,
’
.
.
,
.
,
’
.
,
’
’
’
,
’
.
LATI TUD E F R OM MOON OR S TAR S
Latitu d e f ro m Moo n
1 75
With a more ext ended
kno wledge of astronomy and mathematic s and w ith suitable
instruments we might ascertain the po sition of the c eles
tial equator in the morning o r eve ning from the moon
planet s or stars as well as fro m the su n At se a the
latitud e is commonly ascertained by making measure ment s
of the altitudes of the su n at apparent noon w ith the sex
tant The d eclination tables are used and allo wances
are m ad e for re fraction and for the
dip of t he horizon
and the resultant calculation usually gives the latitude
w ithin about half a mile
At observatories where the
latitude must be asc ertained w ith the minutest precision
po ssible it is usually ascertained from star observations
with a z enith telescope or a meridian circle te lescope
and is verified in many ways
S tars
or
.
,
,
,
.
.
,
,
.
,
,
,
.
CHAPTER I X
TI D E S
Tid es
Moo n
The
regular rise and fall of the
level of the se a and th e accompanying in flo ws and out
flows o f strea ms bays and channels are called tides S ince
very ancient times this action of the wat er has bee n asso
c iated w ith the moon be cause of th e regular int erval
e lapsing bet w ee n a tid e and th e passage of th e moon o ver
the meridian of the plac e and a some what uniform incre ase
in the height of the tide when the moon in its orbit around
the earth is nearest th e su n or is farthest from it
This
unquestioned lunar in fl ue nc e on the ocean has doubtless
bee n responsible as the basis for thousand s of unwarran ted
associations of cause and eff ect of weather vegetable
gro wt h and even human t e mperament and dise ase with
phases of the moo n or planetary or astral conditions
Oth er P eriod ic E bbs and Fl ow s
S inc e there are other
periodical ebbs and flows du e to various causes it may be
we ll to re me mber that th e t erm tid e properly applies only
to the periodic ri se and fall of wat er d u e to unbalanced
forc es in th e attraction of the su n and moon Othe r con
d itio n s which give rise to more or less periodical e bbs and
fl o ws of th e oc eans seas and great lakes are :
Variation in atmospheric pressure ; low baro meter
a
gives an uplift to water and high barometer a d e pression
b Variability in evaporation rainfall and melting sno ws
produc es changes in level of adjac ent estuaries
Variability in wind direction especially strong and
c
continuous seasonal wind s like monsoons lowers the
an d
th e
,
.
,
,
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,
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,
'
,
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.
,
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,
,
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,
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,
1 76
178
TI D E S
nearest point to the earth is called perigee (from peri
around or near ; and ge th e earth ) and is about
miles I ts most distant point is called apogee ( from apo
from ; and ge earth ) and is about
miles The
average distanc e of the moon fro m t he earth is
°
miles The moon s orbit is inclined to t he ecliptic 5 8
and thus may be that distance farther north or south than
the su n ever get s
The new moon is said to be in conju nc tion w ith the su n
both be ing on the same sid e of the earth I f both are
then in the plane of the ecliptic an eclipse of the su n must
take place The moon being so small relatively (diam
eter
miles ) its shad ow on the earth is small and
thus the eclipse is visibl e along a relatively narrow path
The full moon is said to be in opposi tion to t he su n
it be ing on the opposite side of the earth I f when in
oppo sition the moon is in the plane of the ecliptic it will
be eclipsed by the S hadow of the earth
When the moo n
is in conj u nction or in opposition it is said to be in syz ygy
,
,
.
,
,
.
’
’
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,
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,
,
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.
GR AV I TATI ON
forc e was disc ussed in the first
chapt er where the two laws of gravitation were e xplained
and illustrated The t erm gravity is applied to the force
of gravitation exert ed by the earth (see Appendix p
S inc e the explanation of tid es is simply th e application of
t he laws of g ravitation to th e e arth su n and moon we
may repeat the two la ws :
First law : The forc e of gravitation varies dire ctly as
th e mass of the obj ect
S econd law : The forc e of gravitation varies inverse ly
as t h e square of t h e di stance of th e obj ect
Law s R estated
.
This
.
,
,
,
.
.
.
,
179
S UN S ATT R ACT I ON
’
Attraction Greater, bu t Moo n s Tid e Produ cing
I nfl u en ce Greater
There is a wid ely current notion that
Sun s
’
’
-
.
ince the moo n causes greater tid es than the su n in the
ratio of 5 to 2 the moon must have greater attractive
in fluence for the earth than the su n has
No w this cannot
be t ru e else the earth would swing around th e moon as
c ertainly as it does around the su n Applying th e laws of
gravitation to the proble m we see that t he s un s attrae
tion for the earth is approximate ly 1 76 times that of the
*
moo n
The reasoning w hich ofte n lead s to the erroneous con
elus ion just re ferred to is probably so mething lik e this :
M ajor p remi se : Lunar and solar attraction causes tides
M inor premi se : Lu na r tid es are higher than solar tid es
Conclu sion : Lunar attraction is gre ater than solar
attraction
We have just seen that the conclusion is in e rror One
Or both of t he pre mise s must be in e rror al so
A study
o f t he cause s of tid es will set this matte r right
s
,
,
.
,
.
’
,
.
,
.
.
'
.
.
.
.
CAUS E S
TI D E S l
OF
‘ '
ometimes erroneously stated that wind is caused
by heat I t would be more nearly correct to say that
wind is caused by t he unequal heating of the atmo sphere
S imilarly it is not t he attraction of the su n and moo n
for the earth that causes tides it is t he unequal attraction
for di ff erent portions of the earth that gives rise to u n
balanced forc es which produc e tides
Fo r the m e th od o f de m o ns t ratio n see p 19
Th e fo llo wi ng da ta
m oo n s m ass s’r
are n ec ess a ry : E a rth s m ass 1 ; s u n s m ass
m ile s ; d i tan ce o f e art h to moo n
d is tanc e o f ea rth to s u n
I t is
s
.
.
,
,
.
,
’
’
,
,
m iles
h
a
a
i
a
l
A
m
m
c
t
e
t
1
.
.
’
,
,
s
,
.
treatm ent w ill be fo u nd in the Append ix
.
180
TI D E S
P ortion s
of the earth to ward the moon or su n are
miles nearer than portions on the S id e of the earth opposite
t he attracting body henc e t h e forc e of gravitation is
slightly di ff erent at tho se point s as compared with other
points on the earth s surface I t is obvious then that at
A and B (Fig 58 ) there are two unbalanc ed forc es that
is forc es not having counterparts else where to balance
them At these two sides then tid es are produced
'
,
’
.
,
,
,
.
,
.
,
,
,
To S u n
or
Mo o n
Fi g 58
.
ince the water of t he oc eans yield s to the influence of
these forc es That this may be mad e clear let us examine
these tid es se parat ely
Th e Tide o n th e S ide o f th e E arth To ward th e Moon
If A
miles from th e moon B is
miles away
is
from it the diamet er of the earth be ing AB ( Fig
No w th e attraction of th e moon at A C and D is away
from th e c enter of t he earth and thus l essens the forc e of
se point s lessening more at A sinc e A is
ravity
at
tho
g
n earer an d t he moon s attraction is exerted in a lin e
s
,
.
.
.
,
.
,
,
,
,
-
182
TI DES
but a slight tide produc ing power The attraction of
moon while less than that of t he sun is exerted less
evenl y than that of t he su n and hence produc es greate r
tides
I t has been de monstrated that t he tid e producing force
of a body varies inverse ly as the cube of its distance and
dire ctly as its mass Applying this to the moon and su n
has
the
-
.
,
,
.
-
.
Le t T
s
moon s tide produc ing power
moon s
.
un s mass
is
times the moon s mass
’
un s distan ce fro m
distan ce
s
,
-
’
B ut the
’
n s tide produc ing po wer
-
’
t
The
su
’
’
th e
a th is 390 times
e r
,
t he
,
t
“
Combining the two proportio ns we get,
,
T: t
2
5
.
been shown that owing to the very nearly eq ual
attraction of the sun for d iff erent parts of the earth a
body s weight is d ecreased When the su n is overhead as
compared with th e weight S ix hours from then by only
I t has
,
,
’
,
,
that
is
,
an obj ect we ighing a ton varies in
s
of
a
grain
from
unrise to n oon I n case of the
2
moo n this diff erence is about 2 5 times as great or nearly
2 grains
Weight
.
,
.
THE TI D E ON S I D E o r E AR TH OP P OS I TE MOON
Tid es
Moo n
183
may be of interest to note that
the eff ect of the earth s attraction on di ff ere nt S id es of t he
moon must be twenty times as great as this so it is
thought that w hen the moo n was warmer and had oc eans
the tre me ndous tidal waves sw inging aroun d in the oppo
s ite direction to its rotation caused a gradual retardation
of its rotation until as ages passed it came to kee p the
The planet s n earest th e su n
same fac e to w ard t he earth
Mercury and Venus probably kee p t he same side toward
t he su n for a si m ilar reason
Applyi ng the same reasoning
to the earth it is believed that the period of rotation must
be gradually short ening though the rate se e ms to be
e nt ire ly inappre ciable
on
th e
It
.
’
,
,
,
.
,
,
’
.
,
,
.
Th e Tide
on
th e S id e
of
th e E arth Oppo site th e
Moo n
.
A
planet revolving around the su n or a moon about a planet
takes a rate w hich vari es in a d efinite mathematical ratio
The su n pulls the earth to
to its distanc e (see p
ward itself about one n inth of an inch every se cond I f
the earth w ere nearer its revolutionary motion w ould be
fas ter I n c ase of planets having several satellites it is
obse rved that t he n earer ones revolve about the planet
faster than the outer ones (see p
No w if t he
e arth w ere divid ed into three se parat e portions
as in
Figure 59 the oc e an ne arest th e su n th e earth proper
and the oc ean opposite the su n would have three se parate
motions some w hat as the dott ed lines S ho w Ocean A
I f these
would revolve fast er than e arth C or ocean B
three portions were connect ed by w eak bands their stretch
ing apart w ould cause them to se parate entirely The
,
,
.
.
,
.
.
,
,
,
,
.
.
.
Th e p rese n c e
of
o c ean s
o r an
tm osph ere is
in to ac co u n t
a
theo ry indeed is n o t u su ally tak en
tain th at the earth is n o t pe rfec tly rigid
,
the p lan e ts
tides
.
,
an d
th e m oo n h a v e
n o t ess e n
It
see ms
tial
to th e
t
m os c e r
d th e h eo ry assu m es h a
, an
s u ffi c ien
visc os i y to p ro d u ce bo dy
.
t
t
t
t t
184
TI D E S
.
tide producing power at B is this tend ency it has to fall
away or more strictly spe aking to fall toward th e su n less
rap idly tha n the rest of the earth
-
,
,
.
Mo o n
Gravity
.
o lu t io n
an d
E arth R evol ve Abou t
What
around
h as
the
Co mm o n Center
a
of
been said of the earth s annual rev
su n applies e qually to the e arth s
’
’
To S u n
(
or
)
Mo o n
F ig 59
.
monthl y swing around the c enter of gravity common to
We commonly say the e arth
the earth and t h e moon
revolves about the su n and th e moon revolves about the
e arth
No w the earth attracts th e su n in its measure
just as truly as t h e su n attract s th e earth ; and the moon
attract s the e arth in th e ratio of its mass as the earth
attract s the moon Strictly s peaking the earth and su n
revolve around their common center of gravity and the
moon and earth revolve around their c enter of gravity
.
,
,
.
,
,
.
,
.
86
TI D E S
wave with
t extending north and so uth st arts twic e a
Th e general
day off the western coas t of S outh America
position of this crest is shown on t he co tida l map one line
for every hour s diff erence in time The tidal wave is
ret arded along its n orthern ext remity and as it sweeps
along th e coast of northern S outh America and North
Ame rica t he w ave assu mes a northweste rly direction and
swee ps down the coast of As ia at th e rate of about 850
cres
.
-
,
’
.
,
,
Co ti dal ll nes
-
m iles per hour
I ndian Oc e an
Th e
outhern portion passes ac ro ss the
being retard ed in the north so that the
southern portion is south of Africa whe n th e north e rn por
tion has just reached southern I ndia The time it has
taken the crest to pass from S outh America to south Africa
B e ing re tard ed by the African coas t
is about 30 hours
t he no rthe rn portion of th e w ave ass umes an almost north
erly dire ction swee ping up th e Atlantic at t he rate of about
I t moves so much fast er northward
700 miles an hour
in th e central Atlantic than along th e coasts that the crest
.
s
,
.
.
,
,
.
TI ME B E TWEE N S UCCE S S I VE TI D E S
187
bend s rapidly northward in the c enter and strikes all points
of the coast of th e United S tates within two or three hours
of the same time To reach Fran ce the wave must swing
arou nd S cotlan d and then so uthward across the North S ea
reac hing the mouth of the S e ine about 6 0 hours after
startin g from S outh America
A new wave be in g formed
about every 12 hours there are thus several of these tidal
waves followin g one another across the oceans each
slightly d iff ere nt from t he others
While the term wave is correctly applied to this tidal
movement it is very liable to leave a wrong impress ion
upon the minds of those who have ne ver se en the sea
When thinking of this tidal wave swee ping across the
ocean at the rate of several hundred miles per hour we
should also bear in m ind its height and l eng th (by he ight
is meant the vertical dist anc e from th e trough to the crest
and by length the dist ance fro m crest to crest ) Ou t in
midocean the height is only a foot or two and the length
is hundred s of miles
S ince th e wave requires about three
hours to pass from trough to crest it is evident that a S hip
at se a is lifted up a foot or so durin g S ix hours and then
as S lowly lowered again a motion not e asily d ete cted
On
the shore th e height is great er and the wave l ength shorter
for about S ix hours the water gradually rises and then for
about six hou rs it e bbs away again B reakers bores and
unus ual tide phenomena are discussed on p 189
Tim e B etw een S u cc essive Tid es
The time elapsing
from the passage of the moon across a meridian until it
*
crosses the s ame meridian again is 24 hours 51 min
This
.
,
.
,
,
.
.
,
,
.
.
,
,
.
-
,
.
,
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,
.
.
.
Mo re p rec ise ly
,
Th is is th e m ean lu n ar d ay , o r
in te rval be t w ee n s u c cess iv e p ass ages o f th e m oo n o v e r a giv en m e ridian
Th e app a re n t lu n ar day v aries in le n gt h fro m 2 4 h 38 I n to 2 5 h 5 I n
f o r c au se s so m ew h at s im i la r to t h os e p ro d u c in g a v ariatio n in th e le n gt h
o f th e app are n t so lar d ay
,
2 4 h 50 m 51
.
.
s
.
.
.
.
.
.
.
.
188
TI D ES
in contradist inction to the solar and sidereal day may
I t takes the moon
solar days
be termed a lunar day
to revolve around the earth a sidere al month I n one
day it journeys $7 3 of a day or 51 minutes S o if the
moo n was on a given meridian at 10 A M on one day
by 10 A M the next day the moon w ould have moved
e ast w ard and to dire ct t h e same meridian a se cond
time to ward the moon it takes on the average 51 minutes
longer than 24 hours t he actual time varyin g fro m 38 I n to
,
.
.
,
0
.
.
.
.
,
,
.
,
.
,
Fig
s
LOW tid e
61 .
m for v arious re ason s The tid es of on e day then
are l at e r than t h e tid es of t h e pre c eding d ay by an av erage
interval of 51 minutes
I n studying th e m ove m e nt of t h e tid al w ave we obse rved
that it is retard ed by shallo w w ater The spring tides
being higher and m ore po werful move fas ter than the
ne ap tides the int erval on successive d ays averaging only
Neap tid es move slo w er averaging somew hat
38 minutes
over an hour l ater from day to day The e stablishment
of a port as previously explained is t he average time
1h 6
.
.
,
.
.
,
.
,
.
,
.
,
,
,
CHAPTE R X
M AP P ROJ E C TI ON S
re present the curved surfac e of the earth or any
po rtion of it on the plane surface of a m ap involves
I nd eed it is impossible
se rious mathematical di fficulti es
to do so with perfect ac
curac y The term pro
i
h
e
n
ec
t
o
appli
d
to
s
e
t
a
j
represe ntation on a plane
of points corresponding
to points on a globe is
n ot a l w a y s u s e d i n
geography in its strictly
m athe matical sense but
d enotes any representa
tion on a plane of paral
lels and m eridian s Of the
earth
To
,
,
,
.
,
.
,
,
,
.
THE OR THOGR AP HI C
P R OJ E CTI ON
This is perh aps th e
most read ily u nd erst ood
proj ection and is o ne o f
,
,
,
old est known having
been u sed by the anci ent
Greeks f o r c el estial re presentation
The globe trul y repre
sent s t h e relative po sitions of point s o n the earth s surfac e
th e
,
.
.
’
.
190
AND ME R I D I ANS
P AR ALLE LS
191
It
might see m that a photograph of a globe would
correctly represent
on a flat surfac e
the curved surfac e
of the earth A
glanc e at Figure 6 2
from a photograph
of a globe shows
the parallels n ear
the equator to be
farther apart than
those near the
poles This is not
t he way they are
on the globe The
t h g p h i p j ecti
Eq at i al
Fig 63
orthographic pro
n
e
i
c
t
o
i
s
h
h
t
e
r
e
pr
s
ntation
of
t
glob
a
photo
e
e
e
e
a
s
j
graph would S how it from a great distanc e
.
,
,
.
.
.
.
or
u
or
o ra
c
on
ro
.
Fi g 64
.
Paral l el s
an d
Meridian s Farth er Apart in Cen ter
Viewing a globe fro m a dist anc e
,
we
of
observe that
Map
r
a
p
.
MAP P R OJ E CTI ONS
192
allels and meridians appe ar s omewhat as re present ed in
Figure 63 be ing farther apart toward the c enter and ih
creas ingly nearer toward the outer porti o n Now it is
obvious from Figure 64 that the farther t he eye is plac ed
from the globe the l ess will be the distortion although a
re moval to an infinite distanc e w ill not obviate all distor
tion Thus th e eye at :c sees lines to E and F much
nearer togeth er than lines to A and B but t he eye at the
greater distance sees less diff erenc e
Wh en the rays are perpe ndicular to the axis as in Figure
6 5 th e parallels at A B C D and E will be see n on the
tangent plane X Y
at A B C D
and E W
h ile th e
distanc e from A to
B on the globe
is practically the
d is
same
as t h e
tanc e from D to E
to the distant eye
A and B w ill ap
pe ar much n ea rer
together than D
and E
S inc e A
E
E
h
or
r
pr
nt
a
pol
and
or
q
tor
lin
A
e
t
e
e
e
e
se
s
u
a
e
(
)
)
(
X Y is e quivalent to a c e ntral me ridian and po ints A B
etc
are wh ere the pa rall el s cro ss it
,
'
,
,
.
,
.
,
,
,
’
’
,
’
,
,
,
,
’
,
,
’
.
,
’
’
’
’
.
’
’
,
’
’
,
.
.
,
How to Lay
03
an
E q u ato rial Orth ographic P roj ec ti o n
I f parallels and m eridians
th e circl e into twenty four
'
.
d esired for e very
divide
e qual part s ; any d esired number
of parallels and meridians of course may be drawn Now
connect opposite points w ith straight lines for parallels
i
r
h
s
s
e
in
T
r
a
s
on
why
parall
l
a
e
traight
li
n
e
F
s
e
a
s
e
g
(
are
-
,
.
,
.
MAP P R OJE CTI ONS
194
where the meridian must cross and tying a string as a loop
aro u n d these three pins then withdraw ing the one at the
e quator th e e llipse may be mad e as d escribed in th e first
chapter
How to Lay 03 a P olar Orth ographic P roj ec ti on
Thi s
Here
is laid Off more e asily than the former proj ection
th e eye is conc e ived to be directly above a pol e and the
e quator is t he boundary
of the he misphere seen
I t is apparent t hat
from this position the
eq uator and parallel s
will appe ar as circles
a nd
s inc e th e planes
Of th e meridians pass
through the eye each
meridian must appear
as a straight line
Lay o ff for th e e qua
tor a circle the sam e
siz e as th e pre c eding
Fi g 57
Porn orth og phi p j c ti on
F
i
s
o ne
b
u
( g
dividing it into twenty four part s if meridian s are d esired
for every
Conn e ct these points w ith t he c enter
w hich re presents the pole
On any diameter mark Off
distanc es as on the c enter meridian Of t he equatorial
Through these points
orthographic proj ection (Fig
draw circles to re present parallels You will then have
the compl et e proj ection as in Figure 6 7
P roj ections may be mad e w ith any point on the globe as
c enter though the limits of this book will not permit the
rather difficult e xplanation as to ho w it is done for lati
°
With the parallels and
tudes other than 0 or
,
,
.
.
.
.
,
,
.
.
.
ra
c
ro e
.
-
,
,
.
.
.
.
,
m
'
195
LAY OFF A P OLAR OR THOGR AP HI C P R OJE CTI ON
meridians proj ected the map may b e drawn The student
should re me mbe r that all maps which make any claim to
accuracy or correctness are mad e by locating points of
an area to be re presented according to their latitudes and
longitudes ; that is in re fere nc e to parallels and meridians
I t will be Obse rved t hat th e orthographic syste m of pro jec
tion crowd s together areas to ward the outside of the map
and the scale Of miles suitable for the central portion will
not be co rrect for the oute r portions For this reason a
scal e of miles never appears upon a he mi sphere mad e on
this pro j ection
.
,
,
.
.
.
S UMMAR
I n th e
th ograph ic
or
l
.
Th e
2
.
Me ridians
3
.
Wh en
a
4
.
Wh en
a
eye
is
i
n
o
p
t
j tio n
r
o
e
c
p
c o n c eiv ed
an d
Y
to b e
r
l
a
l
l
s
a
e
p
in th e
at an
infin ite distan ce
farth er
a re
t
eq u a o r
.
t to w ard
ap a r
t
is th e
th e
p arallels
cen e r,
t
c en e r of
t
are s rai h t
g
is at th e c en te r, m e ridians a re s t raigh t lines
I f th e
n o rth e rn h em isp h e re is rep res e n ted , no rth is n o t to ward th e to p
of th e map b u t to w ard th e c en te r
l
o
e
p
.
.
S TE R E OGRAP HI C P ROJE CTI ON
I n the stereographic proj ection th e eye is conceived to be
upon the surf ac e of the globe vi e wing the opposite hemi
P oints on the opposite hemisphere are proj e cted
s phe re
,
.
upon a plane tangent to it Thus in Figu re 68 the eye is
at E and sees A at A B at B C at C etc I f the earth
were transparent we should see Obj ects on the opposite
h alf of the globe f rom the vie w point Of t his proj e ction
.
’
’
,
’
,
,
.
,
.
MAP PR OJE CTI ONS
196
How to Lay 03 an E q u ato rial S tereographic P roj ection
I n Figure 68 E represe nt s t he eye at t he equator A and
,
,
are
the
poles
.
an d
th e
A N is the corresponding meridian
’
’
Of
proj ection w ith B C etc as the points w here the
parallels cross the meridian Taking the line A N of Figure
68 as di amet er construct upon it a circle (see Fig
’
’
,
,
.
,
’
.
,
.
MAP P R OJ E CTI ONS
198
Areas
crowd ed together toward the cente r Of the
map when made on the st ereographic proj ection and a
scale Of mil es suitable for th e c e ntral portio n w ould be too
This proj ection is Ofte n u sed
small for th e out er portion
ho wever be cause it it so eas ily laid Off
are
.
,
.
,
Fi g 7a
.
.
Hemi sp h eres i n
eq u at ori al st ereograp h i c
j
pro ec ti on
S UMMAR Y
I n th e
t
s e reo g rap h ic
Th e eye is
c o n c e iv e d
Me rid ians
an d
t h e m ap
3
.
Wh en
j tio n
r
o
ec
p
to b e
l
r
a
l
l
s
a
e
p
on
a re
th e
f
th e glo b e
togeth e r to w a rd
s u r ac e o f
n e a re r
.
th e
t
c en e r o f
.
t is th e c en te r o f th e m ap p arallels
m e rid ians a re rep res en ted a arc s Of c irc les
Wh en a p o le is th e c en te r m e rid ians a re s t raigh t lin es
a
i
n
o
p
t in
th e
eq u a or
-
s
4
.
,
.
.
,
GL OB ULAR P R OJ E CTI ON
an d
.
With the eye at an infin ite distanc e (as in th e ortho
graphic proj ection ) parallel s and me ridians are neare r
together tow ard th e ou tside of t he map ; w ith the e ye on
th e surf ac e (as in t h e st ere ographic proj e ction ) they are
n eare r togethe r tow ard th e cen ter of th e map I t wou ld
see m reasonabl e to e xpe ct that w ith t h e eye at some point
,
,
.
THE POLAR S TE R E OGR AP H I C P R OJ E CTI ON
199
inte rmediate between an infinite distanc e from the surfac e
and the surfac e itself that the parall els and meridians
would be e quidistant at dif
ferent portions Of the map
That point is t he S ine of an
angle of
or a little less
than the length of a radius
To
away from th e surfac e
find this di stanc e at which
the eye is conc e ived to be
placed in the globular pro jec
tion make a circle Of t he same
S ize as th e o ne w hich is th e
basis of the map to be mad e
n
h
e
o
e
e
e
t
dra w two radii at an angl e Of
ighth
of
circl
)
(
and draw a lin e
AB from the ex
.
.
,
,
'
,
,
Of
trem ity
ra
on e
d iu s
perpendicular
to the other rad ius
The length Of this
perpendicular is the
distan c e sought (AB
.
,
Fig
Thus with th e e ye
at E ( Fig 74 ) t he
.
.
pole A is proj ected
to th e tangent plane
at A B at B etc
and the distanc es
’
’
,
,
Fi z
74
AB
’
’
.
B C
’
’
,
etc
.
,
,
are
prac tically equal so that the y are constructed as though
they were e qual in proj ecting parallels and meridians
.
MAP P ROJ E CTI ONS
200
How to Lay
03 an
E q u ato rial Gl ob u l ar P roj ectio n
.
As in
orthographic or st ereographic proj ections a circle is
divid ed into e qual part s
according to the number
Of parallel s d e sired th e
c entral meridian and
be ing su bd i
e quator
v ided into half as many
e qual
parts P arallel s
Fi g 75
Hem i p h e . i n eq at ial gl b la
”m a l “
and meridian s may be
drawn as arc s of circles be ing sufficiently accurate for
ordinary purpo se s (see Fig
Th e po lar gl o bu lar proj ectio n is laid Off preci sely
like the orthographic and the stere ographic proj ections
having t he pole as the c e nt er e xc epting that the con
c e n t r i c c i r c l e s representing
parallel s are e quidist ant (see
the
,
,
,
re
s
.
u
or
o u
r
.
e
,
.
,
Fig
By
.
mean s Of starlike ad di
tions to the polar globular pro
n
F
i
i
h
e
o
se
e
ntir
t
c
t
e
e
e
(
g
j
globe may be re prese nted I f
fold ed back the rays Of t he
star w ould m eet at t he south
pole I t S hould be notic ed
P l
F i g 76
that
in this pro
south
gl b l
p j ti n
n
i
i
s
in
a
lin
dir
ctl
c
t
o
e
e
e
y
j
a way from th e c enter ; that is t he top Of the map is south
While
th e bottom south and th e S id es are al so south
portion s of the southern hemisphere are thus s pread out
propo rtional areas are well re presented S outh America
and Africa be ing shown w ith little distortion of area and
outline
.
.
,
.
.
o ar
.
o u ar
ro ec
o
,
,
,
.
,
,
.
MAP PR OJ E C TI ONS
202
of ce lestial bodie s thi s proj e ction is a very old one having
Oft en been used by t he ancient s for c ele stial maps
S inc e the eye is at t he c enter for mapping t he c el estial
S phere it is conc e ived to be at t h e c e nt er Of t he e arth in
proj ecting parallels and me ridian s Of the earth As will
be see n from Figure 78
th e distortion is very
great away from the
center of th e map and
an entire hemisphere
c ann ot be shown
All great circles on
this proj ection are repre
F
se nted as straight lines
G
Thi s will be apparent if
o n e i m agin es hi mse lf at
if
t h e c enter Of a trans
parent globe having par
allels and meridi ans
traced upon it S inc e
the plane of every gre at
circle passe s through the
c enter Of the globe the
e ye at that point will
see eve ry portion Of a
gr
eat circl e as in o n e
Fi g 78
plane and will proj ect
it as a straight line As will be shown later it is be
cause Of this fact that sailors fre quent ly u se maps mad e
on this proj ection
To Lay 03 a P ol ar Gn o m o n rc P roj ec tio n
Owing to th e
fact that parallel s get so much farthe r apart away from
th e c ent er of th e map th e gno m onic pro j ecti on is almos t
,
,
.
'
,
.
,
.
'
.
'
.
,
.
‘
,
.
.
.
,
203
GR E AT CI R CLE S AI LI NG
never mad e with any other point than th e pole for center
and then only for latitu d es about forty d egrees from the
pole Th e polar gno
monic proj ection is
mad e like the polar
proj e ctions previously
described
exc e pting
that paralle ls intersect
the meridians at th e
distanc es represe nted
in Figure 78 The
meridians being great
circles are represent ed
as straight lines and
t h e paralle ls as conee n
Pola g m i p j t i
tric circles
I t w ould see m at first thought
Great Circl e S ail in g
that a ship sailing to a
point du e eas t ward
say from Ne w Yo rk to
Oporto would fol lo w
the course Of a para l
lel that is would sail
d u e east ward
Thi s
ho wever would not be
its
course
short est
The solution Of the
following little catch
p r o b l e m in mathe
matic al geography w ill
Fig 8
make clear the reason
for this
A m an was forty rod s d u e e ast of a he ar
h is gun wo u ld carry only thirty rod s yet with no change
,
.
,
.
,
,
r
no
on c
ro ec
on
.
'
.
,
,
,
,
.
,
,
.
.
0
,
,
,
MAP P ROJE CTI ONS
204
of position he shot and killed the bear Wh ere on earth
were they ?
S olution : This could occur only near the
pole where parallels are very sm all circles The bear was
west ward from the man and west ward is along the course
of a parallel The bear was thus di stant forty rod s in a
curved line from the man but the bullet flew in a straight
line (see Fig
Th e short est distanc e between t wo point s on the earth
A great circle passing
is along the arc Of a great circle
through Ne w York and Oporto passes a little to the north
of the parallel on which both cities are located Thus it
is that t he course of vessels plying bet wee n the United
S tates and E urope curves somewhat to the north ward of
parallel s This follo w ing Of a great circle by navigators
Th e e quator is a great circle
is call ed great circle sailing
and parallel s n ear it are almost Of the same length I n
sailing w ithin th e tropic s there fore the re is little adv an
tage in d eparting from th e course Of a parallel B esides
this the trad e wind s and doldrums control the choice of
routes in that region and the Mercator proj ection is al ways
used in sailing there I n higher latitudes the gnomonic
proj ection is commonly used
Although the gnomonic proj ection is rarely used ex
ce ptin g by sailors it is important that stud ent s und erstand
the principl es und erlying its construction sinc e th e most
important proj ections yet to be discussed are based upon it
.
”
.
.
.
.
.
,
.
.
.
,
,
.
,
.
.
,
.
S UMMAR Y
j t
I n th e gn o m o n ic p ro ec io n
1 Th e eye is c o n c eiv ed to b e at th e c en e r Of th e e a r h
Th e re is g re a d is o r io n o f d is an ces aw ay ro m th e c e n e r o f th e m ap
3 A h em isp h e re c ann o be sh o wn
4 All g re a c i rc les a re sh o w n as s raigh lin es
a
Th e re o re it is us e d large ly f o r gre a c irc le sailing
t
.
t
.
.
5
.
Th e p o le is
t t
t
f
u s u ally
th e
t
t
t
f
.
t
.
t
t
ce n e r o f
t
.
t
th e m ap
.
.
.
06
MAP PR OJE CT I ONS
these points of subdivision and
meridians
the
poles draw ellipses for
,
.
To draw the
ou ter elli p tical
meridian s
S et the points of
the compasses at th e distanc e fro m t he point t hrough
which the meridian is to be drawn to t he central meridian
P lac e o n e point of the compasses thus set at a pole and
.
.
mark Off points on the equator for foci Of the ellipse
Drive pins in these foci and al so o ne in a pole
Around
these three pins f orm a loop with a string Withdra w
the pin at the pole and draw the ellipse as d escribed on
.
.
.
page 22 This process must be repeated for each pair of
meridians
The parallel s are straight lines as in the orthographic
proj ection somew hat n earer together toward the poles
I f nine parallel s are drawn on each sid e of t he e quator
they may be draw n in the following ratio Of distances
2
15
1g 1 3 1 3 1
beginning at the equator : 2 1 3
This will give an approxi mately correct re presentation
One Of th e rec e nt books to make fre quent u se of this
proj ection is the Commercial Ge ography by Gann ett
Garri son and Houston (see Fig
.
.
,
.
,
,
,
,
,
,
,
,
.
,
.
.
,
.
E QUATO RI AL D I S TANCES OF P AR ALLE LS
207
The
follo wing table
h
s
iv
h
xact
r
lativ
e
di
s
t
anc
e
of
parall
e
l
s
from
t
e
e
e
e
s
t
e
g
Thus if a map twenty inches wid e is to be
e quator
drawn ten inches from equator to pole the first parallel
will be 69 Of an inch from the equator the seco nd
inches etc
E q u ato rial D istan c es
of
P arall els
.
.
,
,
,
.
.
,
tan ce
°
5
10
15
.
06 9
137
205
°
20
25
30
.
.
272
33 9
404
.
.
°
50
55
60
4 68
53 1
592
.
76 2
The h omolographic proj ection is
metimes called the
Mollweide proj ection fro m its inventor
and the
B abinet or B abin et homolographic proj ection fro m a
n oted cartographer w h o used it in an atlas ( 1857)
From
the fact that within any given section bound ed by paral
lels and meridians the are a of the surfac e of the map is
e qual to the are a wit h i n s imilar m eridians and parall els
of the globe is it so metimes called the eq ual s urface pro
n
i
o
c
e
t
j
so
-
,
,
-
,
.
S UMMAR Y
I n th e h o m o lo grap h ic p ro j ec tio n
1
.
Th e m e ridians are s e m i ellipses , d rawn as in t h e glo bu lar p ro jec
°
tio n , 36 0 o f th e eq u ato r being rep res en te d
Th e p aralle ls are s t raigh t lines as in th e o rth o g raph ic p ro j ec tio n
-
.
.
Areas
of
th e m ap
re p res e n
Th e re is n o dis to rtio n
o f fo rm o f c o n tin e n ts
5
.
of
t eq u al a re as
a re a an d
Of
n ot
t h e glo be
.
a v e ry se rio us
dis to rtio n
.
The glo be is rep rese n ted as th o u gh its
an ex ceed i n gly o b late s ph e ro id
.
f
s u r ac e
co v e red
h alf
of
MAP P R OJ E CT I ONS
08
THE VAN
DE R
GR I N TE N P R OJ E CTI ON
The
homolographic proj e ction was invented early in the
nineteenth c entury At the close of the century Mr
Alphon s Van der Grin ten Of Chicago invented another pro
r
h
s
h
i
w
e
e
by
hich
ntir
urfac
e
of
a
th
may
n
t
e
e
t
e
o
b
e
e
c
t
j
This inge niou s syste m reduc e s greatly t he
re prese nted
.
.
.
j
F ig 83 Worl d in V an d er Grinton pro
.
.
ecti on
angular dist ortion incident to the homolographic pro jec
tion and for the inhabitable portio ns of the globe there is
very li ttle exaggeration of areas
I n the Van der Grin ten proj ection th e oute r boundary
is a meridian circl e the c e ntral m eridian and equator are
straight lines and other parallel s and m eridians are arc s
Th e area of th e circl e is e qual to the surfac e
Of circl es
of a globe Of on e half the diameter of this circle The
but the meridians are of
e quator is divid ed into
course divid ed into
.
,
,
.
.
,
,
MAP P R OJECTI ONS
2 10
proj e ction the parallels are increasingly farther apart away
from the e quator
An examination of Figure 86 will show the nec essity
for the in creasing distances of parallel s in higher latitudes
The eye at the c ente r ( E ) sees A at A B at B etc
Be
°
yond 45 fro m the e quator the distanc e between parallels
A B re present s the same di st an c e
becomes very great
°
H
i
s
1
a
s
G
of
latitud
but
ov
r
twic
long
on
e
e
5
e
h
a
s
e
t
(
)
'
°
map At A (60
north latitud e ) the
meridians Of the
globe are only half
as far apart as they
are at th e e quator
but they are repre
sent ed on the map
as though they were
just as far apart
there as at t he eq ua
tor B e cause Of the
rapidly increasing
distanc es of paral
,
.
.
’
’
,
’
.
’
.
’
’
,
.
,
.
higher
latitud e than
°
60 would re quire a
very large sheet so
th e proj ection is u su
e arth as a whol e sometimes
,
ally modified for a map of the
arbitrarily
G H is th e di st anc e from th e equator to th e first par
allel and S inc e a d egree Of latitud e is about e qual to a
d egree of longitude there this distance may be taken
betwee n meridians
,
.
’
’
,
,
.
THE ME RCATOR ( CY LI ND R I CAL) PR OJ ECTI ON
S tereographic Cylindri cal P roj ecti o n
For
21l
reasons just
given the gn omonic or c entral cylindrical proj ection need s
reduction to S how t he poles at all or any high latitud es
without great distortion S uch a reduction is well shown
in the stereographic proj ection I n this the eye is con
c eiv ed to be on the e quator proj ecting e ach me ridian from
Figure 87
the view point of the meridian opposite to it
S hows t he plan on which it is laid Off m e ridians being par
allel straight lines
an d eq uidi stant and
parallel s being paral
lel straight lines at
increasin g distances
away from the eq ua
tor
Th e Mercato r (Cyl
indrical ) P roj ectio n
E
I n the orthographic
st ere ographic globu
lar gnomonic hom
olographic and Van
der Grinten projec
tions parallels or
meridians or both
represented as
are
It
cu rved l i n e s
Pi z 6 7
should be borne in
mind that directions on the earth are d ete rm ined from
parallels and meridians North and south are along a
meridian and when a meridian is re prese nted as a c u rved
line north an d south are along that curved line Thus the
t wo arrows S ho wn at the top of Figure 8 1 are pointing in
almost exactly o ppos ite directions and yet each is point
.
,
.
.
,
.
,
.
.
,
,
,
,
,
,
,
,
.
.
.
.
,
,
MAP
2 12
ing du e
P R OJ E CTI ONS
orth The arrows at the bottom point opposite
e ach other yet both point d u e south
The arrows point
ing to the right point the same way yet o ne points north
and the other points south A line pointing toward the
top of a map may or may not point north S imilarly
parallels l ie in a du e east west direction and to the right
on a map may or may not be to the east
I t S hould be Obvious by t hi s time that the map projec
tions studied thus far re prese nt directions in a most u n sat
isf actory man ner however well they may re present areas
Now to the sailor th e principal value Of a chart is to show
dire ction s to steer his course by and if the direction is rep
resented by a curved line it is a slow and d ifficult proc ess
for him to d etermine h is co urse We have seen that the
gn omonic proj ection employs straight lines to re present
arc s Of great circles and consequently this proj ection is
used in great circle sailing The Mercator proj ection S hows
all parallels and meridian s as straight lines at proportional
distan c es henc e directions as straight lines and is another
and the only other kind Of map used by sailors in plotting
their courses
M ap s i n Ancien t Ti me s B efore th e middle of the fif
teenth c entury sailor s did not cover very great portion s
Of t h e e arth s surfac e in continuou s journeys out of s ight
Of land w here the y h ad to be guid ed almost w holly by the
Mathematical accuracy in maps was not of very
stars
great i m portance in navigation until long journeys had to
be mad e with no opportunity for verification Of calcula
tions Various roughly accurate map proj e ctions were
made The map se nt to Columbus about the year 14 74
by the I talian astronomer Toscanelli with which he su g
gested sailing directions across the S ea of Darkness is
an interesting illustration of a c ommo n type of his day
n
.
.
,
,
.
.
,
-
.
.
,
.
,
,
,
.
,
,
,
,
.
.
,
’
.
.
.
.
,
”
,
.
MAP
14
P ROJE CTI ONS
The long jo urneys of the P ortuguese along the coas t Of
Af rica and a round to As ia and the many voyages across
the Atlantic early in the sixtee nth c e n tury mad e accu rate
map proj e ction nec essary About the middle of that cen
tury E mperor Cha rles V of S pai n e m ployed a Fle mish
mathe matician named Gerhard Kramer to make maps for
the u se of his sailors
The word Kramer mean s in Ger
man
retail merchant and thi s translated into Latin
,
.
,
,
.
,
,
,
then the universal language of scienc e be comes Mercator
and his invention of a very valuable and now w ide ly used
map proj e ction acquired his Latinized name
P lan of M ercato r Cha rt The Mercator proj e ction is
mad e on the same plan as t he other cylindrical projec
tions exce pting as to the distanc es between parallels
The meridians are re presented as parall e l lines whereas
on the globe the y converge There is thus a distortion of
longitudes greater and greater away from the e quator
Now the Mercator proj ec tion makes the parallels farther
apart away from the e quator exactly proportional to the
°
meridional error Thus at latitude 6 0 the meridians o n
the earth are almost e xactly half as far apart as at the
eq uator but being e quidi stant on th e map the y are re p
rese nt ed as twic e as far apart as they should be The
paralle ls in that portion Of the Mercator map are accord
in gly mad e twic e as far apart as they :are near the eq u ator
S inc e the di stortion in latitud e exactly e qual s the d isto r
tion in longitude and parallels and meridians are straight
lines all dire ctions are re prese nted as straight lines A
n avigator h as simply to draw u pOn the map a line from
the point w here he is to the point to w hich h e wishes to
sail in a dire ct course m easure t h e angle which t hi s line
forms with a parallel or meridian and steer his ship accord
ing to the bearings thus Obtained
,
,
.
.
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,
,
.
.
,
,
,
.
,
,
.
.
.
,
,
,
.
THE ME R CATOR
To Lay
(CY LI ND R I CAL) P R OJ E CTI ON
M ercato r P rojection
how
h
s
t
e
fi
s implest method of layin g off thi s proj e ction
From the
e xtre mity Of e ach radius drop a line to the n earest radi us
parallel to the tange nt A L Th e lengths of these lines
respectively represent the d istanc es
between parallels
’
Thus N M equal s C P K N e qua ls B N A K equals A K
The meridians are
e q uidist ant and are
the s ame distanc e
apart as the first
parallel is from the
e quator
The table of m e
r i d i o n a l parts
on
page 2 1 7 gives the
relative distances of
parallels from the
B y me ans
e quator
of this table a more
exact
proj ect ion
may be laid Off than
by the method j ust suggested To illustrate : S uppose we
wish a map about twenty inches w ide to include the 7oth
is th e di st anc e
parallels We find in the table that
to the e quator Then S ince the map is to exte nd 10inches
‘
o
a
Figure 89
2 15
.
s
.
,
’
.
,
.
,
’
’
’
’
.
,
,
.
'
.
.
.
.
on each
S I de
of
,
t he
e
quator
in making the map ; that
re presented by 10 inches
10
18
,
is
,
1
the
s
cale to
be
u sed
inch on the map will be
S uppose we wi sh to
Tech n ic ally speaki n g, th e dis t an ce is th e t ange n t o f th e angle o f
latit u de and any t ab le o f n at u ral t an gen ts w ill ans w e r n ea rly as w e ll
as th e t ab le Of m e ridio n al p arts , alth o u gh t h e la tte r is m o re ac cu rate ,
being co rrec ted f o r th e o blate n ess o f th e m e ridi an
.
MAP P R OJ E CTI ONS
2 16
lay Off parallels ten degrees apart The first parallel to be
drawn north of the e quator has according to the table
for its meridional dist an c e? This multiplied by
.
,
,
10
e
°
quals
lightly more than
s
1
Hence the parallel
.
hould be laid Off 1 inch from the e quator
parallel has for its meridional distanc e
10
s
tiplied
th e
by
s
cale
10
gives
5944 3
.
The 20th
Thi s mul
inches from
t he
.
e
quator
The 30th
.
F i g go
.
parallel
.
Worl d
has
a meridional dist ance
j
in mercator pro
ection
thi s multipli ed by the scale gives
like manner the other parallel s are laid Off
will
be
3
1
x 6 0 or 6 00 inches
5
59 13
1
inches I n
The meridian s
.
.
for every
de
gree or for ten d egrees 6000 inches
w hich e q ual s
inches Thi s makes the map
inches long
inches x 36
inches )
We see then that the same scal e of mil es cannot be used
°
for diff erent parts of the map though within 30 Of the
e quator re presentation s of are as w ill be in v ery n early tru e
proportions The parallels in a map not wid er than this
say for Afri ca may be drawn e quidi stan t and the sam e
,
.
.
,
,
,
.
,
,
2 18
4
.
MAP
P R OJEC TI ONS
The re i great dis to rtio n o f areas and ou tlines O
f con tinents in
high lati tu des ; Greenl and app ea rs larger th an So u th Ame ric a
t
.
5
6 TI L
‘
.
:
m
u
s
scal e o f
used neae
the
miles
canno
t
be
used
f or high latitu des th at is
eq u ato r
.
CO NI C P ROJ E CTI ON
The
portion of a sphere betwee n the
o
w
es
l
n
of
par
ll
l
wh
ch
n
ar
a
a
s
i
a
re
t
e
e
p
together is very similar to the zone of a
Henc e if we imagin e
cone (see Fig
a paper in the form Of a cone placed
upon the globe and parallels and
meridians proj ec ted upon this cone from
the c ent er of theglobe then t his coni
cal map unrolled we can understand
this system
Along the parallel tangent to the
cone poi nts on the map will correspond
F" 9
exac tly to points upon the globe P ar
allels which are near the line of tangency will be repre
sente d ve ry much in the relative
positions they occupy on the
globe I n a narrow zone there
fore near the tangent parallel
there will be very little distor
t ion in latitudes and longitudes
and an area mapped Withi n the
zone will be very similar in form
and area to the form an d are a
as it appears upon the globe
m
l
9
h
o
s
itsel f F r thi reas on t e conic
proj ection or some modification of it is almost always
employed in representing small areas of the earth s surface
.
,
,
,
.
,
’
.
,
.
,
,
"
.
'
,
,
’
.
TO LAY OFF A CONI C P R OJE CTI O N
To Lay OE
is the c enter
a
Conic Proj ecti on
I f the
.
of the
area to be mapped
draw two straight
lines tan gent to the
forty fif th parallel
of a circle (see Fig
P roj ect upon
these lines points
for parallels as in
the gnomonic pro
i
n
e
c
o
t
With
h
t
e
j
apex as c enter
draw arc s of circles
through these po ints for parallels
forty
-
fif th
219
parall el
,
-
.
.
,
.
Meridians are straight
lines meeting at the
apex and are eq u idis
tant along any paralle l
I t will be Observed
that parallels are farther
apart away fro m the
tangent parallel
in this c ase ) as in
the Me rcator proj ection
they are farther apart
away from the equator
which is tangent to the
globe in that proj ection
There is also an exag
O
f
e
longitud
r
i
n
e
t
o
s
a
g
away fro m the tangent
N t h Ame i a in co i r i ti
Fi z 94
parallel B ecause of this
lengthening of parallels meridians are sometimes curved
.
.
,
.
.
.
or
r c
n c
,
ro ec
on
.
MAP P R OJ EC TI ONS
220
inwardly to prevent too much distortion of areas The
need for this will be apparent if o ne draws parallels be
.
l 'i g 95
.
th e
.
The w orl d in coni c projecti on
quator for he wi ll find they are longer than
the equator itself unless meridians curve inwardly there
B y taking the tan
gent parallel ten d egrees
north of th e equator and
red ucing distanc es of
parallels a fan shaped
map of the world may
I n thi s map
be shown
of th e world on the
con ic proj ection there
is even greater dist e r
e
s
s
tion
of
parall
l
outh
of
n
o
Europe i n conic projecti
r u 96
th e equator but sinc e
meridians converge somewhat north Of the e quator there
t
h
e
e
s
s
S
e
l
di
tortion
in
north
rn
latitud
inc
mo
t
of
e
s
is ess
land area of th e globe is in the n orthern h emisph ere this
yond
e
,
.
-
,
.
,
.
.
,
.
,
MAP P R OJ E CTI ONS
222
n
i
s
i
s
and
th
r
littl
di
tortion
th
pla
b
tt
r
A
B
e
i
s
e
s
e
e
e
(
)
,
apted for a map showing greater width north and south
than is the conic projection
The map of E urope well illustrates this di ff ere nc e
°
°
E urope lies between 35 and 75 north latitud e
On a
Near
conic proj ection the tange nt parallel would be
this parallel there would be no exaggeration of areas
°
but at the extreme no rth and south 20 away from this
parallel there would be consid erable distortion I f instead
we make an intersecting conic proj ection we should have
°
°
th e cone pass through parall el s 4 5 and 6 5 and along
these parallels there would be no di stortion and no part
°
of the map being more than 10 away from these lines
there would be very little exaggeration anywhere
I t S hould be notic ed that th e region between the inte r
se ction s Of th e m eridians must be proj ected back to w ard
th e c ent er of t he sphere and thus be mad e smaller in the
map than it appears on the globe The c entral parallel
would be too short in proportion to the rest S ince this
°
is the most impor
area of E urope ( between 4 5 and
tant portion and should S how most details it would be a
from the practical map maker s po int of
se rious d e fe ct
vie w to minify it
P o lyc oni c Proj ectio n
Thi s d iff ers from the conic pro
n
i
s
o
in
that
it
r
e
a
d
ju
s
t
e
d
at
e
ach
parall
l
w
h
i
ch
i
s
t
i
e
c
e
j
drawn S O that each one is tangent to the sphere This
makes the circumscribing cone bent at each parallel a
seri es
of conic sections Th e word polyconic mean s
“
The map con stru cted on thi s proj e ction
many cones
is thus accurate along each parallel in stead of along but
o n e as in th e conic proj ection or along t w o as in t h e int er
proj ection For representing small areas
sectin g con ic
t his is d ec id edly the most accurate proj ection known
ad
.
.
.
,
.
,
,
,
,
,
.
.
.
,
’
,
,
.
.
,
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,
.
”
.
,
.
.
.
POLYCONI C P R OJ E C TI ON
S inc e t he
zone along each pa rallel is proj e cte d on an
inde pend ent cone the po int
which is the apex for one cone
will not be the same for any
other (unless both north and
south latitud es are shown
in
I n th e conic
the same map )
proj ection the parallels are all
mad e from the apex of the
cone as the c ente r I n the
polyconic proj ection each par
allel h as its own conical apex
and henc e its own c enter This
may easily be o bserved by a
comparison of the parallel s in
i
n
”
f
“
E
m
“
“
9
Fi
!
9
l
Figure 94
r
conic
o
i
n
c
e
t
o
9
(
p i
pol yconi w m an
all mad e from o ne center) and
those in Figu re 98 ( po lyconic proj ection each mad e fro m
a d iff erent c enter )
,
.
.
.
'
f
,
c
o
,
S UMMAR Y
I n th e
1
.
A
j tio n
co ni c
co n e
is
p ro ec
c o n c eiv ed
to be fi
tted
abo u
t
a
tio n
Of
o
r
p
th e glo be,
tangen t to so m e p arallel
Th e tang en t p arallel sh o w s n o dis to rtio n an d p o rt io n s n ea r it h ave
Th is p ro j ec tio n is th e re fo re u sed ex tensively f o r
b u t little
.
2
.
.
m app ing sm all are as
a
I n th e co ni c p ro j ec tio n o n th e gn o m o n ic o r c en t ral pl an,
th e eye is co n c eived to b e at th e cen te r o f th e glo b e,
rd th e ce n t ral
l
l
h
a
r
ar
a
l
a
w
d
e
d
o
t
t
e
t
w
e
l
s
r
e
c
o
c
r
o
e
r
o
se
p
g
ll
l
d
r
r
d
d
i
s
x
r
a
e
t
t
e
t
a
a
e
a
n
a
n
a
e
a
s
a
r
e
e
a
,
p
gg
Th e c o n e m ay be c o n c e iv ed to in te rsec t th e glo b e at tw o
r
n
i
i
i
f
a
a
s
a
d
l
l
i
m
n
n
o
e
a
l
s
t
n
h
h
t
h
t
o
w
u
a
r
b
e
w
e
r
e
i
s
a
d
e
ee
c
,
p
beyo nd whi ch th e re is an exagge ratio n Of areas
.
.
.
.
MAP P R OJ EC TI ONS
224
b
t
f
c u rve d
c
j t
I n th e B o n n e p ro ec io n p arallels are d rawn at
in e rvals ro m a c o m m o n c e n e r an d m e ridian s
.
t
t
t
t
a re
to p re ve n d is o rtio n in lo ngi u des
l
i
i
h
r
r
o
n
m
s
n
i
n
n
o
co
c
e
c
o
o
o
a
c
c
p y
y
p
j t
t t
sligh tly
eq u idis an
.
t
t
I n th e
sec io ns a re
co n c e iv ed to be p lac e d abo u
th e gl o be , o n e f o r e ac h p a ral le l
rep rese n ed
P arall els a re d raw n ro m th e ap e xes o f th e
.
t
co n es
t
f
.
.
THE S CALE
The area of any map bears some proportion to th e actual
area re presented I f the map is so drawn that e ach mile
shall be re present ed by on e inch on th e map S inc e o ne
mile equals
inches the scale is said to be 1 :
.
,
,
This is
fte n written fractionally
O
1
A
,
s
f two
cale O
These of course can be
inches to the mile is 1 :
used only when small areas are mapped The following
s cal es with the ir e quival e nt s are mo st commonly used in
the Unite d S tat es Geological S urvey the first being the
scale e mployed in the valuabl e ge ological folio s cove ring
a large po rtion of the United S tates
,
,
.
,
.
S c ale
S c ale
S c ale
S c ale l :4 5,000,
1 m i le
in ch es
1 m ile
in c h es
.
1 m i le
in c h es
.
1 m ile
in ch es
.
.
S OM E CON C L US I ON S
The following generalizations fro m the discussion of
map proj ections see m appropriate
1 I n all maps north and south lie along me ridians and
Th e top of th e map may or
e ast and west along parallel s
may not be north ; indeed the cylindrical proj ection is the
only one that re prese nts meridians by pe rpendicular lines
.
.
.
,
.
CHAPTE R X I
TH E UN I TE D
S TATE S GOVE RN M E N T LAN D S UR VE Y
All ow an ce f o r Cu rvatu re
On e
of the best proofs that
th e earth is a sphere is the fact that in all careful measure
ments over any con siderable area allowanc e mu st be m ad e
for the curvature of the surfac e I f two lines be drawn
d u e no rthward for on e mile in the northern part of the
United S tates or in central E urope say from the 4 8th
parallel the y will be found nearer together at the north
ern e xtre mities than they are at th e southern end s
Origin of Geom etry
On e Of the great est of th e prac
tical problems of mathe matic s and astronomy has bee n
th e syst e matic location of l ines and po ints and the meas ure
ment of surfaces of the earth by something more d efinite
m ore e asily d escribed and relocated than metes an d bounds
I ndeed geom etry is belie ved to have had its origin in the
need of the ancient Egyptians for surveying and reloca
ting the boundaries Of the ir land s after the Nile fl ood s
Lo catin g by Metes an d B o u n ds
Th e system of locating
land s by metes and bound s prevails extensively over the
world and naturally e nough was followed in this country
by the e arly settlers from E urope To locate an area by
landmark s some po int of beginning is established and t he
bo u ndary lines are d escribed by means Of natural Obj ects
trees well established highways and
such as stre ams
The
stakes pil es of ston e etc are plac ed for the purpose
directions are usually indicated by re ferenc e to the magnetic
compass and di stanc es as asc ertained by surveyors chains
B u t landmarks d ecay and change and rivers change the ir
.
,
.
,
,
.
.
,
.
,
.
.
,
,
.
,
'
,
,
,
,
,
.
,
.
’
.
,
226
22 7
LOCATI NG B Y ME TE S AND B OUND S
cou
Th e magnetic needle of the compass does not
point du e north (excepting along two or three isogonal
lines called agones ) and varies from year to year This
gives rise to endless confusion unc ertainty and litigation
Variation almost without limit occurs in such descrip
tions and farm s assume innumerable forms sometimes
having a score of angles The transitory character of such
platting of land is illustrated in the follow ing exc erpt from
a d eed to a piec e of prope rty in Massachusetts B ay Colony
bearing th e date : An no D omini one thousand seven hun
dred an d thirty six and in the tenth year of the reign of
I n this
our sovereign Lord George the Second King
A c ertain par
E mma B lowers d eed s to William S tanley
cel of Uplan d and S wam p Ground S ituate and lying in th e
Township Of Man chester be ing the thirty first lot into the
Westerly D ivision of Comm on R ights mad e in said Man
chester by the proprietors thereof in the year of our Lo rd
on e thousand S ix hundred ninety nine S aid lot containing
Ten Acres more or less be in g cutted and bo u nded as
followeth Viz : At the Northeast Co rner with a maple tree
between S owest and Abraham Master s from that S outh
*
rses
.
.
,
,
.
,
,
,
,
.
,
-
”
.
,
,
,
-
-
,
,
,
’
,
Wh ere
m e an de ring rive r co ns titu tes th e bo u n d ary o f a n at io n
o r s tate , c h an ges in th e co u rse o f th e s t ream giv e rise to p ho b le m s in
c iv il go v e rnm en t , as th e fo llo win g in c id e n t il lus t ra tes
A m inis te r in
th e so u th e rn p art o f S o u th D ak o ta w as c alled u p o n to Offic iate at a
weddin g in a h o m e in a ben d o f th e Misso u ri R iv e r
D u ring th e h igh
w ate r o f th e p rec ed ing sp ring, th e riv e r h ad b u rs t o v e r th e n arro w
n ec k at th e be n d an d at th e tim e o f th e w ed din
i
i
t
fl
n
w
a
s
o
w
g
g on
bo th s ides o f th e c u t o ff so th at th e re w as a do u b t as to w h e th e r th e
m ain ch ann el o f th e s t ream , th e in te rs tate bo u n dary line , w as n o rth
o f th em an d t h ey w e re i n Neb ras k a , o r so u th an d th ey w e re s till in
To be as su re d o f th e legality o f th e m arriag e rite ,
S o u t h D ak o t a
th e b ridal co u p l e, m inis te r, an d w it nesse s ro we d to th e n o rth b an k ,
an d u p o n th e S o u th D ak o ta bl u ff th e m arriage se rvic e w as
er
p
fo rm ed, th e b ridal p arty re tu rn in g th ey cared n ot to w h ich s tate,
f o r th e fes tivities
a
.
.
-
.
.
2 2 8 THE UNI TE D S TATE S GOVE R NME NT LAND S UR VE Y
a t rly thirty nine poles to Morgan s S tum p so called
from that S outheasterly fourty four poles upon said west
Farm Line to a black Oak tree from that S ixt y S ix poles
Northward to the first bound s or however Otherw ise the
S aid Lo t is or ought to have bee n bounded
S u rvey of North w est Territo ry
When in 1785 practi
cally all of th e territory north and west of the Ohio R iver
had been c ed ed to th e United S tates by the withdrawal of
st ate claims
Congress
provid ed for its su r
ve y profitin g from th e
e xperienc es
resulting
from has tily marked
Thomas
boun daries
H ut c h i n s was ap
r
int
d
e
ograph
e
of
o
e
G
p
the United S t ates and
after the selection of
thirteen assi stant s he
was instructed to begin
S tarting in
its surve y
Fi g 99
1 786 fro m the south
w e st corne r of P ennsylvania h e laid Off a line d u e no rth
to a po int on th e north bank of the Ohio R ive r From
t h is point he started a line west ward According to the
directions of Congress every six miles along this e ast
g eographer s line m eridian s were to be laid Off
w est
and parallel s to it at intervals Of six miles each of the
S quare
s ix mil e s square to be divid ed into thirty S ix
miles and these divided into quarters thus spread ing a
huge gridiron over th e land The larger squares w ere
c all ed townships an adaptation of the Ne w E ng
land to wn
They are commonly call ed Congress ional
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e s e
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230 THE UNI TE D S TATE S GOVE R NME NT L AND S UR VE Y
Each
tion
of
the
s
quare miles
is
commonly called a
sec
”
.
law passed by Congress May 20 1785 provided t hat
surveyors
shall proc eed to divid e th e said ter
ritory into townships of six mil es square by lin es runn ing
du e north and south and others crossing these at right
Owing to t he convergenc e of
angles as near as may be
the meridians this of course w as a mathe matical im po s
as near as may be
however has been broad ly
sibility
interpreted According to the provisions of this act and
the act s of May 18 1 796 May 10 1800 and Fe b 1 1 1805
and to rules of com missioners of the general land Office a
complete system has been evolved the main featu res of
which are as follows :
P rin cipal Meridian s
These are ru n d u e nort h south
or north and south from some initial point selected
with great care and located in latitude and longitude by
astronomical means Thirty two or more of these prin
c ipal meridian s have bee n su rve yed at i rregular int e rvals
and of varying lengths S ome of these are known by
numbers and some by names The first principal meri
dian is the boundary l in e bet ween I ndiana and Ohio ;
th e se cond is west of the c ent er of I ndiana e xtending the
e ntire length of th e st ate ; th e third is in th e c enter of
I llinois e xtending th e entire length of th e state ; the Talla
hassee principal meridian passes directly through that
city and is only about twenty three miles long ; other
principal meridians are named B lack Hills New Mexico
*
I ndian Louisiana Mount D iablo S an B em ardin o
etc
Th e e n ti re p lattin g o f th e p o rtio ns o f th e Uni te d S tates to w h ich
th is dis cu ssio n refers is clea ly sh o wn o n th e large an d e xc ellen t m aps
v
n
h
l
h
G
o
r
n
m
n
i
e
d
b
t
e
e
e
t
a
d
o
b
t
a
i
n
a
u
b
ble
o f th e Uni te d S tates
p
y
at th e ac t u al cos t e igh ty cen ts f ro m th e Co m m iss io n e r o f th e Ge n e ral
The
Th e
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r
s
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Lan d
Offi ce,
Was hingto n
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D
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C
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23 1
B AS E L I NE S
To the
a t west or east and west of principal merid ians
north and south rows of townships call ed ranges are laid
E ach principal meridian together w ith t he syste m of
o ff
town ships based upon it is inde pendent of every other
principal meridian and w here two systems come together
irregularities are foun d
Through th e initial po int se lected from
B ase Lin es
which to ru n the principal meridian an east west base line
is run at right angl es to it and correspond s to a true geo
graphic parallel As in case of the principal meridian
thi s line is laid Off with great care since the accurac y of
these controlling l ines determ ines the accuracy of the
measu rements based upon the m
Tiers of town ships are laid Off and numbe red north and
I n locating a town ship the word
south of these base lines
tier is u sually omitted ; township number 4 north range 2
west of th e Michigan principal meridian means the town
ship in tie r 4 north Of t h e base line and in th e se cond range
west Of the Michigan principal meridian Thi s is th e
township in which Lansing Michigan is located
The fou rth principal meridian in w e stern I llinoi s and
Wisconsin has two base lines on e at its southern extre mity
e xte nding west ward to th e Missi ssippi R ive r and t he other
constituting th e inte rstate boundary line bet wee n Wi scon
Th e townships of west ern I llinoi s are
sin and I llinois
numbered from the southern base line and all of those in
Wisconsin and northeastern Minnesota are numbered fro m
Th e fourth principal meridian is
th e northern base line
in three se ctions being divid ed by an eastern bend of the
Mi ssissippi R iver and by the western portion of Lake
S uperior
The largest area embraced w ithin o ne syste m is that
based upon the fifth principal meridian This meridian
e s
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2 34
THE UNI TE D S TATE S GO V E R NME NT L AND S UR VE Y
measure ments are m ad e for a n ew set of town ships These
lin es are also called correction li nes for obvious re asons
D ivisio n o f D ak otas
When D akota Territory was
di vided and per mitted to ente r the Union as two st ates
the dividin g line agreed upon was t he seven th stan dard par
al lel fro m t he ba se line of th e fifth principal meridian
°
This line is about four miles south of the parallel 4 6 from
th e e quator and was chose n in pre ferenc e to th e geo
h
raphic
parall
l
b
cau
it
w
a
s
e
boundary
lin
b
tw
n
s
e
e
t
e
e
e
e
e
g
farms sections town
ships and to a con sid
c rable e xt e nt coun tie s
The bo un dary line be
tween Min nesota and
I owa is w hat is called
a secondary base line
an d corre spond s to a
st andard
parallel be
twee n tiers 100and 101
no rth Of the base line
of the fifth principal
meridian
Fi g
s
Th e st andard paral
lels have bee n run at varying intervals t he present dis
tance be ing 24 miles None at all were u sed in th e earlier
surve y s
S inc e public road s are u sually built on section
and quarter se ction line s wherever a north south road
crosses a correction line there is a jog in t he road as a
glanc e at Figure 103 will S how
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re
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Town sh ips
North w ard
S urveyed
an d
W estw ard
.
The
practic e in surve ying is to begin at the southeast corner of
a to wn ship and meas ure o ff to the north and west Thus
the se ctions in the north and west are liable to be larger
‘
.
LEGAL S UB D I V I S I ONS OF A S E C TI ON
de pending u pon the ac curacy of
I n case of a fract ional township mad e by the
intervention of large bodies of water or the m eetin g of
or smal er
l
than
6 40 acres ,
,
“Le t I
.
S e c ti on I
.
nother syste m Of surve y or a state line the sections bear
the same numbers they would have if th e township were
full I rregular surve ys and other causes sometimes make
t he town ships or se c
t i o n s c o n s id e r a b l y
larger than the desired
area I n such cas es 40
acre lots or as near
that S ize as possible
appear in the northern
row of se ctions the
other half se ction re
maining as it would
otherwise be
These
lots may also appear
in the western part of
Fi g
s
a to wnship and the
disc re pancy should appear in the western half of each
se ction
This is illu strated in Figure 104
Legal S u bdivisions of a S ec tion
The legal subdivisions
a
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,
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,
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ro
,
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.
.
236 THE UNI TE D
S TATE S GOVERNME NT LAND S UR VE
Y
of a se ction are by halves quarters and half quarters The
designation of the po rtions of a section is marked in Figure
105 The abbreviation s l ook more uninte lligible than they
really are Thus N E 5of S E 5of S ec 24 T 123 N R
64 W 5 P M m ean s the northeast quarter of t he southeast
quarter of se ction 24 in tier Of town ships number 123 north
An y
an d in range 64 west of th e fifth principal meridian
such d e scription can e as ily be locat ed on t h e Unit ed S tates
map issued by the Ge neral Land Office
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238
TR I ANGULATI ON I N ME AS UR E ME NT AND S UR VE Y
you measure bot h to the right and to
average of the two you will get a
To Measu re th e Heigh t
le ft and tak e the
m ore nearly correct
the
In
a similar man
n er o n e may m easure t h e he ight of a flagst a ff or building
Let X re prese nt the highest point in the flagstaff ( Fig 108)
with the
and plac e th e triangle on or n ear th e ground
The di stanc e to
short sid e toward X and long s id e leve l
I t is easy to see from
the foot of the pole is its he ight
this that if we did not have a triangle just as described
say th e angle at t he
f
S
i
s
oint
ight
ng
O
w
a
p
less by measuring
that angle and look
ing up the value of
o f an
Obj ect
.
.
.
,
.
.
,
,
its tan gent in a trigo
n o metrical
table one
\
\
could
as e asily cal
C
:Q Q
culate the height or
st anc e Th e angle
di
m ,
of the triangle from
its tangent is 1 0000 that is
which sighting was done is
X B equal s
times B C I f the angle used were
in
its tan ge nt would be 36 40; that is X B would
st ead o f
I f th e angle were
e qual 364 0 times B C
the tangent
would be
that is X B would equal that number
ti m es B C A complete li st of tangent s for whole d egrees
is given in the Appendix
With the grad uated quadrant
th e stud ent can get th e noon altitud e of t h e su n (th o righ
for this purpose it need not be noon ) and by getting the
length of shad ow and multiplying this by its natural tan
gent get the he ight o f the Obj ect I f it is a bu ilding that
is thus measured the distanc e should be measured fro m
I
x
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TO ME AS UR E THE HEI GHT OF AN OB J E CT
th e
2 39
end
of th e shad ow to the place directly und er the point
casting the longest shadow measured
Two examples may suffice to illustrate how this may
be don e
1 S ay an Obj e ct cast s a shadow 100 feet from its base
when the altitud e of the su n is observed to be
The
°
table S hows the tangent of 58 to be
The height
of the obj ect then must be
times 100 feet or
feet
2 S uppo se an Obj e ct cast s a shadow 100 feet when the
°
sun s he ight is Obse rved to be 6 8
No w the tabl e does
not give the tangent for fractions of d egrees so we must
°
ad d to tan 6 8 5 of the d iff erenc e between th e valu es of
°
°
tan 68 and tan 69 ( 12
The table shows that
.
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,
,
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’
,
’
°
tan 6 9
°
tan 68
diff erence
of
1
3
0
0
5
°
tan 68
and sinc e
and we have found
it follows that
.
’
tan 12
°
tan 68 12
Multiply ing
value of tan
feet by this number re presenting
100
°
68
’
th e
’
12
100 feet x
feet ans wer
,
.
imple proportion one m ay al so measure the height
of an obj ect by the length of the S had ow it casts Le t X B
re present a flagst aff and B C its S hadow on the ground
n
e (any other len gth w ill
lac
a
foot
pol
e
t
e
P
i
F
( g
do ) perpendicularly and measure the length of the shad ow
By
s
.
-
.
240 TR I ANGULATI ON I N ME AS UR EME NT AND S UR VE Y
it cast s and immediat ely mark th e limit of the shad ow
of th e fl agstaff and measure its length in a level line
No w th e length of th e fl agstaff w ill bear the same ratio to
th e length Of th e po le that th e l ength of the S hado w of
th e fl agstaff be ars to th e l ength of the S had o w of the
po le I f the le ngth of th e flagstaff s S had o w is 60 feet and
that of the po le is 6 feet it is Obvious that th e former is
I n formal
ten times as high as th e latt e r or 100 feet high
propo rtion
.
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,
BX
To Measu re th e
:
B X
’
W idth
BC
’
Moo n
measure the
width of th e moon if its distanc e is known Ou t from a
piec e of paper a circle o ne inch in diamet er and past e it
of
th e
.
To
.
Mo o n
Pi g
.
t og
high up on a wrnd ow in V iew of the full moon Find how
far th e eye mu st be plac ed from the disk that th e fac e of
To get this
the moon may be ju st covered by th e di sk
distanc e it is well to have o ne person hold th e end of a
tapeline again st th e window n ear the disk and th e Obse rver
.
.
TRI ANGULATI ON I N ME AS URE ME NT AND S UR VE
242
Y
base of the triangle that th e parallaxes of about forty stars
have been d etermined and eve n then the d eparture fro m
the parallel is so exc eedingly slight that the distance can
The parallax of s tars is
be given only approximately
c alled helioc entric s inc e the base passes t hrough t h e cen
,
.
,
ter
Of
t he
su n
.
S UR V E Y
BY
TR I ANG ULATI ON
A me thod very e xte nsively e mployed for exact m easure
ment of land surface s is by laying Off imaginary triangles
across the surface and by measurin g the length of o n e side
and the includ ed angles all other dimensions may be accu
I m mense areas in I ndia R ussia and
rately comput ed
North America have been thus surveyed The triangu
lation su rveys of the United S tates compri se nearly a
,
.
,
,
.
Fi g
.
n o
quare miles e xtend ing from the Atlanti c to the
Thi s work h as been c arried on by the United
P acific
S tates Geological S urvey for th e purpo se of mapping the
topography and m aking geological maps and by the Un ited
S tate s Coas t and Geodetic S u rvey
million
s
.
,
.
DE TE R MI NATI ON OF B AS E LI NE
D eterm inatio n
The
243
rveyor selects two
po int s a few m iles apart where the interve n ing surface is
level
The distan ce betwee n these point s is asc ertained
i
r
s
f
e
a
s
e
ss
o
r
t
c
b
ng
u
d
to
mak
it
corr
ct
po
ibl
a
re
e
e
a
s
e
a
e
g
this is the base line and all calculations rest for the ir accu
racy upon this distance as it is the only line measured
The following extract s from the B ullet in of the United
S tate s Geological S u rve y on Triangulation No 122 illus
t rate the method s e mployed
The Albany base line fin
central Texas ) is about nine miles in length and was meas
0 foot stee l tape str etched und er a
u red t wice with a 30
tension of 20 po und s The tape was suppo rted by stakes
at inte rvals of 50 feet which were aligned and brought to
the grad e established by more substantial support s the
latter having been previously set in the groun d 300 feet
apart and upon which markings of the extre mities of the
tape were mad e The two direct measure ments diff ered
by
foot but when te mperature corre ctions were
applied th e resulting disc repancy was so mewhat greater
Owing possibly to diffi culty e xperie nc ed at the time of
measure ment s in obtaining the true temperature of the
tape The adopted length of the line after applying the
corrections for temperature length of tape diff erence on
post s inclination sag and se a level was
feet
The base line ( near R apid City S outh Dakota ) was
measured three times with a 300 foot steel tape ; temper
ature was taken at each tape length ; the line was supported
at eac h 50 feet and was u nd er a uniform tens ion of 20
pound s The ad opted length of the line after m ak ing cor
rections for slope te mperature reduction to sea level etc
is
feet (nearly 5 miles ) and the probable error
The Gunni
of the three meas urements is
inch
son line (Utah ) was measured und e r the dire ction of Prof
of
B ase Lin e
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su
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244
TR I ANGULATI ON I N ME AS UR E ME NT AND S UR VE
Y
A H Thompson in 1875 the m eas ure ment be ing made
.
.
,
,
by wooden rod s carried in a trussed wooden c ase These
rod s were oiled and varnished to prevent absorption of
m oist ure and the ir length was care ful ly d eterm ined by
comparisons w ith standard steel rod s furnished by the
Unit ed S tates Coast and Geod etic S urveys
Com pl etion of Trian gl e
From e ach extremity of the
base line a third point is sighted and with an instrument
the angle this l ine forms with th e base line is d etermined
Thus suppose AB (Fig 111 ) re present s the base line At
A the angle CA B is d et ermined and at B the angl e CB A
is d etermined
Then by trig
on om etric al tables the lengths
n d B C are ex
of lines CA a
An y one
actly d et er m ined
of these lines may now be
used as a base for an other
triangle as with base AB
I f the first base l ine is cor
Fi z m
rect and the angles are de
term in ed
accurately
and
proper allo wanc es are mad e for elevations and the curva
ture of the earth the measure ment is very accurate and
e as ily obtained w hate v er th e int ervening obstacles betwee n
I n some plac es in the western part of th e
the po int s
United S tates long lines sometimes many miles in length
are laid o ff from o n e high el evation to another
The
longest sid e thu s laid o ff in the R ocky Mountain region
is 183 mil es long
On th e rec e nt primary triangulation much of the
observing h as been done at night upon acetylene lamps ;
direction s to the distant light keepers have been sent by
the telegraphic alphabet and flashes of light and the
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THE E AR TH I N S P ACE
Th e S olar System
Th e
which the earth belongs is
group of heavenly bodies t o
called after its great central
The me mbers of the solar system
su n th e solar syst e m
are the sun ; e ight large plan ets some havin g att endant
sat e llites or moon s ; se veral h u ndred s maller planet s called
as t eroid s or plan etoid s ; and occasional com et s and m et e ors
The planet s with their sate llites and the asteroid s all
revolve around the sun in the same direction in elliptical
orbits not far from a common plane Those vis ible to the
naked eye may be seen not far from the ecliptic the path
of the su n in its apparent revolution The comet s and
s w ar ms of met eors als o revolve aroun d th e sun in greatly
e longat ed orbit s
The solar syst e m is w id ely separated from any of the
stars with which t he plan et s should not be confu sed
If
o ne could fl y from th e earth to th e su n
miles
in a single day it would take him only a month to reach
th e orbit of the most di stant planet Ne ptune, but at that
same t errific rat e it w ould take over seve n hundred years
to reach the very nearest of the distant stars I f a circle
three feet in diameter be made to represent the orbit of
th e e arth an obj ect over seventy mil es a way would re pre
se nt t h e ne arest o f th e distant st ars
The earth s orbit as seen from t he nearest st ar is as a
circle a trifle over h alf an inch in diamet er seen at a d is
tanc e of a mile D o not imagine that the brightest stars
are nearest
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247
NE B ULAR H Y P OTHE S I S
foregoing one should not fail to appreciate t he
immensity of the earth s orbit I t is small only in a rela
tive se nse The earth s orbit is so large that in travelin g
e ighteen and one half mile s the e arth d e part s from a
perfectly straight l ine only about one ninth of an inch; it
is nearly
m iles in length and the average
orbital velocity of the earth is
miles per hour
I t has been d e mon strat ed that
Su n s Onw ard Mo tio n
many of the so c alled fixed stars are not fixed in relation
to each other but have proper motions of their own
I t is altogether probable that e ach star has it s own motion
in the universe Now the sun is simply one of the stars
h
s
s
a
ee
i
p
and
it
b
n
d
mon
trat
d
th
t
with
e
e
e
s
e
a
s
t
(
perhaps
syste m of planet s it is mov ing rapidly
miles per hour toward the constellation Hercules Many
spe culations are curre nt as to whethe r our su n is controlled
by so me other sun somewhat as it controls the planet s
and also as to general star syste ms An y state ment of
such condition s with present k nowledge is little
if any
more than a guess
Nebu lar Hypo th esis
Time was when it was consid ered
impious to endeavour to as c ertain th e proc esses by which
God works
in His mysterious way His wond ers to per
form ; and to assign to natural c auses and conditions
what had bee n attributed to God s fiat was thought sacri
legiou s
I t is hoped that day has forever passed
This gre at the ory as to the succ essive stages and con
d ition s in the d evelopment of the solar system while
doubtless faulty in some d etails is at prese nt almost the
only working hypothesis ad van ced and forms the fou n
dation of all the current speculations on the su bj ect
It
gives the fact s of the solar system a unity and significan ce
sc arc ely otherwise obtainable
From the
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48
THE E AR TH I N S P ACE
A theory or a hypo the sis if worthy of
riou s attention
is al ways based upon fact s
S ome of t he fact s upon
which the nebular theory is based are as follo ws :
1 All of the planet s are not far from a common
plane
2 They all revolve around th e su n in th e same d irec
tion
3 P lanetary rotation and revolution are in the same
direction exce pting perhaps in case of Uranu s and
Neptun e
4 Th e sat ellites revolve around the ir respective planet s
in the dire ction of the ir rotation and not far from the
plan e of revolution
5 All th e me mbers see m to be m ad e up of th e same
kind s of material
6 Analogy
Th e n ebul ae we see in th e heavens have th e same
a
general appearanc es this theo ry assumes the solar system
to have h ad
b The swarm s of meteorit e s making th e rings of S aturn
are startlingly suggestiv e of th e theory
0 Th e gaseou s condition of th e su n w ith its corona
The fact that
suggest s po ssible earlie r e xt en sion s of it
th e su n rotat es faster at its e quator than at other part s
al so point s to ward the nebular theory The contraction
theory of the sourc e of the sun s heat so generally acc epted
is a corollary of th e n e bular theory
d Th e heat ed interior of the earth and the charac
terist ic s of th e ge ological period s suggest this theory as
th e explanation
These fact s reveal a syst em intimately
The The ory
related and po inting to a common physical cause Accord
ing to the theory at on e time countless ages ago all
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2 50
THE E AR TH I N S P ACE
P lanets
from
F orme d
Ou tlyi n g
P ortion s :
S inc e th e
mass Was
matte r in the outlying portion s as in the whole
some what un evenly di stributed
th e part s of it consoli
dated The greater masses in th e outer series hast ened
by their attraction th e lesser particles bac k of them
retarded those ahead of them and thus one mass was
formed which revolved aroun d the parent mass and
rotated on its axi s I f this body was not too dense it
m ight collect into th e satellites or moons revolving around
it This proc ess continued until nine such rings or lumps
had been thrown o ff or rather left 07
h
many
mall
T
e
s
7
planet s aroun d th e sun betwee n the orbit of Mars and
that of Jupiter were probably formed from one whose parts
were so nearly of th e same mass that no o ne by its pre
ponderatin g attraction could gather up all into a planet
The e xplan ation of th e rings of S aturn is essential ly the
s ame
This theory
Concl u sion as to the Nebu la r Hypothes is
with modifications in detail forms the basis for much of
s cie ntific spe culation in subj ect s having to do with the
That it is th e ultimate explanation f e w will be so
e arth
hardy as to affirm Many questions and doubts have been
thrown on c ertain phas es rec ently but it is in a se nse
th e point of d e part ure for other t h eorie s w hi ch may d is
place it P erhaps even the best of recent theories to
rec e ive the thoughtful attention of th e scientific world
planetesi m al hypothesi s can best be un derstood
the
in general outline in terms of the nebular theory
Th e P lan etesim al Hyp o th esis
This is a n ew explana
tion of the genesi s of our so lar system which has been
worked out by P rofe ssors Chamberlin an d Moul ton of
the University of Chicago and is bas ed upo n a very
care ful study of ast ronomical facts in the light of mathe
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NEB ULAR HYP OTHES I S
matics
251
assu mes the systems to have
been evolved from a spiral nebula similar to the most
common form of nebulae obse rved in the heavens I t is
supposed that t he n e bulou s condition may have been
caused by our sun passing so near a star that the tremeu
dous tidal strain caused the eruptive prominences (which
th e su n shoo ts out at fre quent inte rvals ) to be much
larger and more vigorous than usual and that these when
proj ected far out were pulled forward by the pas sing st ar
and given a revolutionary course about t he su n The arms
of spiral nebul a} have knots of d enser matter at interval s
which are suppo sed to be du e to special explosiv e impul ses
and to become the c enters of accretion later The mate
rial thus shot out was very hot at first but soon cooled
into discr ete bodies or particles which moved indepen d
e ntly about th e su n like planet s (hence the t erm planetesi
Wh en their orbit s cro ssed or approached eac h other
mal )
the smaller particles were gathered in to the knots and
these ultimat ely grew into planets Less than one seven
hun dredth of the su n was ne c essary to form the planets
and satellites
Thi s hypo thesis d ifl ers from the nebul ar hypothesi s in a
number of important particulars The latter assumes the
e arth to hav e bee n originally in a highl y he at ed condition
w hile und er th e planetesimal hypothesis the e arth may
have been measurably cool at th e surfac e at all times t he
in terior heat be ing du e to the compression caused by
h
h
s
T
s
e
e
a
s
ravity
n
bular
hypoth
i
s
vi
w
atmo
ph
r
e
e
e
s
e
t
e
g
th e thin remnant of voluminous orig inal gases where as
th e n ew hypothesi s conc e ives th e atmosphere to have bee n
gathered gradually about as fast as consumed and to have
come in part from t he heat ed interior chie fly by volcanic
action and in part from outer s pac e The oc eans accord
an
d astrophysic s
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It
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52
THE E AR TH I N S P ACE
ing to the old theory were conden sed from t he great
masses of original aqueous vapo rs surrounding t he earth ;
according to t he new theory th e water w as d erived from
t he same sourc es as th e atmosphere
According to the
planetesimal hypothesis t he earth as a w hole has been
sol id throughout its hi story and n ever in th e molt en state
assumed in t he nebular hypothesi s
Solar S ystem n o t E ternal
Of o ne thing we may be
reasonably c ertain t he solar syste m is n ot an eternal o ne
Whe n we ende avor to extend our thought and imagina
“
tion backward toward the beginning it is only toward
creation ; when fo rward it is only toward eternity
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Th y kin gdo m is an e v e rlas tin g kin gdo m ,
An d th y d o m in io n e n d u re th th ro u gh o u t all gen e ra tio ns
.
L
P S A M S , 14 5, 13
TH E MATH E MATI CAL GE OGR AP H Y
AN D
OF
.
P LAN E TS , MOON ,
TH E
S UN
Th e following bri e f sketches of the mathematical geog
of
t he
planet s give their conditions in term s corre
The data and
spo n d in g to tho se appli ed to th e earth
The
c ompari son s w ith t he earth are only approximat e
more exact figures are found in the table at the en d of
the chapt er
S triving for vividness of d escription occasionally result s
in language which implies th e po ssibility of human in hab
itan c y on other c elestial bodie s than the e arth or suggest s
interplanetary locomotion (see p
S uch condition s
An atte mpt to e xclud e
exi st on ly i n the i magi n ati on
astronomical fact s not bearing upon the topic in hand and
not con si stent with t he purpose of the study makes n ec
e ssary the omi ssion Of some of t h e most int eresting fact s
raphy
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2 54
THE E AR TH I N S P ACE
watch however would run esse ntially the same there as
here As we shal l see prese ntly either instrument would
have to be adjusted in order to kee p Martian time as the
day there is longer than ours
R otation
Because of its well marked surfac e it has
been possible to as c ertain the period of rotation of Mars
with very great precision I ts sid ereal day is 24 h 37 m
The solar day is 39 minutes longer than our solar
s
day and o wing to the greater ellipticity of its orbit the
solar days vary more in l ength than do ours
R evol u ti o n and Seaso ns
A year on Mars has 668
*
Martian days and is nearly t w ic e as long as ours The
orbit is much more elliptical than that of the earth peri
helion being
miles ne arer the su n than aphelion
For this reas on there is a marked change in the amount of
heat rec eived when Mars is at tho se tw o points being
almost on e and one half times as much when in perihelion
The northern summers occ ur when
as w he n in aphe lion
Mars is in aphelion so that hemis phere has longer cooler
summers and shorter and w arm er winters than t h e southern
hemis phere
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NO R TH E R N H E M I S P H E R E
S O UTH E R N HE MI S P H E R E
Z on es The equator makes an angle Of 24 50 with th e
°
planet s ecliptic (in st ead Of 23 2 7 as with u s ) so the change
in se ason s and zones is very similar to ours the climate
Of course be ing vastly diff ere nt probably ver cold be cause
y
Of th e rarity of t h e atmosphere (about the same as on our
°
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M ars, by
P e rciv al Lo w ell.
,
FORM AND DI ME NS I ONS
5
highest mountains ) and abse nce of oceans The distance
from the su n too makes a great diff erenc e in climate
Being about one and on e half times as f ar from the e arth
the su n has an apparent diameter only two thirds as
e
i
s
e
e
e
r
at
and
only
four
nth
s
much
h
t
r
c
iv
d
ov
r
n
i
s
a
e
a
e
g
a similar area
Satellites
Mars has t wo sate llites or moo ns S inc e
Mars w as the god of war of the Greeks these two satellites
have bee n given the Greek names of Deimos and P hobos
“
“
meanin g dread and te rror
appropriate for d Ogs
of war
They are very s mall only six or seve n miles in
diameter P hobos is so near to Mars
miles from the
surfac e ) that it looks almost as large to a Martian as o u r
moo n does to u s although not nearly so bright P hobos
being so near to Mars has a very swift motion aroun d th e
s
u
n
lan
t
making
mor
than
thr
r
volution
aro
d
it
e
e
e
e
e
p
during a single Martian day Now our moon travels
°
aroun d th e earth from west to east but only about 13 in
a day so because of the earth s rotation the moon rises
in the east and sets in the west I n case of P hobos it
revolv es fas ter than the planet rotat es and thus rises in
the west and sets in the eas t
Thus if P hobos rose in the
west at sunset in less than three hou rs it would be at
meridian height and show first qu arter in five and one
half hours it would set in th e east somewhat pas t the
full and before su nrise would rise again in the west almost
at the full again Deimos has a sid ereal period of
hou rs and thus rises in th e east and sets in the west the
period from rising to setting being 6 1 hours
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V E N US
Form
and
h as
an d
D im ensions
a diameter of
.
Venus is very nearly sph erical
miles very nearly that of t he
,
256
THE EAR TH I N S P ACE
arth so its latitude and longitude are very si milar to ours
9
I ts surfac e gravity is about T“that of the earth
A man
weighin g 150 pound s here would weigh 135 pounds there
R evol u tio n
Venus revolves around t he su n in a period
of 225 of our days probably rotating onc e on the journey
thus kee ping essentially the same fac e to ward the su n
The day there fore is prac tically the same as the year and
the z ones are t wo o ne of perpetual sunshi ne and heat and
th e other of perpetual darkness and cold
I ts atmosphere
is of nearly the same d en sity as that of th e earth
B e ing
a little more than seven t enths the distanc e of the earth
from the sun that blazing orb seems to have a diameter
nearly on e and on e half times as great and pours n early
t wice as much light and heat over a similar area I ts
orbit is more nearly circular than that of any other planet
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J UP I TE R
Form
and
D im en sion s
Aft er Venus this is the bright
.
,
t he
of
heavenly bodies be ing immense ly large and
having very high re flecting po wer Jupit er is d ecid edly
oblate I ts e quatorial diamet er is
miles and its
polar diamet er is
miles Degrees of latitude near
th e e quator are thu s n early 785 mil es long in cre asing to
over 800 miles near the pole The area of the surfac e is
12 2 times that of the earth its volume
its mass or
weight 317 and its d ensity about o ne fourth
S u rf ac e Gravity
Th e weight of an obj ect on t he surfac e
of Jupiter is about t wo and two third s times its weight
here A man weighing 150 pound s here would weigh 400
pound s there but would fin d he weighed nearly 80 pound s
more near the pole than at the equator gravity being so
much more po werful there A pendulum clock taken fro m
e st
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258
TH E E AR TH I N S P ACE
t he
planet s I ts mean diameter is about
miles I t
therefore has 768 times the volume of t he earth and 84
times the su rf ace I ts density is the lo west of t he planets
only about one eighth as d ense as t he earth I ts surface
gravity is only slightly more than that of the earth vary
ing however 25 per cent fro m pole to equator
R o tatio n
I ts sidereal period of rotation is about 10 h
14 m
v arying S lightly for d ie ren t portions as in case
of Jupiter The solar day is only a f e w second s longer
than t he sidereal day
R evol u tio n
I ts average distanc e from the su n is
mil es v aryin g considerably be cause of its
of our
I t re volves about t he su n in
ellipticity
years thus th e annual calendar must co m prise
of the planet s days
°
Th e inclination of S aturn s axis makes an an gle of 2 7
bet ween the planes of it s e quator and its ecliptic Thus
°
t he vertical ray swee ps over 54 giving that width to its
°
°
torrid zone 27 to t he frigid and 36 to t he temperate
so we
I ts e cliptic an d o ur ecliptic form an angle of
al ways see t he planet very near t he sun s apparent path
S aturn has surroun ding its e quator immense disks of
thin gauzelike rings extendin g out nearly
miles
from t he surfac e These are swarms of meteors or tiny
moons swinging around the plan et in very nearly the
sam e plan e t h e inner one s mo v ing fast e r than t h e oute r
ones and being so very minute that they e xe rt no appre
c iable attractive in fl uenc e upon t h e planet
I n ad dition to t he rings S aturn has ten moon s
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U R A N US
Fo rm
an d
D im en sio n s
visible to t he unaided
.
e ye ,
Thi s
is
planet which is barely
also d e cidedly oblate nearly
,
,
D I ME NS I ONS
F OR M AND
259
much so as S aturn I ts mean diameter is given as
from
miles to
miles I ts volume on bas is
of the latte r (and late st ) figures is 4 7 times that of t he
earth
I ts d en sity is very lo w about three te nths that of
the e arth and its surfac e gravity is about t he same as
ou rs at t he equator in creasing some what to ward the
pole
Nothing c e rtain is known conc erning it s rotation as it
has no di stinct markings upon it s surfac e
Consequently
we kno w nothing as to t he axis e quator days cale ndar
or se as on s
I ts m ean distanc e from the su n is
ti mes that of the
of our years
earth an d its sidereal year
Uranus has four sate llites swin ging around t he planet
°
in very nearly the same plane at an angle of 82 2 to the
plane of t he orbit The y move from west to east around
t he plan et not for th e same re ason P hobo s doe s about
Mars but probably be cause t he a xis of t he planet t he
plane of it s e quator and the plane of these moons has
been tipped
fro m the plane of t he orbit and the
north pole has been tipped down belo w or south of the
ecliptic be coming t h e south pole and giving a back w ard
rotation to t he planet and to its moons
as
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NE PTUN E
most distant planet fro m the su n is
probably somewhat larger than Uranus and has about
the same d en sity and slightly great er surfac e gravity
Owing to t he absenc e of d e finit e markings nothi n g is
known as to its rotation I ts o ne moon like those of
Uranus moves about th e planet from west to east in a
°
plane at an angle of 34 4 8 to its e cliptic and its back
ward motion suggests a similar explanation the inclina
Ne ptune is the
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260
THE E AR TH I N S P ACE
tion of
ecliptic
its
axis
is
more than
°
from
90
the
plane of its
.
ME R C UR Y
This is the
nearest of the planet s to the su n and as it
n eve r get s away fro m the su n more than about t he width
of forty suns (as seen from t he e arth ) it is rarely visible
and then only after sunset in March and April or be fore
sunrise in S e pte mber and Octobe r
Mercury has about three
Form and D im ensio ns
e ighth s th e diamet er of t h e e arth o n e se venth of t h e sur
face and one eighteenth of th e volume I t proba bly has
nine tenths of t he density
o n e t we ntieth of th e mass
and a little less than o ne third of t he surfac e gravity
R o tatio n an d R evol u tio n
I t is beli eved that Mercury
rotates once on its axi s d u ring o n e revolution Owing to
its elliptical orbit it moves m uch more rapidly w hen ne ar
perihelion than when near aphelion and thus the su n
loses as compared with the average position just as it
does in the case of the earth and swee ps e ast ward about
°
When in aphelion it gains
234 from its av erage po sition
and swee ps west ward a si m ilar a m ount Thi s shifting
“
slo w
and west ward making
e ast w ard making t he su n
t he su n
fast is c alled libration
Thus there are four zone s on Mercury vastly di ff erent
from ours indeed they are not zones ( belt s ) in a te rres
trial se nse
a An
elliptical
c entral zone of perpetual sun shine
°
in longitud e I n
e xt ending from pol e to pol e and 133
°
this zone the vertical ray shift s east ward 234 and bac k
again in the short summer of about 30 days and westw ard
a similar e xtent during t he longer Winter of about 58
days Two and one half times as much heat is rec eived
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THE E AR TH I N S P ACE
26 2
I f it s day were
moon ’
8 h 44 m
s
s solar day hav e 70
divid ed into t wenty four part s as is ours e ach o ne w ould
be longer than a w hol e day with u s
R evolu tio n an d Seaso ns
The moon s orbit around the
su n has esse ntially the sa me characte ristic s as to pe ri
helion aphelion longer and shorter days etc as that of
The fact that t he moon goes aroun d the e arth
the earth
does not materially aff e ct it from the su n s vie w point
To illustrate t he moon s orbit about the su n dra w a circle
Make 26 e quidi stant dot s in
78 inches in diameter
this circle to re prese nt the earth for eac h n ew and full
moon of t he year No w for each n e w moon make a dot
o n e t we ntieth of an inch to w ard th e c ent e r (sun ) from
e ve ry other dot re pre se nting t he e arth and for e very full
moon make a dot o ne t wentieth of an inch beyond the
alternate ones These dot s representing the moon if
conn ected being never more than about one twenti eth
of an inch from the circle w ill not vary materially from
th e circle re pre senting the orbit of th e e arth and t he
moon s orbit around the su n will be seen to have in every
part a concave side toward the su n
The solar day of the moon be ing
of our days its
tropical year must contain as many of those days as that
number is contained times in
days or about
days Th e cale ndar for the moon does not have any
thing corre sponding to o u r m onth unless each day be
treated as a month but h as a year of
long days of
nearly 709 ho u rs e ach The exact length of the moon s
d its cale ndar would have the
solar year b e ing
peculiarity of having o n e lea p ye ar in every three that is
t w o years of 12 d ays each and then o n e of 13 days
with an extra leap year every 28 years
The e arth as see n from th e moon is much like the moon
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AB S E NCE OF ATMOS P HE R E
63
n from the earth though very much larger about
four times as broad B ecause th e moon kee ps th e same
face constantly to ward th e earth the latter is visible to
only a little over half of the moon On this earthward
sid e our planet w ould be al ways visible
passing through
precisely th e same phases as the moon does for u s though
in the opposite ord er the time of our n ew moon be ing
“
full e arth for the moon S o brightly does our earth
then illuminate the moon that w hen only the faint cres
cent Of the sunshin e is visible to u s on the rim of the
moon we can plainly see the , earth shine on the rest
of the moon s surfac e which it toward u s
Z on es The inclination of th e plane of the moon s
°
32 (in stead of
equator to t h e plan e of t h e eblipt ic is 1
°
Thus its zone corre
23 27 as I n th e case of the earth )
°
*
spo n d in g to our torrid
zone is 3 4 w id e the frigid zone
°
°
1
and the temperate zones 86
Absen c e of Atm o sph ere
Th e absenc e of an atmosphere
on th e moon makes conditions there vast ly diff erent fro m
those to which we are accustomed S u nri se and sun set
S ho w no crim son tint s nor be autiful coloring and there
Owing to t he very slo w rotation of the
is no twilight
moon 709 hours from su n noon to su n noon it takes
nearly an hour for the disk of the su n to get entirely above
th e horizon on th e e quator fro m th e ti m e t he first glint
of light appears and the time of sun set is e qually pro
longed ; as on the earth the time occupied in ri sing or
The stars
setting is longe r to ward th e pol e s of t h e moon
as see
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Again w e re m in d th e re ad e r t h at t h es e te rm s a re n o t ap p ro p riate
Th e m o o n h as alm os t
in c as e o f o th e r c eles tial b o d ie s th an th e e a rth
’
n o at m o sp h e re to re t ain th e s u n s h e at d u rin g its lo n g n igh t o f n e arly
354 h o u rs an d its d ark s u rfac e m u s t ge t e x c ee dingly c o ld, p ro b ably
se v e ral h u n d re d d eg rees be lo w z e ro
.
.
26 4
THE E AR TH I N S P ACE
do not t winkle but shine with a clear penetrating light
The y may be see n as eas ily in t he daytime as at night
e ve n tho se ve ry ne ar t he su n
Mercury is thus v isibl
the most of t he time during the long daytime of 354
hours and Ve nu s as well Ou t of t he dire ct rays of the
su n
pitch darkness prevails Thus craters of the vol
canoe s are very dark and al so cold I n the tropical portio
t he t em pe rature probably varies from t w o or three h u ndrec
d egrees belo w z ero at night to e xc eedingly high te mpera
t u res in the middle of the day D uring what is to the
moon an eclipse of t he su n whi ch occurs whenever we see
t he moon e clipse d the sun s light shining through ou
atmo sphere makes the mo st beautiful of colorin g a
vie wed from t he moon The moon s at m o sphere is S c
rare that it is incapable of tran smitting soun d so that
d eathlike sile nc e prevail s there Oral conversation i
utterly impo ssible and t he tele phone and telegra ph as we
have them would be of no u se whatever Not a drop o f
w at er e xi st s on that cold and cheerless sat ellite
P erhaps it is w orth n oting in conclusion that it i
believed that our o w n atmo sphere is but the thin remnant
of d e n se ga ses and that in age s to come it w ill get more
and more rarified until at length the earth w ill have the
sil enc e
whi o
et c
same condition s as to t e mpe rature
n o w pre vail on th e moon
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TH E S UN
The
dia mete r is
miles ne arly
four times t he di stanc e of th e moon fro m the earth I ts
time s that of the earth and
surfac e area is abo u t
I t s d e n sity is about
its volume over a million tim es
time s and
o n e fourth that of th e e arth it s mas s
times our earth s A m an
it s surfac e gravity is
D im en si on s
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THE E AR TH I N S P ACE
2 66
tion and counter attraction of all the others They go in
I magine the spac e occupied by a swarm
every direction
of bees to be magnified so that the distance between eac h
The
bee and its neighbor should e qual o ne hund red miles
inse cts wou ld fly in e ve ry po ss ible d ire ction of the ir o wn
.
.
.
SO
Th e dim ens io n s
table
of
geo g rap hic al
of
LA
th e
S Y S TE
R
th
t t
p
TA B
an d
e ar
co ns an s
M
.
o
3 10
.
LE
th e r
d ata
a re
i
v
n
e
i
n
th e
g
267
THE S UN A S TAR
olition S un s move in e very conce ivable dire ction not
They
as the y will but in abj e ct se rv itud e to gravitation
must Obey the omn ipresent force and do so with
m at ical accuracy
From
New Co nce pt ions in Astron
omy by E dgar L Larkin in S cie ntific American Fe br u ary
v
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3 , 1906
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CHAPTER XI V
H I S TOR I CAL S KE TCH
THE FOR M
O F TH E
E AR TH
WHI LE variou s views have bee n held regard ing the form
*
of the earth those worthy of atte ntion may be grouped
under four general divisions
Doubtless the unive rsal be lie f of
I Th e E arth Flat
primit ive man was that save for the irregularities of moun
tain hill and valley the surface of the earth is flat I n all
t he earliest literature that condition seems to be assumed
The anc ient n avigators could hardly have failed to obse rve
the apparent convex surfac e of t he Sea and very ancient
literature as that of Homer allud es to the bend ed sea
Thi s ho wever d oes not n ec essarily indicate a be lief in the
s phe rical form of the e arth
Although previous to h is time the doctrin e of the spher
ical form of the earth had bee n ad vanced Herodotus
i
4
B
4
2
4
C
e
R
C
born
about
8
d
d
about
5
did
not
b
li
v
e
e
e
)
(
in it and scouted whatever evide nc e was advanced in its
favor Thus in giving the hi story of the Ptolemys kings
of Egypt he re lates the incid ent of Ptolemy Necho ( about
6 10 595 B C ) se nding P hoenician sailors on a voyage
around Africa and after giving the sailors re port that
they saw the su n to the n orthward of them he says
I
As f o r m od e rn n o t to ay rec en t p seu do sc ientis ts an d alleged
d iv in e re veale rs wh o co n ten d f o r e arth s o f d ivers fo rm s th e re ad e r
i re fe rre d to th e en te rtainin g ch ap te r en titled
S o m e Cran ks an d
th eir Cro tch ets in Joh n Fis k e s A C ntu ry of S cience als o th e foo tn te
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on
2
2
7
6
6
8
V
l
I
o
,
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pp
—
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of
e
h is Di scovery
2 68
,
e
r
A
a
m
i
c
f
o
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o
HI S TOR I CAL S KE TCH
2 70
phere would have answe red for his con
He was al so the first to teach t hat the earth
c e ptio n
rotates on its axis and revolves about the su n
B e fore th e t ime of P yt h agoras Thales (about 640 546
and other Gree k philosophers had div ided the earth
into five zon es the torrid zone be ing usually consid ered
so fiery hot that it could not be cro ssed much less in hab
ited
Thales is quoted by P lutarch as beli eving t hat the
e a rth is a sphere but it se em s to h ave been proved t hat
Man y of the ancie nt philosophers
P lutarch w as in error
did not dare to teach publicly doctrines not commonly
acce pted for fear of pun ishment for impiety I t is
possible that his private teachin g was diff erent from his
public utteranc es and that after all P lutarch was right
Heraclitus P lato E udoxus Ari stotle and many others
in the n ext two c enturies taught the spherical form Of the
perhaps some of them its rotation Most of
e arth and
the m however thought it not in harmony w ith a perfect
universe or that it was impious to con sider the sun as
predominant and so taught the geoc entric theory
The first really scientific att e mpt to calculate t he size
of the earth was by E rato sthenes (about 2 75 195
He was t he kee per of the royal library at Alexandria and
made many ast rono m ical m easurement s and calculation s
of very great value not only for his o wn day but for ours
S yene th e most southerly city of t he Egypt of
as we ll
h is day was situated w here t he sundial cast no shadow
at the summer solstic e Measuring carefully at Alexan
but a perfect
s
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S t ric tly sp eak in g P y th ago ras s ee ms to h ave tau gh t th at bo th
s u n an d e arth re v o l v e d ab o u t a cen t ral fi re an d an o ppo site e arth
re v o l v ed ab o u t th e e arth as a sh ie l d f ro m th e c en t ral fi re
Th is rath e r
c o m p lic ate d m ac h in e ry o ff e re d so m an y d ifficu l t ies th at h is fo llo w e rs
”
ab an d o n e d th e id e a o f th e c e n t ral fi re an d
o p p o s ite e a rt h
an d h ad
th e ea rth ro tate o n its o wn ax is
,
-
.
.
THE E AR TH A S P HE R E
271
dria he fou nd the n oon su n to be o ne fiftieth of the cir
He then multiplied
c u m f eren ce to t h e south of ove rhe ad
the di stanc e betwee n S ye ne and Ale xandria
st ad ia
by 50 and got the whole c ircumference of the earth to be
stadia
The dist an ce between the cities was not
known very accurately and his calculation probably con
tained a large margin of error but t he exact l ength of t he
Gree k stadium of his day is not known and we cannot
tell ho w near the truth he came
Any sketch of ancient geography would be inco m plete
2 1 A D ) w h o is
without me ntion of S trabo (about 54 D C
He be lieved
father of geography
so m etimes called t he
the e arth to be a sphere at the c e nte r of the un iverse
He continued the idea of the five zones used such circles
as h ad commonly been e mployed by ast ronome rs an d
geographers be fore him such as the equator tropic s and
i
s
w
s
olar
circl
H
work
a
s
tandard
authority
for
s
a
e
p
many centuries
About a c entury after t he time of Eratosthenes P osi
d o n ius a conte mporary of S trabo mad e another m easure
ment basing his calculations upon obse rvations of a star
inste ad of the su n and getting a smaller circumfere nc e
though that of E ratosthenes was probably too small
S trabo Hipparchus Ptolemy and man y others mad e esti
mates as to the size of the earth but we have no record of
any fu rther measurements w ith a view to exact calc u lation
until about 814 A D when the Arabian caliph Al Mamoum
se nt astrono mers an d surveyors northward and southward
care fully meas uring the distance until each party found a
star to have shifted to the south or north on e d egree
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The m os t
was 6 06 4
fee t
.
re l iable
data
see m
to in dic a
te th e length
of
th e
t
s adiu
m
HI S TOR I CAL SKETCH
2 72
This
distance of two d egrees was then multiplied by 180
and the whole circumferenc e obtained
The period of the dark age s was marke d by a de cline in
learning and to some extent a re version to primitive con
c e ptio ns conc erning the s ize form or mathe matical prop
Almost no additional knowledge
o rti es of the e arth
was acquired u ntil ea rly in the seventee nth ce ntury
P erha ps this state me nt may appear strange to some
read ers for thi s was long after the discove ry of America
by Columbus I t should be bo rne in mind that his voyage
and the resulting d iscoveries and e xplorations contributed
nothing directly to the kno wledge of the form or size of
That the earth is a s phere was ge nerally
the earth
believed by practically all educated people for c enturies
be fore the days of Columbus The Gree k astronome r
Cleo m edes writing over a thousand years be fore Co lum
bu s was born said that all com petent persons e xce ptin g
the E pic u rean s acc e pt ed the doctrine of the s pherical
form of the earth
I n 16 15 Wille brord S ne ll professor of mathe matic s at
t he University Of Le yd en mad e a care ful triangular su r
ve y of t he l eve l surfac e s about Le yd e n and calculated
miles A
t he le ngth of a d egree of latitud e to be
re calculation of his data w ith correction s which he su g
gested gives the much more accurat e measure ment of
miles About twenty ye ars later an Engl ishman named
R ichard Norwood mad e mea sure m ent s and calculations
in southern E ngland and gave
as the l e ngth of a
d egree of latitud e the most accurate me asure ment up to
that time
I t was about 16 6 0 w he n I saac Ne wt on ( 1642 1 727 )
discovered the law s of gravitat ion but whe n he applied
th e l aws to the motions of the mo o n h is c alcul ations did
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HI S TOR I CAL S KE TCH
274
accepted reaso n assigned for the shorter e quatorial pen
dulum is the follo wing e xplanation which w as given to
Jame s I I of E ngland whe n he mad e a visit to t he P ari s
“
Observatory in 16 97
While Jupiter at times appears
to be not perfectly spherical we may be ar in mind the
fact that the theory of the earth be ing flattened is sufh
c ie nt ly di sprove n by t he circular shadow which t he e arth
throws on the moon The apparent nec essary shortenin g
of the pe ndulum to ward the south is really only a co rrec
tion for the expansion of the pendulum in con se quenc e of
I t is interest ing to note t hat if
th e higher t emperature
this e xplanation we re t he true o ne the average tempera
°
ture at Cayenne would have to be 4 3 above the boiling
point
E arly in the e ighteenth c entury Giovanni Cassini t he
astronome r in charge Of t he P ari s Observatory assi st ed by
h is son cont inued the me asurement begun by P icard and
came to the conclusion that t he e arth is a prolate spheroid
A warm discussion aro se and the P ar is Acad e my of
S cienc es de cid ed to settle th e matt er by care ful measure
ment s in polar and equatorial region s
I n 1 735 two expedition s were sent out o n e into Lap
l and and the other into P eru Their measurement s while
not w ithout appreciable errors showed t he d ecided d iff er
e nc e of ove r half a mile for o n e d egree and d e mon strated
conclusively the oblateness of a meridian and as Voltair e
“
wittily re marked at the time
flattened the pole s and
t h e Cassin is
The calculation of the oblat e ne ss of t he e arth h as o c cu
pied the attention o f many sinc e t he time of Newt on His
i
calculation was fi g that is the polar diameter was ! n
Huygen s estimated the flat
shorte r than t h e e quatorial
h
st commonly acc e pte d
T
mo
e
tening to be about F 5
W5
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THE E AR TH A GE OI D
pheroid represent ing the earth is the on e calculated in
1866 by A R Clarke for a long time at the he ad of the
P urely astronomical
E nglish Ordnance S urvey (see p
calculation s based upon the e ff ect of the bulging of the
see m to indicat e
e quator upon the motion of the moon
P ro
slightly l ess oblat ene ss than that of Ge neral Clarke
f essor William Harkn ess formerly astronomical director
of the United S tates Naval Obse rvatory calculated it to
be very nearly w35
D u ring rec ent years many
I V Th e E arth a Ge o id
care ful measurement s have bee n mad e on various portions
of the globe and e xt e nsive pendulum test s given to asoer
tain the forc e of grav ity These measure ments d emon
strat e that the e arth is not a true sphere ; is not an Oblat e
spheroid ind eed it s figure doe s not corre spond to that of
any regular or symmetrical ge ometric form As e xplained
in Chapte r I I the e quator parallels and meridian s are
not true circles but are more or less elliptical and wavy
in outline The e xt e ns ive triangulation surveys and the
application of astrophysic s to astronomy and geod esy
make po ssible and at the same time make imperative a
care ful d etermination of the e xact form of the geoid
s
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THE MOTI ON S
OF TH E
E AR TH
The P ythagore an s
maintained as a principle in the ir
philo sophy that the earth rotate s on its axis and revolves
about t he su n B asing the ir theory upo n a priori reason
ing they had little bette r ground s for the ir be lie f than
tho se wh o thought otherwi se Ari st archus (about 3 10
2 50
a Gree k astronomer seems to have been the
first to advanc e t he helioc entric theory in a syste matic
manner and o ne based upon c are ful observations and cal
From this time ho weve r u ntil t he time of
c u latio n s
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HI S TOR I CAL S K ETCH
2 76
Co pernicus the
,
geoc entric theory
was
al m o st universally
ad opted
The geoc entric theory is ofte n called the Ptolemaic sys
tem from Claudius P tolemy (not to be confused with
ancient Egyptian kings of the same name ) an Alexandrian
astronomer and mathematician who see ms to have done
most of his work about the middle of the se cond ce ntury
AD
He seem s to have adopted in ge neral the valuable
astronomical calculations of Hipparchus ( about 180 1 10
The syste m is called after hi m becau se he com
piled so much of t he obse rvations of other astronomers
who had prec ed ed him and invented a most ingenious
“
e picycles
cycles
d e ferents
c entri es
syst e m of
and e ccentric s ( n o w happily swept away by the Coper
nican system ) by which practically all of the known fact s
of the c elestial bodies and their movement s could be
acco unted for and yet assume the earth to be at the c enter
of the universe
Among Ptol emy s contribution s to mathematical geog
ra ph y were h is e mploym ent of th e latitud e and long itud e
of plac es to re prese nt their position s on the globe ( a scheme
probably invented by Hipparchu s ) and he was the first
to u se the terms meridians of longitud e and parallels
I t is from the Lat in tran slation of his su b
of latitude
d ivi sion s o f degrees that we get the terms minute s and
i
i
i
s
h
s
for
c
ntur
e
div
on
had
b
e
e
n
follo
w
e
d
se cond s
e
t
e
(
The S ixty
originating w ith t he Chaldeans S ee p
min u
subdivision s he called fir st small part s ; in Latin
Th e sixty su b
whe nc e our term minute
tae p rim es
divi sion s o f the m inute he called second small part s in
se cond
min u tes secu n dce
w he nc e our te rm
Latin
The Cope rnican theory of t he solar syste m which has
universally displa ced all others get s its name from the
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HI S TOR I CAL S KE TCH
2 78
how s phases just as our moon does and appears larger
The o n ly
w hen in th e cre sc e nt than when in the full
logical conclusion w as that it revolve s aroun d t he su n
again confirming by analogy the Copernican theory Gali
lei was a thorough going Copernican in private be lie f but
was not permitt ed to te ach t he doctrin e as it w as con
sidered un scriptural
As an illustration of the humiliating subterfuge s to
w hich he was co m pe ll ed to re sort in orde r to prese nt an
argument based upo n the heretical the ory the following
is a quotation from an argument he e nt ered into con
c e rning t hree comet s which appe ared in 16 18 He based
h is argument as to the ir motion s upon the Copernican
profe ssing to re pudiate that theory at the same
syst e m
time
S inc e t he motion attribut ed to t he earth which I as
a pious and Chri stian person con sid er most fal se and not
to exi st accommodates it se lf so well to e xplain so many and
such di ff e re nt phe nome n a I shall not fe el sure that fal se
as it is it may not just as d e ludingly corr e s pond with the
phenomena of comet s
One of the best suppo rt ers Of this the ory in t he n e xt
ge neration was Ke pler ( 1571
t he Ge rm an ast ro no
m er and frie nd and succ e ssor of B rahe
His laws of
planet ary motion ( see p 284 ) were of course based upon
the Copern ican theory and led to Ne wt on s d iscovery of
the laws of gravitation
Jame s B rad ley ( 1693 176 2 ) di scovered in 1 727 the
an d t h e supporte rs of th e
aberration of light ( see p
P tolemaic syst em were routed logically though more
than a c entury had to pass be fore the helioc entric theory
be came universally acc epted
s
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AP P E ND I X
GR AV I TY
’
art h s attractive
S inc e the attractive in fl uenc e
in flue nc e for an obj ect
of the m ass of the earth for an obj ect on or near its su r
face is lessened by c entrifugal force (see p 14 ) and in
other ways ( see p
it is more accurate to say that
the force of gravity is the resu ltant of
a The attractive force mutually exi sting bet wee n th e
earth and the obj e ct an d
b The lesse ning influence of c entrifugal force d u e to
the earth s rotatio n
Let u s con sid er these two factors separate ly bearing
in mind the laws of grav itation (see p
particle of matter attract s every other
a E very
particle
h
i
H
nc
point
of
ravity
for
any
g
v
n
obj
ct
e
e
t
e
1
e
e
g
( )
on the surface of the earth is determined by the mass of
The
t he obj e ct it self as well as th e mass of the e arth
obj ect pul ls the earth as truly and as much as the earth
attract s the obj ect The common cent er of gravity of the
e arth and t hi s Obj ect lies some w here between t he c e nt e r
of t he earth s mass and the c enter of the mass of the
obj ect E ach obj ect on the earth s surface then must
have its own inde pend ent common c enter of gravity be
twee n it and the cente r of the e arth s mass The position
of this common c enter w ill vary
i
s
i
n
A
s
e
a
h
obj
ct
var
amount
of
matt
r
fi
t
t
e
e
e
rs
( )
(
law ) and
GR AV I TY is fre quently d efined
as
the
e
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’
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,
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AP P E ND I X
280
b
A
s
h
t
e
( )
th e
’
di st ance of the obj ect from the c enter of
mass varies ( inversely as the square of the
a th s
distanc e )
2 ) B e cau se of thi s principle the po sition of the su n
or moon S lightly modifies the e xact po sition of the center
of gravity just e xplained I t was shown in the d is
although the tidal lesse n in g of
c u ss io n of tid e s that
the we ight of an obj e ct is as yet an immeasurable
quantity it is a calculable one and produc es tides ( see
p
b The rotation of the e arth give s a c e ntrifugal force
to every obj ect on its surfac e save at the poles
i
1
ntrifugal
forc
thu
s
x
r
t
s
a
s
light
lift
i
ng
fl
C
e
e
e
e
n
u
( )
increasing toward the e quator This
e nc e on obj e ct s
lightening in fl ue nce is sufficient to d ecrease the weight
of an obj e ct at the e quator by
of the whole That
is to say an obj e ct w hich we ighs 288 pound s at the
e quator w ould we igh a poun d more if th e e arth did not
rotate D o not infer from this that the c entrifugal forc e
at the pole be ing z ero a body we ighing 288 pound s at t he
not be ing
e quator w ould we igh 289 pound s at the pole
lighte ned by c entrifugal force Thi s would be true if the
The bulging at the e quator d ecreases
earth were a sp he re
a body s weight there by g as compared with the weight
at the poles Thus a body at the e quator has its weight
se
b
cau
s
of
ro
ation
and
by
b
e
cau
e
t
e
lesse ned by 2 1
t im
,9
of greater distanc e from the c e nter or a total of 1 53 of
A
its we ight as compared w ith its we ight at the pole
body we ighing 195 pound s at the pole there fore we ighs
but 194 pound s at the e quator Manifestly the rate of
the earth s rotation d et ermine s the amount of t hi s ce n
I f the earth rotated seve ntee n times as
trif u gal forc e
f ast this force at the e q uator would e xactly e qual the
e r
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AP P E ND I X
282
trif u gal
’
force is S O sm all as compared with the earth s
attraction that this d eviation is not great I t is greatest
at the 4 5th parallel w here it amount s to 5
or nearly
o ne te nth of a d egree
There is an almost e qual d evia
°
tion d u e to the oblateness of the earth At latitud e 4 5
the total d e viation of the plumb line fro m a line drawn
to the c enter of the earth is 11
“
.
’
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.
’
LATI TUDE
I n Chapter I I t he
latitude of a plac e was simply d efined
as the arc of a meridian interc e pted betwee n that plac e
Thi s is true geographical latitud e but
an d the e quator
t he di scu ssion of gravi ty place s u s in a position to und er
st and astrono m ical and ge oc e ntric latitud e and h o w geo
graphi c latitud e is d etermined from astronomical latitud e
Owing to the e lliptical form of a meridian
circle the
verte x of the angle consti tuting t he latit ude of a place is
not at th e center of the globe A port i on of a meridian
circle near the equator is an arc of a smaller circle than
a portion of th e same meridan near the pole ( se e p 43
and Fig
Geoc en tric Latitu de
I t is sometimes of value to spea k
of the angle for med at the c enter o f t he earth by two
lines o ne drawn to th e place whose latitud e is sought
and the other to the equator on t he same meri dian Thi s
is call ed th e geoc entri c lati tud e o f t h e plac e
Astron om ic al Latitu de
The astrono m er asc ertain s lati
tud e from c elestial measurement s by re f ere nce t o a level
line or a plumb line Astronomi cal la ti tude then is the
angle formed bet ween t h e plumb line and th e plane of
the e quator
I n the discu ssion of gravity the las t eff ect o f c ent ri
.
,
,
.
”
,
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.
.
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,
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.
.
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,
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,
,
'
283
LATI TUD E
f ugal f orc e noted was on the dire ct ion o f the plumb line
I t was shown that this li ne e xce pting at the e quator and
po les is deviated slightly toward the pole The eff e ct of
this is to increase correspondingly the as tronomical lati
tude Of a plac e Thus at latitud e
astronomical lati
’
the amount of this d eviation
tude is increased by 5
I f there were no rotation of the earth there w ould be no
°
d eviation of the plumb line and what we call latitud e 60
.
,
.
,
.
.
,
,
°
’
Were the earth to rotate twice
would become 59 54
as fast t hi s latitud e as d ete rmined by the same astronom
’
°
ical instrume nts would become 60 15
I f ad jacent to a mountain the plumb line deviates
toward the mountain because of its attractive influence on
the plumb bob ; an d other de viations are al so observed
such as with th e e bb and flow of a ne ar by tidal wave
These d evi ations are called st ation errors and allowance
must be made for them in making all calcul ations based
upon the plumb line
Geograph ical latitu de is simply the as tronomical latitud e
Were it not
corrected for the de viation of t he pl u mb line
for these d eviations the latitud e of a place would be deter
mined wit hi n a few feet of perfe ct acc u racy As it is
errors of a f ew hundred feet some times may occur (see
p
Cel estial Latitu de
I n the discussion of the celestial
s phere many c ircl e s of th e c elestial s phere were d escribed
in the same terms as circles of the earth The celest ial
are imaginary circles w hich
eq uator Tropic of Canc er etc
correspond to the terrestrial equator Tropic of Cancer etc
Now as terrestrial latitud e is dist anc e in d egrees of a me ri
dian north or south of the e quator of the earth one would
infer that celestial latitud e is the correspondi ng d istance
along a celest ial meridian from the celest ial eq uator bu t
,
,
,
,
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”
,
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,
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,
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,
.
84
APP E NDI X
this is n ot the case Astronomers reckon celestial latitude
from the ecliptic in ste ad of from the celestial e quator As
previously explained the di stance in d egrees from the
c elestial equator is called declination
Cel estial Lo ngitu de is measured in d egree s along the
e cliptic from th e vernal e quinox as the initial point meas
°
u red al ways east w ard t he 360 of the e cliptic
°
I n ad dition to the c e lestial pole 90 fro m the cele stial
°
eq uator there is a pole of the e cliptic 90 from t h e e cliptic
A c elestial body is thus located by re fere nc e to two set s of
circles and two poles
I
h
i
e
e
d
cl
ation
from
c
l
tial
quator
and
po
i
a
s
n
t
e
e
s
s
t
e
)
(
tion in relation to hour circles as c elestial meridians are
commonly called (see Glossary )
I
h
b
c
l
s
tial
latitud
from
cliptic
and
c
l
e
s
t
ial
e
t
s
e
e
e
t
e
e
( )
longitude from e cliptic meridians
.
.
,
.
,
.
,
,
.
.
,
.
”
.
KE P LE R
S LAWS
’
These
three laws find their explanation in t he laws of
gravitation al though Ke pler discovered the m before New
ton mad e the di scovery whi ch h as immortaliz ed his name
First Law The orbi t of each planet is an ellipse having
the su n as a focus
S econd Law The planet moves about the su n at such
rates that the straight line connect ing the ce nter of the
su n with th e c e nt e r of t he planet ( thi s line is call ed th e
planet s rad ius vec tor) swee ps over e qual areas in equal
times (see Fig
The di stanc e of the e arth s journey for each of the
twelve months is such that the ellipse is divid ed into
twelve equal areas I n the di scu ssion of seasons we
obse rved ( p 1 69) that whe n in pe rihe lion in January the
,
.
.
,
.
.
’
.
’
.
.
,
,
AP P E ND I X
286
di stance Of a planet to the su n we have
three of the quantities for our proportion calling the
and c an find the year of the planet ; o r
e arth s year 1
knowing the time of the planet we can find its distance
the
su n an d
the
,
,
’
"
,
,
.
,
M OTI ON S OF THE E A R TH S A X I S
’
I n the
chapter on se ason s it was stated that exce pting
for e xceedingly S lo w or minute changes the earth s axis
at one time is parallel to it se lf at other timm There are
three such motion s of the axis
P rec ess io n o f th e E q u in oxes
S inc e the earth is slightly
oblate and the bulging e quator is tipped at an angle
°
of 235 to the e cliptic the sun s attraction on this rim
te nd s to dra w th e axi s over at right angle s to t he e quator
The rotation of the earth however t e nd s to keep the
axi s parallel to it se lf and t he eff ect of t he ad ditional accel
eratio n of th e e quator is to cau se th e axi s to rotate S lo wly
keeping the same angle to the ecliptic however
At the time of Hipparchu s (see p
wh o di scovered
t hi s rotation of the axis the present North star Alpha
°
Ursa Minori s was about 12 from the true pole of the
c elestial sphere toward which t he axi s poin t s The course
wh ich the pole is taking is bringing it somew hat nearer
°
the pole star ; it is n o w about 1 15 away but a hundred
years henc e will be only half a d egree from it The period
of thi s rotation is very long about
years or
Nin ety d egrees from the e cliptic is the pole
e ach ye ar
of t he ecliptic about w hich the pole of the c ele st ial equator
rotates and from which it is di stant
As t h e axi s rotat e s about the pole of the ecliptic the
point where t he plane of t he e quator inte rse ct s the plane
’
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,
'
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,
,
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,
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,
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’
,
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,
,
MOTI ONS OF THE E AR TH S AXI S
287
’
of the e cli pt ic that is the eq uinox grad ually shi ft s aroun d
westward
S inc e the vernal e quinox is at a give n point
in t he e arth s orbit one year and the ne xt year is reached
a little ahead of w here it was the year before the term
i
T
h
i
s
s
r
c
u
appropriat
id
r
al
s
n
o
x
e
e
e
e
e
h
s
e
e
s
i
o
n
o
t
e
e
p
f
q
year ( see p 132 ) is the time re quired for the earth to
make a complete revolution in its orbit A so lar or tropi
cal year is the inte rval from one vernal e quinox to the
ne xt vernal eq uinox and S ince the e quinoxes prec ed e
a tropical year end s about t wenty m inutes be fore the
e arth reache s the same po int in it s orbit a se cond time
As is S hown in the di scussion of t he earth s revolution
D
p
arth
i
in
p
rih
e
lion
c
mb
r
3
1
making
t
h
e
s
e
e
e
e
e
(
the northern summer longer and cooler day by day than
it would otherwi se be and the winter short er and warmer
The traveling of the vernal equinox around the orbit
however is grad ually shift ing the date of perihelion so
that in ages yet to come perihelion will be reached in July
and thus terrestrial climate is gradually changing Thi s
perihelion point (and with it aphelion ) has a S light west
e ach year making with
ward motion o f its o wn of
a
the ad dition of t he prec e ssion of the e q uinoxes of
total S hifting of the perihelion point (see Apsides in
At this slow rate
years
the Glossary ) of 1
must pass before perihelion will be reached July 1 The
amount of the ellipticity of the earth s orbit is grad ually
d e creasing so that by t he time this shifting has taken
place the orbit will be so nearly circular that there may be
but sl ight climatic eff ect s of this S hift of perihelion I t
may be of interest to note that some have reasoned that
ages ago the earth s orbit was so e llipt ical that the
northern winter occ u rring in aphelion was so long and
c old that gre at g lacie rs were formed in northern North
,
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’
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”
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’
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,
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,
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’
,
,
288
AP P E ND I X
America and E urope whi ch the short hot summers could
,
not melt The fact of the glacial age cannot be di sputed
but this explanation is not generally acce pted as sati s
factory
Nu tatio n of th e P ol es
S everal set s of gravitativ e in flu
en ces cau se a slight pe riodic motion of the earth s axis
toward and from the pole of the e cliptic I nst ead of
°
preceding around the circle 4 7 in diameter the axis
makes a slight wavelike motion a nodding as it is
called The principal nutatory motion of the ax is is
d u e to the fact that t he moon s orbit about th e earth
°
inclin
d
e
5
8
h
to
t
cliptic
glid
about
h
cliptic
in
e
e
s
t
e
e
e
(
)
18 years 220 days just as the earth s e q uator glid e s about
the e cliptic onc e in
years Thus through period s
o f nearly nin et ee n years each th e obli quity of t he e cliptic
se
e
1
1
s
s
pp
14
g
r
adually
incr
a
and
d
cr
a
again
8
7
e
e
e
s
s
e
e
(
)
The rate of thi s nutation varies somewhat and is always
very slight ; at present it is
in a year
W andering of th e P ol es I n the di scussion of gravi ty
s
w
h
p
it
s
hown
that
any
chang
in
e
po
ition of
a
s
e
t
(
particles of matter eff ect s a change in the point of gravity
common to them S light changes in the crust of the earth
are con stantly taking plac e not simpl y t he grad ational
c hanges of we aring do wn mountain s and building up of
d epositional features but great diastrophic changes in
mountain structure and continental change s of level
Be sid es these physiographic changes met eo rological con
d ition s must be factors in displac eme nt of masses the
accumulation of snow th e fl uctuation in the leve l of great
rivers etc For these reason s minute changes in the
po sition of the axis of rotation must take place within the
S inc e 1890 such changes in the po sitio n of the axis
earth
within the globe have bee n obse rved and re corded The
.
,
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’
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,
”
,
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’
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.
.
AP P E ND I X
290
M ATHE MATI CAL TR E ATME NT O F TI D E S
The
xplanation of the cau se of tid es in the chapter
on that subj ect may be relied upon in every particular
although mathematical d etails are om itted The mathe
m atical treatme nt is diffic ul t to make plain to those wh o
have not studied higher mathe matic s and physic s S im
i
s
lifi
s
s
s
s
s
a
w
s
:
much
po
ibl
it
follo
a
e
a
e
d
p
Let it be born e in mind that to find t he cause of tid es
we must find u n balanc ed forces whi ch chan ge the ir position s
S urfac e gravity over th e globe varies slightly in diff erent
plac es being less at the equator and greater toward the
poles As shown elsewhere th e forc e of gravity at the
e quator is less for tw o reasons :
a B e cau se of great er c e ntrifugal forc e
b Be cause of the oblat en ess of the earth
h
C
e
e
t
a
ntrifugal
forc
b
ing
gr
at
r
at
quator
than
e
e
e
e
e
( )
e lse w here there is an unbalanc ed forc e w hich must cause
th e waters to pile up to some exte nt in th e e quatoria l
region I f c entrifugal force were sometimes greater at the
e qu a tor and sometim e s at th e pole s there w ould be a cor
responding S hi ft ing of the accumulated waters and we
and it w ould be an imm e nse one
should have a tid e
B u t we know that thi s unbalanc ed forc e doe s not change
its po sition and henc e it cannot produc e a tide
h
E
s
s
s
b
xactly
t
am
cour
of
r
a
oning
appl
to
e
e
e
e
i
e
s
h
t
e
( )
unbalanc ed forc e of gravity at the equator d u e to its
greater di stanc e from the center of gravity The po sition
of this unbalanc ed forc e does not shift and no tid e results
S inc e t he earth turn s on its axi s und er th e su n and
moon any unbalanc ed forc es they may produc e will neces
sarily shift as diff erent portions of t he e arth are succ es
Ou r problem the n
sively turned to w ard or fro m the m
e
,
.
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,
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,
MATHE MATI CAL TR E ATME NT OF TI D E S
2 91
is
to find the cause and dire ction of the unbalanced forc es
produc ed by the moon or su n
I n Figure 1 14 let CA be the acc eleration toward t he
moon at C du e to the moon s attraction Let B D be
.
,
’
,
.
Fig
.
1 14
acc eleration at B Ne w B is nearer the moon than
C so B D will be great er than CA sinc e th e attraction
varies inverse ly as the square of the di stance
From B con struct B E e qual to CA
Comparing forc es
B E and B D the latter is greater
Completing the paral
lelogram we have B F D E
Now it is a S imple d emonstra
tion in physic s that if two forc es act u po n B o ne to F and
th e other to E the resultant of th e t wo forc es will be th e
d iagonal B D S inc e B E and B F combined result in B D
it follo ws that B F re present s the unbalanced force at B
At B then there is an unbalanced forc e as compared
with C as re presented by B F At B the unbalanced
force is re presented by B F
Note the pu llin g di rection
in which these unbalanced force s are exerted
t he
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,
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,
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,
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,
,
’
.
’
’
.
.
NOTE
Fo r p u rp oses o f illu s t ratio n th e distan c e o f th e m oo n
Th e d is tan c e CA is
re p resen te d in th e figu res is g rea t ly d im in ish ed
t ak en arb it rari ly, lik ewise th e distan c e B D I f CA w ere lo nge r,
h o w e v e r, B D w o u l d b e still lo nge r ; an d w h ile givin g CA a d iff e re n t
len gth , w o u ld m o dify th e fo rm o f th e diagram , th e m ath em at ic al rela
t io ns w o u ld rem ain u nch an ged B ec au se o f th e sh o rt distan c e giv en
CM in th e figu res , th e d iff eren c e b e tw e e n th e B F in F igu re 1 14 an d B F
Th e d iff e ren c e b etw ee n th e
in Figu re 1 15 is g reatly e xag ge rated
u n b alan c e d o r t id e p ro d u c in g fo rc e o n th e sid e to w ard th e m o o n an d
th at o n th e o ppo site side is app ro xim ately 046 7 B F (F ig
.
.
.
.
.
-
.
.
AP P E ND I X
2 92
I n Figure 1 15 B is
farther from the moon than C henc e
B E (e qual to CA) is greate r than B D and t h e unbalanced
force at B is B F directed a way fro m the moon A study
of Figures 1 14 and 1 15 will S how that the un balanc ed forc e
on the sid e toward s t he moon ( B F in Fig 1 14 ) is slightly
greater than t he unbalanc ed forc e on the S l Cle opposite the
The d iff ere n ce howe ver is ex
moon ( B F in Fig
,
,
,
,
.
.
.
,
,
Fi z
.
u
s
light and the tid e on the opposite sid e is prac
tically e qual to the tid e on the sid e toward the attracting
body
Combining t he arro w s show in g the dire ction s of the u n bal
an c ed forc es in th e tw o figure s we have the arro ws show n
c eed in gly s
,
.
,
Fig
.
rrG
in Figure 1 16 The distribution and d ire ction of the u n
balanc ed forc es m ay be thu s summarized : The di sturbing
force produc es a pull along AA and a squeez e along B B
.
’
’
M athematica l Astro no my, B arlo w
an d
B ryan , p 3 77
.
.
AP P E ND I X
294
nc e between t he sign s and the const e llations of the zodiac
is that t he star clu sters are of une qual length some more
°
than 30 and some less whereas the signs are of uniform
length The po sitions and widths of th e signs and con
e
,
,
.
Fi z
stellatio n s
s
ho wn in
with th e
Figure 1 1 7
date
.
117
w he n th e
su n
e
nters e ach
are
.
first S ign was named after the ram probably
be cause to the ancient Chald eans where t he name seems
to have originated thi s was th e month of sacrific e The
I t is re pre
su n is in Ari e s from March 2 1 until April 20
Aries , t he
,
,
,
.
,
.
ZOD I AC
THE
nted by a
glyphic ( T )
sm
se
all pict u re of a ram
295
or by a hiero
fl
.
cond sign ( i215? was dedicated to the
bull I n ancie nt times thi s was the first of the signs
the vernal e quinox be ing at the beginning of this S ign
According to very ancient myt hology it w as t he bull that
drew the su n along its furrow
in the sk y There
are howe ve r many other theori es as to the origin of t he
d esignation The su n is in Taurus from April 20 until
Tauru s, the
se
.
,
.
.
,
,
.
May
21
.
ign signifies tw ins M and get s its
name from two bright stars Cast or and P ollux whi ch u se d
to be in this S ign but are now in the S ign Canc er The
su n is in Gem ini from May 2 1 until Jun e 22
w as named after the
Can c er the fourth S ign ( age
c rab probably from t he fact that whe n in thi s S ign th e
Th e
su n retre at s back again crablike toward th e south
su n is in Canc er from Jun e 22 un til July 23
Leo , signifyin g lie n is the fifth S ign
se
s
and
m
e
W
to have been ad opted becau se the lion usually w as u sed
as a symbol for fire and w he n t he su n w as in Le e the
hottest weather occurred The su n is in thi s S ign from
July 23 un til August 23
V irgo , t he virgin
h
s
r
f
r
to
hald
an
myth
of
e
e
t
e
e
C
g
th e d esc e nt of I shtar into had es in se arch of h er husband
The su n is in Virgo from August 2 3 until S e pt ember 23
The foregoing are the summe r S igns and conse quently
the corresponding const ellations are o u r w inte r co n stel
latio n s
I t mu st be re membered that t he S ign is always
°
to t he
about 30 (the e xtre me length of the D ipper
west of the constellation of the same name
5
Libra, the balanc e s
i
appropriat
ly
got
nam
e
t
s
e
33
from the fact that the autum nal e q uinox or e q ual balan c
Gem ini , the t hi rd
S
,
,
,
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,
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,
,
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,
,
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,
,
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.
»
.
.
,
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.
,
,
AP P E NDI X
296
in g
of day and night occu rred whe n the su n w as in the
conste llation thus named the B alanc es The su n is now
in Libra from S e ptember 23 until October 24
T
S c o rpio is th e e ighth S ign ( fin
h
s
corpion was a
e
e
symbol of darkness and was probably u se d to re present
the shorte ning of days and lengthe ning of n ight s
The
su n is now in S corpio from Octobe r 24 until Novembe r 23
Sagittariu s me aning an archer or bowman is
as
a Ce ntaur with a
sometime s re prese nted
bow and arrow The su n is in thi s S ign from November
2 3 until D e c e mbe r 2 2
Capric o rn S ignifying goat is Ofte n re prese nted as hav
I t probably has its origin
ing t he tail of a fish ( Q 2
as t he m yt hological nur se of t h e youn g solar god
The
su n is in Capricorn from D e c e mbe r 22 unt il January 20
Aq u ariu s the wat er be arer
i
s the e l eve nth S ign
Q
an d probably h as a met e orological origin be ing a ssociated
as t h e cau se of t he wint e r rains Of Medite rrane an coun
trie s The su n is in thi s S ign from January 20 un til
Fe bruary 19
P isc es is the last of the twe lve sign s
I n accordance
with the meaning of the term it is re presented as two
W
I t s significanc e w as proba bly th e same as
fi shes
The su n is in thi s S ign from Fe bruary
the w at er be arer
19 unt il th e ve rnal e qu inox March 2 1 w he n it h as com
i
f
s circuit
h
O
t
l
labor
s
only
to
b
gin
ov
r
e
t
e
d
t
e
e
e
p
again
The twe lve sign s Of the ancie nt Chine se zod iac were
dedicated to a quit e d iff erent set of animal s ; be ing in
order the R at the Ox the Tiger the Hare t he D ragon
t he S erpe nt t he Horse t he S hee p t h e Monk ey th e Hen
The E gypti an s adopted w ith a f ew
th e D o g and t he P ig
change s t he sign s Of th e Gree ks
,
.
'
.
,
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.
,
Q
,
’
.
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,
,
,
.
.
-
,
,
.
.
.
,
“
-
.
,
,
”
,
.
,
,
,
,
,
,
,
,
,
.
.
,
,
,
,
AP P E ND I X
298
Taurus the arms were give n ove r to Ge mrm the stars of
Canc e r were to rule the breast the heart was presided
ove r by Le o and so on d own to P i sce s which was to rule
No w anyone wh o was born whe n t he moon was in
the feet
Aries would be strong in the head inte lle ctual ; if in Taurus
he would be strong in the neck and self willed etc
More
over sinc e the moo n makes a circuit of the signs Of the
zodiac in a month according to h is simple scheme whe n
the moon is in Aries the head is e specially aff e cte d then
di se ase s of the head rage (or is it then that the head
is stronger to resist di se ase
and during the next few days
w he n the moon is in Taurus beware of aff e ctions of the
nec k and so on down the list The very simplicity of this
sche me and e ase by w hich it could be re me mbered led to
its s peedy ad option by the masses w ho from time imme
,
,
,
,
.
,
,
-
.
,
,
,
,
,
.
morial have sought e xplanations of variou s phenomena
by re ferenc e to c elestial bodies
No w there is n o astronomical or geographical ne cessity
for conside ring Aries as the first S ign of the zodiac Ou r
year begin s practically with the ad vent of the su n into
Capricorn
the beginn ing of t he year was mad e January
1 for thi s ve ry purpose
The moon is not in any pe culiar
po sition in relation to the earth March 2 1 any more than
it is Dec embe r 23 I f w he n the cale ndar w as revised the
numbering of the signs of the zodiac had been changed
al so the n Capricorn the divinit ie s of w hich n e w rule the
knees would have bee n mad e to rule t he head and the
whole artificial sche me would have been changed ! B esides
th e S ign Capricorn does not includ e the con ste llation Capri
corn so with the precession of t he equinoxes the su btle
in fluenc es once assi gned to the heavenly bodies of one
conste llation have bee n shifted to an e ntirely d iff erent set
o f stars ! The association of storms with the s un s cross
.
.
.
.
,
,
,
,
,
,
’
ZODI AC
THE
299
ing the e quinox and with the angle the cusps of the moon
S how to th e observe r (a purely ge ometric position varying
w ith the po sition of the observer ) is in the same class as
bad luck atte nding the taking up of the as hes afte r the su n
has gone do wn or t h e wearing of charms agains t rheuma
tism or the
e ye
e vil
.
Th e
fau lt
B u t in
dea r B ru tu s is
o u rsel ves , th at w e
,
,
no t
in
o u r stars,
are u n d erlings
”
.
AP P E ND I X
300
P R ACTI CAL
I N MATHEMATI CAL
WOR K
GE OGR AP HY
work in this subj ect has been suggested directly
by implication or by suggestive q ueries and problems
throughout the book No instrument s of spe cific char
ac ter have bee n suggested for u se exc e pting such as are
compasse s an
as a grad uated q uad ran t
e asily provid ed
isosc eles right triangle etc
I nterest in the subj ect w ill
be greatly augme nted if th e following simpl e in st ruments
or S imilar de vices
are
mad e or pur
chased and u sed
Concrete
,
,
.
.
,
,
,
.
,
,
,
.
TO MAK E
A
S UN D I AL
This is not espe
and
c ial ly d ifficult
be
may
aecom
l
i
h
s
e
in
s
v
ral
d
e
e
p
8
Fig
ways
A simple
plan is sh own in Figure 118 An gle B AC should be the
c c latitude of th e plac e that is t he lat itud e subtract ed
from
though this is not at all essential The hour
lines may be marked Off accord ing to two syste ms for
standard time or for local time
S tandard Tim e D ial
I f you wi sh your dial to indicate
cl ock time as corre ctl y as po ss ible it w ill be ne c e ssary to
c on sult th e anale mma or an almanac to asc ertain t he e q ua
tion of time when the hour lines are d rawn S inc e t he su n
is ne ither fast nor slow April 14 June 15 S e pte mber 1 or
De c e mber 2 5 those are t he ea si est days on w hich to lay
o ff th e hours
On o ne of those dates you can lay the m o ff
according to a re liable time piece
.
11
.
.
-
,
,
.
,
.
.
,
.
,
,
,
.
.
,
AP P E NDI X
302
hadow is north One hour later mark the S hadow line
for the I hour line two hours later mark the I I hour line
etc
This dial will indicate the apparent solar t ime of
your meridian
You can set your watch by it by first
conve rtin g it into mean solar time and then into standard
t ime (This is explained on pp 128
I t should be noted that these two sundial s are e xactly
t he same for pe rson s who u se local time or li ving on the
standard time meridian use standard time
S
.
,
,
.
.
.
.
,
,
,
.
,
TH E S UN B OAR D
The
uses of the mounted quad rant in determining lat
shown in t he chapt e r on se asons (se e p
.
F ig
.
1 19
J P aul Ge ode of the University of Chicago has
designed a very convenient little in strument which an
swers w ell for thi s and other purpo ses
A vertically placed q uadrant enables on e to asc ertain
Dr
.
.
,
,
.
P R AC TI CAL
303
WOR K
al ti tude of the su n f or determining latitu de
c u latin g the h eights of obj e c ts
B y means of a graduate d circ le
place d horiz on tall y the azimuth
of the su n (see Glossary ) may
be ascer taine d A simple vernie r
h
iv
azimuth
r
ading
e
e
s
t
o
e
s
t
g
quar ter degrees I t al so has a
device for showing the area cov
ere d by a sunbea m of a given
size and h e nce its heatin g power
th e
.
.
.
.
,
THE HE LI ODON
Thi s appliance was designed by
Mr J
of th e Me dill
High S chool Chicago I t vividly
il lus tra tes th e apparen t pa th of
th e su n at th e e q uinoxes an d S 01
i
m
F
r
h
T
e points
stices at any latitude
of sun rise and su nset can al so be S hown and hence
le ngth of the longest day or nigh t can be calcula te d
.
.
F Morse ,
.
.
,
.
.
.
304
AP P ENDI
X
WHAT KEE PS THE ME MB E RS OF THE S OLAR
S YSTEM I N THE I R OR B I TS ?
Wh en a body is thrown in a d irection paralle l to the
horizon as t he bullet fro m a le vel gun it is acted upon by
two forc es :
a
T
h
e proj e ctile forc e of th e gun AB
i
F
( )
( g
b
T
h
e attractive forc e of t he earth AC
( )
The course it will actually take from point A is the
’
diagonal AA Whe n it reaches A the forc e AB still
,
,
.
,
,
.
.
’
.
F it
.
mx
act s ( no t considering the friction of the air ) impell ing it
’
in the lin e A B
Gravity continues to pull it in the line
”
A C and t he proj e ctile t ake s t he d iagonal dire ction A A
and makes the curve ( not a broken line as in the figure )
AA A
I t is Obvious fro m thi s diagram that if t he im
pelling force be suffi ciently great line AB will be S O long in
relation to line AC that the bullet will be drawn to the
earth just e nough to k ee p it at th e same di stanc e from
the surfac e as that of its starting point
The amount of such a proj e ct ile forc e near the surfac e
of the ea rth at the e quator as would thu s kee p an obj e ct
,
’
’
’
’
’
”
,
.
AP P E ND I X
306
forc e of rotation (c) t he revolution of t he e arth
h
d
i
e
h
e
t
r
volut
on
of
moon
frict
on
of
air
t
e
i
h
t
h
e
e
t
e
)
(
()
a variable quantity impo ssible of calculation with abso
lute accuracy (f ) the ine vitable swe rving in the air by
reas on of its current s and varying de nsity and (g) the
in fl ue nce on t he course by the attraction of t he su n and
planets I n ad dition to these mathe matical calculations
as to dire ction and proj ectile forc e there would be th e
problem of ( h ) supply of air ( i ) air pressure to whi ch our
bodies through the evolution of ages have be come adapted
h
h
t
e
mom
ntum
th
wh
ch
would
trik
e
into
t
s
e
e
i
w
w
i
e
( j)
“
moon if we did aim right etc
R eturning to our original proble m we may notice that
if the bullet were fired horizontally at a distan ce of
m iles from the surfac e of the earth the pull of gravity would
be on ly o ne fourth as grea t ( se cond law of gravitation )
and the proj e ctile would not need to take so terrific a speed
to revolve around t he earth As we noticed in the di scus
sion of Mars ( see p
the sate llite P hobo s is S o near
its primary
miles from the surface that it revolves
at just about the ra te of a can non ball making abo ut three
revolutions while the planet rotates once
Whi le allusion has been m ad e o n ly to a bullet or a moon
in noticing the application of the law of proj e ctiles the
principle applies eq ually to t he planet s Governed by the
law here illustrated a planet will revolve about its prim arV
in an orbit varying from a circle to an elongated ellipse
He nc e we conclud e that a combinat ion of proj e ctile and
attractive forc es kee ps the membe rs of the solar syste m
in their orbits
trifu gal
,
,
,
,
,
,
,
.
.
,
,
,
,
.
,
,
,
,
.
.
,
,
,
.
,
,
.
,
.
.
FOR MULAS AND TAB LE S
307
FOR MU LAS AN D TAB LES
S YM B OL S CO MMON L Y E MP LO Y E D
There
v ral symbols which are generally used in
works dealing with the earth its orbit or some of its other
properties To the follow ing brie f list of these are ad ded
a few mathematical symbols employed in thi s book
which may not be familiar to many who will u se it The
general plan of using arbitrary symbols is shown on page
14 whe re G re prese nts un iversal gravitation and g re pre
sent s gravity
C re present s centrifugal force and c c entri
fugal forc e du e to the rotation of the earth
Phi
S
latitud
e
)
q (
2: ( E psilon ) Obli quity of the e cliptic als o eccentricity of
an e llipse
n ( Pi ) t he nu mber which w he n multipli ed by the diam
a circle equals the circumference ; it is
et er of
nearly
nearly
a ( De lta ) d eclination or distance in d egrees from the
c elestial e quator
cc
varies as ; 2: 0: y means a: varies as y
i
:
s
s
is less than ; a:
m
an
s
a
l
e
s
than
e
y
y
a
:
s
i
s
e
m
a
gr
at
r
than
e
n
e
is greate r tha n ; a:
y
y
are se e
,
.
,
.
'
,
.
.
,
,
,
.
'
,
,
,
.
.
.
.
FOR M ULA s
The Ci rcle
r
d
rad ius
diameter
.
.
and
S phere
circumference
area
.
.
308
AP PE ND I X
7!
m
2
area
surfac e of s phe re
volume of sphere
.
2
4 7rr
m
fi
"
.
n
arly
e
(
)
.
The Elli pse
major
o
oblateness
i
i
i
e
e
m
nor
ax
cc
ntric
ty
e
s
5
r: ab
area of ellipse
1
;
a
b
.
.
.
.
z
a
_ bz
The E arth Com pared with Othe r B odies
rad ius of the body as compared w ith the
rad ius of the earth Thus in case of t he moon the
1081 t he earth s radiu s
moon s rad ius
3959
and P
48g?
»
P
the
.
,
’
’
,
P
2
,
urface of body
e arth
as
compared with that of
th e
volume of body
earth
as
compared with that of
the
s
.
“
P
.
s
a th
e r
.
urface gravity
as
compared
w ith
that of the
310
AP PEND I X
GEOGRAPHI CAL
t
*
CONSTANTS
Eq u a o rial sem i axis
-
in fee t
in m e te rs
in m iles
P olar sem i axi s
in fee t
in m e te rs
-
.
Oblate ness o f e arth
Circ u m fe re n ce o f eq u ato r (in m il es )
Circ u m fe ren ce th rou gh po les ( in m iles )
’
Area o f e arth s su rf ace , sq u a re m iles
V o lu m e o f e arth , cu bic m iles
Mean density ( Hark ness )
S u rface de ns ity ( Hark n ess )
Obliq u ity o f e clip tic (see page 1 18 )
365 d 6 h 9 m
S idere al year
Tro pical year
365 d 5 h 48 m
S ide re al d ay 23 h 56 m 4 09 s o f m e an so lar time
D is tan ce o f e art h to su n , m ean ( in m iles )
Distan ce o f e art h to m oo n , m e an (in m iles )
8
l
.
76
5 576
.
.
.
.
.
23
.
.
.
°
.
.
.
S
.
or
s
.
or
27
’
s
d
d
.
.
.
.
ME AS UR ES OF LENGTH
S tatu te m ile
Nau tical mile ,1 o r k no t
Germ an sea m ile
P ru ss ian m ile , la w o f 186 8
No rwegian an d S wed is h m ile
D an is h m ile
R us sian w e rst , o r ve rs ta
'
Mete r
Fath o m
’
Lin k o f su rve yo r s chain
Dim ens io ns
1866
of
th e
th
ea r
are
u po n
s p h e ro id
.
h
S
a
t
C
o
a
s
t
n
i
t
t
es
t
fi
n
b
e
U
e
d
A
s
e
e
d
d
1
y
“
th e Clark e
an d
Geod e tic S u rv ey
.
of
AP P E ND I X
3 12
TAB LE OF NATURAL TANGE NTS AND COTANGE NTS
Co t
Tan
Co t
Tan
GLOSS ARY
t
t
t
t
t
Aberrati o n , th e app are n d isplac em e n o f s u n , m oo n , plan e , o r s ar pro
du ced as a res u l an o f (a ) th e o rbi al velo c i y o f th e ea r h , and ( b )
ro m th e h eave n ly bo d y
th e ve lo ci y o f ligh
Ac c el erati o n , in c re ase o r e x ces s o f m e an m o io n o r velo c i y
Al ti tu de , e le v a io n in d eg rees (o r an gle o f e le v a io n ) o f an o b e c ab o ve
th e h o riz o n
An al e m m a , a s cale sh o w in g (a ) th e m e an eq u a io n o f im e and (b)
t h e m e an d e c l in a io n o f t h e s u n f o r e ac h d ay o f th e year
’
Ap h eli o n (5 re li o n ) , th e po in in a pla ne s o rb i w h ic h is ar h es
ro m th e S u n
’
Ap o gee (Ep 0 je ) th e po in
ar h es
ro m th e e ar h in an y o rbi ;
’
in th e m oo n s o rbi
u s u a lly ap plie d to th e po in
ro m th e
ar h e s
t t
tf
t
t
t
.
t
t
t
t
.
j t
.
t
t
f
t
.
t
t
t
f t
t
'
.
t f t
t
,
th
e ar
t f
t
tf t
t
tf
.
App are n t
D ay
App are n t ( so l ar) ti m e , see Tim e
’
Apsi d e s (ap S i d ez ) , line o f , a l ine co n ne ctin g p erih elio n and ap h el ion
’
’
of
a p l an e t s o rb it , o r pe rigee a n d apo gee o f a m oo n s o rbit
Aps ides is plu ral f o r aps is , w h ic h m e an s th e po in t in an o rbit
n e are s t to th e p rim a ry o r fa rt h es t f ro m it
Arc , p art o f a c ircle ; in geogra ph y, p art o f th e c ircu m fe ren ce o f a
c irc le
As tero i ds , ve ry s m al l p lanets
A large n u m be r o f as tero ids revol ve
a ro u n d th e su n be t w ee n t h e o rb its o f Mars an d J u p ite r
Au tu m n al e q u i n o x, see E q u ino x
Axis , th e l ine abo u t w hic h an o b j e c t ro ta tes
’
Az i m u th ( dz l muth ) th e ang u l ar d is tan ce o f an o bj ect fro m th e celes tial
m e ridian o f th e plac e o f th e o bse rv er to th e c e les tial m e rid ian o f
th e o bj e c t Th e az im u th o f th e su n is th e d is tan ce in d egrees f rom
its po in t o f ris in g o r se ttin g to a sou th po in t o n th e h o riz o n
Cel esti al sp h ere, th e app are n t h o ll o w s p h ere in w hic h th e su n , m oo n ,
s o l ar
d ay,
see
.
.
.
.
.
.
.
.
.
.
.
n
t
s
l
a
e
,
p
Ce nter
of
t
co m e s, an d s tars see m
th e
i
a
ty
r
v
g
bo d ies ) balan ces
i
n
o
p
t
to be lo c a
abo u
t
ted
w h ich
.
a
b od y
(o r
of
gro u p
.
i
w
r
i
u
l
f
n
a
a
r
o
m
t
f
n
f
a
o
r
ce
t
e
d
a ce n te r
a
)
g
g
y
(
C n trip et l f r e ( S e n tri p e tal ) a fo rce te n d in g to w ard a ce n te r
l
f
h
l
k
h
r
i
i
i
s
o
t
i
l
c
f
es
t
o
u
r
n
c
a
m
er
id
a
n
e
ce
a
e
s
h
t
Co l
(
p
p
p e re
tw o p ass in g th ro u gh th e eq u in o x es an d tw o t h ro u gh th e so ls tices
Ce n trif u gal f o rc e
a
e
’
se n
,
.
’
o c
,
.
u re s
,
.
C o nj u n c ti o n ,
see
S yz ygy
.
GLOSSARY
315
Coperni can syste m (k c per h i can ) , the th eory of the solar system
ad van ced by Co pe rni c us ( 14 73 1 54 3 ) tha t th e su n is th e ce n te r o f
th e so lar system , th e plan e ts ro tating o n t h e ir axes an d re vo l ving
aro u n d th e s u n
S ee Heliocen tric th eo ry
Coti d al li n e s , lines p ass ing th ro ugh places that ha ve high tide at th e
sam e tim e
'
—
.
.
.
.
D ay
.
AS T R ON OM I CAL D AY , a period eq u al to a m e an so lar d ay , re ck o ned
fro m noo n and d ivided in to tw enty fo u r h o u rs , u s u ally nu m bered
fro m o ne to twenty fo u r
CI V I L D A Y , th e sam e as an ast ro n o m ical d ay e xce ptin g that it is
re c k o ne d f ro m m id n igh t
I t is also d iv ided in to twe n ty fo u r
h o u rs us ually n u m be red in tw o se ries , f rom o n e to t w elve
S I D E R E A L D A Y th e in te rv al be tw een two su c cess iVe p as sages o f a
Th e z e ro
celes t ial m e rid ian o ve r a give n terres t rial m e rid ian
m erid ia n fro m w h ic h th e s ide real d ay is re c k o n ed is th e o ne
i
n
h
h
i
h
h
h
a
ss
t
r
ou
h
F
i
r
s
t
n
t
o
f
A
r
i
es
T
l
e
n
t
o
f
t
e
t
e
o
e
p
g
g
g
p
s ide re al d a
s
h
i
s
T
h
s
i
i
s
i
v
a
l
a
i
23
m
e
d
e
r
e
d
e
d
5
6
d
d
y
y
in to t we n ty fo u r h o u rs , e ac h S h o rte r t h an th ose o f th e civ il o r
as t ro n o m ical d ay ; t h e y are n u m be red fro m o n e to t we n ty fo u r
S O LA R D A Y
Appa rent solar da y, th e in te rval be t wee n tw o s u ccess ive p as s ages
’
o f th e su n s ce n te r o ve r th e m e rid ia n o f a place ; t h a t is
fro m
su n n oo n to th e n e x t s u n n oo n ; this varie s in le ng th f ro m 23 h
59 I n
s to 24 h 0 m 30 8
M ea n s olar da y, th e average in te rval be tw een s u c cess ive p as s ages
’
o f th e su n s ce n te r o ve r th e m e rid ian o f a place ; th at is , th e ave r
age o f t he le n gt h s o f all th e so lar d ays o f th e ye ar ; thi s a ve rage
is 24 h as we co m m o nly re c k o n c ivil o r clo c k tim e
D ec li n ati o n is th e distan ce in deg rees o f a ce les t ia l bo dy fro m th e
cele st ial eq u ato r
De clin atio n in th e celes tial S p h ere co rre s po n d s
to la titu de o n th e e a rt h
’
Ecc e n tric ity ( 61: S en tri s I ty ) , see E ll ipse
’
Eclipti c (e k l l p tik ) th e p ath o f th e ce n te r o f th e su n in its app are n t
A gre at circ le o f t h e ce les tial s p h ere
o rb it in t h e celes t ial s ph e re
°
’
w h ose pla ne fo rms an angle o f 2 3 27 w ith the pl ane o f th e eq u ato r
Th is in cl in atio n o f th e pl a ne o f th e ec lip tic to th e plane o f th e
°
Th e po in ts 90
eq u ato r is cal led th e obli q u i ty o f th e e c lip tic
fro m th e ecliptic are called th e pol es o f th e ec liptic Celes tial
la titu de is m eas u red fro m th e e c lip tic
El li pse , a plane figu re bo u nd ed by a cu rved line , eve ry po in t o f w h ich
is at su ch d is tan ces f ro m tw o po in ts w ithin c alled t he fo c i ( p ro
'
no u n ce d to BI ; sin gu la r, fo c u s ) t ha t th e su m o f th e dis t aa
is
-
-
.
-
.
.
,
,
.
.
.
.
.
-
-
.
.
,
.
.
.
.
.
.
.
.
.
.
.
,
.
.
.
.
.
t t
co ns an
.
3 16
GLOSS AR Y
E CCE N TRI CI TY ( 6k s én tris l ty) is th e fract io n o b tained by dividing
th e distan ce of a focus to th e cen te r o f th e m aj o r axis by o ne h alf
’
j o r ax is
th e m a
.
OB L ATE N ES S o r ellip tic ity is th e de v iatio n o f an ellipse f rom a circle
an d is th e f rac tio n o b tained by d ivid in g th e d ifi eren ce be tw een
th e m aj o r and min o r axes by th e m aj o r axis
’
Elli pti c ity (61 l i p t is l ty ) , see E llipse
’
E q u ati o n o f ti m e (s k w a s h u n ) , th e d ifi ere n ce be tw een apparen t
so lar time , o r t im e as ac t u ally in d icated by th e su n , an d t h e m ean
so lar tim e , o r th e ave rage tim e in d ic ate d by th e su n
I t is usu ally
indicated by th e m in u s S ign w h en th e app are n t s u n is fas te r th an
th e m e an su n an d w ith th e plu s S ign w h en t h e ap p aren t tim e is
Th e ap paren t su n tim e co m b ined w ith th e eq u atio n o f tim e
sl o w
i
h
h
t
e
a
n
t
m
e
b
t
a
a
r
e
n
t
s
u
i
s
h
i
i
v
es
e
m
e
e
n
1
t
0
30 m , the
,
; g
pp
g
y
2 m ( su n fas t 2
co m b in ed w e ge t 1 0 h
28 m ,
eq u atio n is
th e m e an su n tim e
S ee D ay
!
E q u ato r (5 h e ter ) , w he n n o t o th e rw ise q u alified m eans te rres trial
.
.
.
.
.
.
.
.
.
.
.
.
.
t
e q u a o r.
CE LE S TI AL E Q U ATO R , th e gre at c ircle o f th e cel es t ial S p h e re in th e
’
h
h
s
u
r
li
n
i
s
a
n
o
a
r
a
t
o
D
e
c
o
n
i
t
t
f
l
a
t
e
e
m
e
a
s
u
e
r
e
f
t
h
r
o
e
d
m
e
q
p
celes tial eq u ato r
°
TE R R ES T R I AL E Q UATO R , th e gre at c ircl e o f th e e arth 90 fro m th e
h
L
i
s
a xis o f ro tatio n
l
n
o
f
t
a
t
t
u
i
f
e
o
es
o
r
e
d
d
e
s
m
e
a
s
ro
u
re
d
m
p
th e eq u ato r
E q u i n o x, o n e o f th e tw o p o in ts w he re th e e c lip tic in te rse c ts th e cele s
tial eq u ato r Als o th e tim e w h e n th e s u n is at th is po in t
AUTU M N AL E Q U I N OX , th e eq uin o x w h ich th e s u n rea c h es in au tu m n
Als o th e tim e w h en th e su n is at t h at po in t , S e p te m be r 23
V E R N A L E Q U I N OX , th e eq u in o x w h ich th e su n re ac h es in sp ring
This po in t is c alled th e Firs t po in t o f Aries, sin ce th at sign o f
th e z od iac begins w ith th is po in t th e S ign e x te n d in g e as tw ard
Th e ce lest ial m e rid ian ( see co l u re ) p ass ing th ro u gh
fro m it
th is po in t is th e z e ro m erid ian o f th e c eles tial s ph ere , from w hich
Th e v e rn al eq u in o x is also th e
ce le s t ial l o ngit u d e is re c k o n e d
tim e w h en th e s u n is at th is po in t , abo u t Marc h 2 1, th e begin ning
S ee Y e ar
o f th e as t ro n o m ic al ye a r
’
Geo c e n tri c (j e 6 sé n trik ; fro m ge, e art h ; centru m , ce n te r) ,
TH E O R Y o f th e so lar s ystem assu m es th e e art h to be at th e ce n te r
o f t h e s o lar sys te m ; s ee Pt o lem aic sys te m
LATI TUD E , s ee Latit u de
P A R ALLA X , see P arallax
’
Ge o desy (is 6d 6 sy ) , a bran ch o f m ath e m at ic s o r su rveyin g w hich
is applied t o th e d e te rm in at io n , m e as u rin g, an d m app in g o f lin es or
areas o n th e s u rfac e o f th e e a rt h
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
318
GLOSS AR
latitu de
tude in Append ix )
Lo c al ti m e , see Tim e
hi
l
r
c
a
eo
a
g g p
are
nearly
Y
th e
sam e
(
d is cu ssio n
see
of
Lati
.
.
Lo n gi tu de
.
CE L m TI AL LON GI TU D E , th e dist an ce in degre es o f a celestial bod y
from lines passing thro u gh the po le s o f th e e cliptic (see E clip tic ) ,
call ed e c lip t ic m e rid ians ; th e z e ro me rid ian fro m w hic h celes tial
lo ngitu d e is re c k o n ed , is th e o ne p ass ing th ro u gh th e First po int
,
Aries (see Eq u in o x )
of
TE R RE S T RI AL
.
LON GI T UD E
n
n
i
h
i
r
f
a
o
o
n
d
e
t
o
ees
t
e
,
g
p
e art h fro m so m e m e rid ian , ca l le d th e p rim e m e rid ian
K ass, th e am o u n t o f m atte r in a bod y , re gardl ess o f its v o lume o r
th e d is
tan ce
.
Mea n s o l a r ti m e,
Meri dia n
Time
see
.
.
CE L ES TI AL
th rou gh
ce les tial
t
th e
celes
t ial
s ph ere
passin g
Th e
th e ce l es ial po les and th e z e n i h o f the o bse rve r
m e ri d ian p as s ing h ro u gh t h e z en i h o f a given place
ly c hanges w i h th e ro a io n o f th e ear h
t
t t
co ns an
ci rcle o f
M E R I D I AN , a gre a
t
t
t
.
t
t t
TE R R m TR I AL M E R I D I AN , an im agin ary line
from po le to po le A me rid ian c ircle is
th ro u gh th e po les
on
a
.
t
.
th e
gre a
t
e ar
th
ss
n
a
i
g
p
c ircle
s
a
s
i
ng
p
.
M o n th
CAL E ND A R
.
T
i
v
n
f
a
o
o
n
n
t
e
d
m
e
o
h
g
y
to th e sa m e n um be re d day o f t h e ne xt m o n th ; e g , J an u ary 3
Th is is th e c iv il o r legal m o n th
to Fe b ru a ry 3
S I D E R E AL M O N T H , th e t im e it ta k es th e m oo n to re vo lve abo u t the
ea rt h in re la t io n to th e s t ars ; o n e e xa c t re v o lu tio n o f th e m oo n
abo u t th e e a rt h ; it varies abo u t t h ree h o u rs in le n gth b u t ave r
ages 27 3 2 166 d
S YN OD I C M ON T H , th e tim e be tw ee n t w o su c ce ss ive ne w m oons or
full m oo ns This is what is co mm o n ly m ean t by t h e lu nar
m o n th , re ck o ned fro m ne w m oo n to ne w m oo n ; its len gth v aries
abo u t t hirte e n h o u rs b u t ave rages
Th e re are se v
d
e ral o th e r k in d s o f l u n ar m o n ths im po rt an t in as t ro n om ical
cal c u lat io n s
S O LA R M ON T H , th e tim e o c c u p ied by th e s u n in passin g th ro rl gh a
S ign o f th e z od iac ; m e an le ngth ,
d
’
Nadir (n a dz r ) , th e po in t o f th e celes tial s ph e re di re c tly u n d er th e
°
i
h
w
n
h
h
n
s
a
n
1
r
o
t
s
o
t
l
ace
o
c
o
e
t
i
n
h
e
f
z
t
d
8
0
m
t
n
i
e
e
h
;
p
p
Ne ap ti des , see Tides
’
Nu tati o n , a s m all pe riod ic ellipt ical m o t io n o f th e ea rt h s axis , d ue
’
n
r
i
c ipally to th e fac t th at th e plan e o f th e m o o n s o rbit is n o t th e
p
sam e as th e p lan e o f th e e c lipt ic , so that when the moo n is o n one
M O N H , th e
tim e elaps ing from
a
.
.
.
.
.
.
.
.
.
.
.
.
GLOS S AR Y
t there
side of the plane o f th e e clip ic
3 19
t
t
til ing enden cy given the
’
bulging eq u ato rial region
Th e in clin a i o n o f th e e ar h s axis , o r
th e o bliq u i y o f th e eclip ic , is h u s sl igh ly changed h ro ugh a
”
”
r
i
o
o
d
f
a
r
s
h
e
r
i
v
a
a
c
e
n
e
2
,
(S ee
p
y
y g
year rom 0 to
Mo ions of the Axis in th e Appendi x )
.
t
t
t
t
Is a
t
t
f
t
t
.
Oblate n e ss , th e
me
sa
as e llip
ticity ;
see
E ll ipse
.
S ph ero id
'
Obliq u ity (6b l ik wi ty o f the e clip tic , see E cliptic
Op po si ti o n . see S ym r
Orbit, th e pa t h des c ribed by a h ea ven ly bo d y in its revolu tion abou t
an o th e r h e a ve n ly bo dy
P arall ax, th e appare n t d is plac em en t , o r diff ere n ce of position , of an
o bje c t as see n f ro m tw o d ifi e re n t s ta tio ns o r po in ts o f v iew
ANN UAL OR H E LI OC E N TRI C P A R AL L Ax o f a s tar is th e d ifl eren ce in
th e s tar s dire c t io n as seen fro m th e earth an d fro m th e s u n
The base o f th e triangle th u s fo rm ed is bas ed u pon hal f th e maj o r
’
axis o f th e ea rth s o rbit
D I U R N AL O R G E OC E NT RI C PAR ALLAX o f th e sun , m oo n , o r a plane t is
’
th e difl e ren ce in its d ire c tion as see n fro m th e o bse rve rs station
Th e base o f th e t rian gle th us fo rm ed
an d th e cen te r o f th e ea rth
is half th e d iam e te r o f th e eq u ato r
'
P eri gse (per I je th e point in th e o rbit o f th e m oo n w h ic h is n eares t
Th e te rm is so m et im es applied to th e ne are st po int
to t he e art h
’
o f a plane t s o rb it
’
'
Peri h eli o n (per i h é Ii On) , th e po in t in a p lanet s o rbit which is neare st
to th e s u n
Oblate
s p h e ro id , see
.
.
.
.
'
’
.
.
'
.
.
.
.
.
P o l es
.
LES TI AL the two poin ts o f th e celest ial sph e re which coin cide
with t h e eart h s axis p ro d u ced an d abo u t w h ic h th e celes tial
s ph e re ap pears to ro t ate
°
Or TH E E CLI P TI C th e two poin t s o f the celest ial sph e re which are 90
f rom the e cliptic
TE RR ES T R I AL th e ends o f the e art h s axis
P t l m ai c ys te m (till 6 ma III ) th e t h eo ry Of th e so lar sys te m ad van ced
by Clau d ius P tolem y ( 100 170 A D ) t hat th e earth is th e ce nte r o f
CE
,
’
,
.
,
.
’
,
.
’
s
o e
,
-
.
th e
t
u n ive rse ,
.
th e h e avenly bo d ies d aily c irc ling
it at d iff ere n t
Geocen t ric )
a ro u n d
Called also the geo ce n t ric th eo ry (see
'
h al f o f a d ia me te r
R adi u s ( pl u ral , rad ii, ra d i
R adi u s Ve cto r, a l ine fro m th e foc us o f an e ll ipse to a poin t in the
Th us a l in e fro m th e su n to any plane t is a radius
bo u nd ary line
’
vect o r o f th e plan et s o rbit
Ref rac ti o n o f li gh t, in ge ne ral , th e c han ge in dire ctio n o f a ray o f
As
ligh t w hen it enters o bliq u ely a m ediu m o f difiere nt density
ra es .
.
.
.
.
.
GLOSS AR Y
in ast ron o m y and in this wo rk , re frac tion is t he change in
direc tio n o f a ray o f ligh t from a celes tial bo d y as it e n te rs th e
Th e efi e c t is to
atm o s ph ere an d pas ses to th e e ye o f th e o bse rve r
cau se it to see m h igh e r th an it re all y is , th e am o u n t v aryin g w it h th e
’
al t it u de , be in g z e ro at th e z e n ith an d abo u t 36 a t th e h o riz o n
R e vo lu ti o n , th e m o t io n o f a plan e t in its o rbit abo u t th e s u n , o r of a
sate ll ite abo u t it s p lan et
R o tati o n th e m o t io n o f a bo d y o n its axis
S ate lli te , a m oo n
Si dereal day, see D ay
Si de real year, see Y ea r
Si d ereal m o n th , see Mo n t h
Si d ere al ti m e , see Tim e
°
Si gns o f th e z o di a c , its d ivisio n o f 3 0 e ac h , begin n in g wi t h t h e ve rn al
eq u in o x o r Firs t po in t o f Arie s
So lar ti m es , see Tim e
’
So ls ti c es (sOl s tl s es ; sol , s u n ; stare , to s tan d ) , th e po in ts in the
ec lip t ic fart h es t f ro m t h e ce le st ial e q u ato r, a l so th e d ates w h e n th e
su n is at t h e se po in ts ; J u ne 2 1 , th e s u m me r s o ls t ice ; De ce m be r 22 ,
the win te r so ls tice
'
S ph e ro i d (s f e ro id ) , a bod y n e arly s ph e rical in fo rm , u su al ly re ferri n g
to t h e m ath em atical fo rm p rod u ced by ro t ating an e ll ipse abo u t
o ne o f its axes ; cal led also an e l l ipso id o r s p h e ro id o f re vo l u tio n
n
h
i
i
s
h
i
t
i
t
t
b
oo
k
a
ro
r
o
a
n
s
o
o
e
d
f
,
)
(
p
OB LA TE S PH E R OI D , a m ath em at ic al so lid prod u ced by ro t at in g an
e ll ipse o n its m in or axis (see E llipse )
P ROLATE S PHE R OI D , a m at h em atical so l id p rod u ced b ro t ating an
ell ips e o n its maj o r axis ( see E l l ipse )
’
S yz ygy ( siz l jy ; pl u ral , s yz ygies ) , t h e po in t o f th e o rb it o f t h e m oo n
a
l
( p ne t o r com e t ) n eare s t to th e e arth o r fart h est f ro m it Wh en
in th e syz ygy n e ares t th e e art h , th e m oo n ( p lane t o r co me t ) is said
to be in co n j u n ct io n ; w h e n in t h e syz ygy fart h es t f ro m th e e arth it
is s aid to be in o ppo s itio n
u sed
.
.
.
.
.
.
.
.
.
.
.
,
.
.
.
y
.
.
.
Ti m e
.
APPA R E NT S OLA R
o f th e su n , so
t
’
su n s ce n e r
so lar
)
L
,
’
th e m e ridian
passes
of
th e
th e
t
ac u al
t
tion
i
o
s
p
m o m en w h e n the
D
n
c
a
a
a
r
e
l
a
s
ee
e
,
(
y pp
p
t
.
AS TR ON OM I CAL
be red u p to
D ay ,
TI M E th e time acco rd in g to
th a t t welve o c lo c k is th e
t
TI M E th e m ean solar tim e re ck oned by ho u rs n u m
t wen ty fo u r be ginn in g w ith m e an so lar n oo n (see
,
as ro n o m ic al
-
,
)
.
CI V I TI M E , le gally ac ce p te d t im e ; u s u ally th e sam e as ast ro n o m ical
t im e e xce pt that it is re c k o ned fro m m id n igh t I t is co mm only
n u m be re d in t w o se rie s o f t we l ve h o u rs e ach d ay, f ro m m idnigh t
.
322
GLOS S AR Y
TROP I CAL
f
th e peri od o c cu p ied by th e s u n in p ass ing ro m o ne
ro p ic o r o n e eq u in o x to t he sam e again , ha ving a m ean leng h o f
A ro pical year is sh o r e r
365 d 5 h 48 m
s or
(1
t
.
than
Y E AR ,
.
a s ide re al
.
.
.
t
t
t
be cau se of the p recess io n o f th e eq u ino xes
'
Ze nith (z e nl th ) , th e po in t o f th e celestial s ph e re dire ctly o ve rh ead
°
1 80 fro m th e nad ir
’
Zo di ac (z O (1! fil l ) , an im aginary be l t o f th e celes tial s ph ere e xte n d in g
I t is d ivid ed in to
abo u t e igh t degrees o n e ac h s id e o f th e e cliptic
°
twelve eq u al parts ( 30 e ac h ) called sign s , each sign being some w hat
Th e e cliptic be ing
to th e w e s t o f a cons te llat io n o f th e sam e n am e
th e cen t ral lin e o f th e z od ia c , th e su n is al w ays in th e cen te r of it ,
appare n tly t ravelin g e as t w ard t h ro u g h it, abo u t a m on th in each
Th e m oo n bein g o nly abo u t a fro m th e e c l ip tic I s alw ays In
sign
°
th e z odiac , travelin g eastw ard t h ro u gh its signs abo u t 1 3 a day
r
a
e
y
.
.
.
.
.
.
I ND E X
Am az o n , b o re s o f , 1 89
American Prac t ic al Navigat o r,
.
Abbe , Clevel an d , 5, 65
Abbo tt , Lym an , 76 , 1 4 2 144
Abe rdee n , S D , 89
Aberratio n o f ligh t (see Gl os
—
.
.
.
sary,
p
.
.
.
.
104 106 , 110,
—
.
2 78
Abrah am , 1 4 1
.
.
.
3 14) 290 2 92
Adelaide , Aus t ralia , 88
Arab ia, 88
Ade n
Af ric a, 102 , 186 , 200, 2 14 , 2 16 ,
223 , 268
Ak ro n , O , 8 1
Alab am a , 90
Alask a , 6 9, 87, 89, 91 , 98 , 102 ,
103
Alban y, N Y , 89
Alban y, Te x 24 3
Alberta, Can ada, 82
Ale u tian I s , 96
Ale xandria, Egyp t , 32 , 83 , 88 ,
2 70, 271
Algeria , 83
Alle ghe n y Obse rvato ry, Alle
h
e
n
P
6
9
a
,
y
g
Alle n , W F , 6 7
Allow an ce f o r c u rv atu re o f
’
e art h s su rf ace , 226 , 2 30,
233
Al Mam ou m , 2 7 1
Al m an ac , 1 18, 123 125, 1 71
Alt itu de , o f n o o n su n , 12 , 13,
170 174 , 302 , 303
o f p ole s t ar o r cele st ial p o le ,
58 6 1 , 170 174
—
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
-
.
-
.
—
.
-
—
.
Ac apu lc o , Mexico , 102
Ac cele rat io n (see Glo ssary , p
.
.
—
.
.
217
Am sterdam , Hollan d , 82, 88
Anale mm a (see Gl o ssary, p
de script io n o f , 126
re pre se ntat io n o f , 12 7
u se s
of ,
128 130, 1 7 1 174 ,
301
’
An ax im an der ( An i x 1 m en de r)
26 9
An nap olis , Md , 89
An n Arbo r, Mich 89
’
An t ipo dal ( i n tip o d al) areas ,
m ap sh ow in g, 4 1
Antw erp , B elgiu m , 88
Aph elio n (see Glo ssary, p
119, 285, 287
’
Apia ( ap e ii ) , S am o a, 88
Apo gee (see Glo ssary, p
178
Apside s (see Glo ssary, p 3 14)
287
’
A u ariu s ( a k w a ri li s) , 2 96
Arabia, 88
’
Arctu ru s (ark t u ru s) , 54 , 109
Area m e th od o f de te rm in in g
i
d
o
e
36 , 3 7
,
g
’
Are a o f e arth s su rf ace , 3 10
’
Are u ip a ( ii ra k é p ii ) , Peru ,
16 4
Arge n tin a (ar jen t e n a) , 8 1
’
Arie s ( a ri é z ) c o n stellat io n , 294
first p o in t o f , 2 93 , 3 16
sign o f z o diac , 118, 297, 2 98
'
Aris t arch u s ( S r i s t iir k ii s) , 275,
277
’
Arist o tle ( Ar l s t o t l) , 270
’
Ark ansas ( fir kfin se) , 90, 233
.
.
—
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q
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q
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’
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.
324
I NDE X
Arkansas Ri ver, 233
Armeni an Chu rch , 145
Asia, 34 , 4 1, 186 , 2 14
Aste ro ids , 50, 246 , 253 , 293 , 3 1 4
Astrono mical day , 130, 3 15
Athens , Gree ce , 42 , 84 , 88
Atlan ta, Ga 89
Atlantic Ocean , 14 1 , 186 , 24 2
Atm osp he re , 16 1 16 7
abse nce o f , on m oo n , 26 3 , 26 4
h ow h e ated , 16 7
.
.
.
.
.
.
.
.
.
—
.
.
.
Ju piter
2
7
5
,
o n Mars , 2 54
o n Me rcu ry, 26 1
on Ven us , 256
origin of , 251 , 252
Attu I slan d , 89, 99
Au ckl an d , New Zeal and , 97
Au gusta, Me 89
Augu stan calendar, 135
Austin , Tex 89
Australia, 4 1, 96 , 97, 102
Austria Hu ngary, 6 8, 82
Axis, c han ges in po sition o f , 288 ,
289
defined , 22 , 3 14
in clinat io n o f , see Obli u it y o f
e clip t ic
4
r
ll
m
f
1
5
a
a
e
li
s
o
p
Az im u t h , 303, 3 14
on
.
.
.
.
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.
.
.
.
.
.
.
.
-
.
.
.
q
.
.
.
B as e line , 23 1 234 , 243 , 244
B atavia, Java, 88
B eh ri ng S trait , 33
Belgiu m , 6 8, 82, 88
B eloit, Wis , 89
Bene t nasch , 6 1
Be rgen , No rway, 88
B e rk ele y, Calif , 89
B erlin , Ge rm an y, 88
B e ssel , F W , 3 1, 32, 35, 109
B ethl ehem , 145
B ig Dipper, 9, 4 8, 60, 6 1 ,
B ismarck Archipelago , 83
B ismarck , N D , s
B lack Hill s Meridiari, 2 30
B ogota (he go
Co l um bia , 83
B oise
I da 89
B o mbay (h em
I ndia, 88
’
B o nne 8 pro j e c ti on,
B onn Obse rvatory, 109
B o rdeau x (ber
Fran ce , 88
B o res, tidal ,
B osph orus , 144
B osto n , Mass , 67, 89
B owditc h , Nat h aniel , 2 17
B rah e (bra) , Tych o , 109, 277,
278
B radley, J am e s, 106 , 278
B raz il , 89
B ritish Co lu mbia, 82
B ri tish E m pire , 82
B ru ssels, B elgi u m ,
’
B u dapest (boo da pes t ) , Hu n
—
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.
.
.
.
.
.
.
.
B abine t , 207
B acc h u s , 134
B ailey , S I , 16 3
B aleari c I s , 86
B alkan S t ate s , 140, 145
’
B all s Hist o ry o f Math ematics ,
26 9
B altim o re , Md 89
B an go r, Me 89
B ank o k , S iam , 88
B arcelona , S ai n , 88
’
B ryan s Math e
B arlow an
m e tical Astron om y, 292
B arom e ter, 16 1, 176
.
.
.
.
.
.
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.
.
.
.
.
.
r
a
g y,
B u en o s
86
.
Ai res
u
s
r
i
z
a
n
b
o
(
),
Arge n tina , 73 , 88
B u fi ale , N Y , 90
B ul garia , 6 8
B u lle t in , U S G S 24 3
B u rmah , 82
’
'
.
.
.
.
.
.
.
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.
.
0
.
.
.
.
Cadiz
Spain , 88
Cae sar, Au gu stu s , 135, 136
J uliu s , 134 , 138
E gypt , 83, 88
Cai ro
.
.
.
.
326
I ND E X
Circ le o f illum in atio n , o r day c ir
cle , 14 9, 151 , 152 , 155 157
Ciu d ad Ju are z , sec Ju are z
Civil day, 130, 3 15
Clark e , A R , 30 32 , 34 , 35, 37
-
.
.
.
-
.
.
Cu ba, 69, 83 , 88
Curvatu re o f s u rf ace o f eart h ,
rate o f , 2 7, 2 8 , 4 3 , 44 , 226 ,
.
233
.
(sIg n tis ; l n d
Cygnus
’
se ssi ve singu
Cle o m ed es (k le om e d ez ) , 2 72
Cle veland , O , 74 , 90
Clo c k , sidereal , 6 9, 70
Co lli n s , Hen ry , 100
Co lo mb ia, 83
Co lo n ( k 6
P anam a, 85
Co lo rad o , 67, 90
Co lo r vib ratio n s , 106 , 107
Col u m b ia, S C , 90
Co lu m b u s , Ch rist o ph er, 137, 138,
’
.
.
.
Bi
an d
c ygni
Cyl in d ric al pro j e c t io n ,
224
)
o
p s
109
209 2 18,
,
.
—
.
.
D
.
.
.
.
.
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.
.
Co l u m b u s , O , 74 , 90
Co m e ts , 50, 24 6 , 278
’
Co m p ass, m agne t ic , o r m arine r s,
.
.
.
D ak o tas , d ivis ion o f , 234
D anish We st I ndie s , 83
D ate lin e , see I nte rn at io nal
d ate line
Day ( see Glossary , p
as
tro no m ic al , 130
c ircle , see Circle o f ill u m in a
tio n
c ivil , 130
len gt h o f , 1 55 158
lu nar, 188
o rigin o f nam e s o f d a ys o f
week , 14 2
sidere al , 1 14 , 130
so lar, 6 2 , 114 , 130
to tal du rat io n o f a, 98
De ad woo d , S D , 90
2 55
De im os
D e clinat ion ( see Glossary, p
125, 12 7, 1 7 1 1 75,
3 15)
284
'
D e la Hire P h ill ip pe ( f é l ép d é
201
la
De n m ark , 68, 83 , 88 , 136
D en sit y, fo rm u la f o r, 309
D e nsit y o f e arth , 3 10
Den ver, Co l , 26 , 2 7, 6 7, 90, 98
I o w a, 90
De s Mo ine s (de
Desh ne f , Cap e , 96 , 99
De t roit , Mic h 6 3 , 73 , 90
De viat io n , o f pe nd u l u m , 54 57
o f pl u m b l in e , 2 8 1 283
De wey, Ge o rge , 103
D iameter o f e art h , 29 3 1, 45,
3 10
D ime nsion s of e arth , 3 10
.
.
.
.
.
.
.
—
.
.
Co nc o rd , N H , 90
Co n gre ss io nal t o w n sh ip , 2 28
Co nic p ro j e c t io n , 2 18 224
Co n j u n ct io n , 178 , 185, 320
Co nn e c t icu t , 90
Co ns t an tino ple , Tu rk e y, 88
Co nve rge n ce o f meridian s , 2 30,
233
Co pe n h age n , D e n m ark , 88
Co pern ic an syste m ( see Gl o s
2 76 2 78
sary , p
’
Co pe rn ic u s (k 6 pe r nI h i s) , 50,
109, 276 2 78
’
Co rd o ba (k 6 r d 6 b a) , Argen tin a ,
.
.
.
.
—
.
.
.
.
.
.
—
.
.
—
.
81
'
Co rin to (k 6 ren t é ) , Nic aragu a ,
85
Co rre ction l ine , 2 34
Co sines , n at u ral , t ab le o f , 3 1 1
Costa R ic a, 83
Co tan ge n t s, n at u ral , t ab le o f ,
3 12
Co tidal l in e s , 186 , 3 15
Cre p usc u lu m , th e , 165
Cresto n , I o wa, 80
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-
.
-
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—
.
.
I ND E X
Dip
h o riz
of
(
see
on
Glo ssary, p
.
D istan ces, o f plane ts ,
o f st ars , 45, 24 6
D istric t o f Co l u mb ia, 77, 91, 124
'
D iu rn al (di fir n al) , m o t ion o f
e arth , see R o tat io n
D ivision o f D ak o tas, 2 34
D rye r, Ch arle s R , 5
D u b lin , I re land , 6 4 , 82 , 88
D u lu t h , Minn 90
.
.
.
E
q at
u
(see Glo ssary,
or
p
150, 170 174,
celestial ,
.
4 7,
283, 284 , 2 94
len gt h o f day at , 157
terres trial , 23 , 33 , 4 8, 4 9, 1 18,
148 152 , 272 , 2 80, 3 10
E u ino x ( see Glo ssary, p 3 16 )
—
.
.
—
.
q
.
.
.
.
.
.
.
r
e
i
n
e
c
ss
o
p
of ,
286 2 88 , 303
’
( fi r a tbs th é n ez )
—
.
E ratost h en es
270, 27 1
E rie , P a , 90
Est abl ish m ent, th e , o f a po rt,
18 1
Eu do x u s, 270
’
E u ripid e s ( II ri p ! d ez ) , 122
E u ro pe , 101 , 166 , 16 8 , 22 0, 222 ,
223 , 226 , 2 88 , 2 93
.
E
Eart h in S p ace , 24 6 26 7
’
E art h s d im e nsio ns, 3 10
Eas te rn time , in E u ro pe , 6 8 , 8 7
in th e Un ited S tate s, 66 , 6 7,
71, 75, 78
Eastw ard de fle c t ion o f f all in g
ob j ects , 51 54
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.
.
.
.
.
.
.
.
'
.
.
—
.
E c l ip tic ( see Gl o ssary , p
11 6 ,
o bliq u it y o f , 11 8, 14 7, 288 ,
3 10
'
Ed inb u rgh (ed l n b ur r6 ) , S co t
lan d , 88
Egyp t, 83 , 88 , 133 , 26 8
’
E l Castillo (él k as tel y6 ) , Nic a
.
.
.
.
ragu a,
85
.
F
Fargo , N D , 90
Farl an d , R W 13 2
Faroe
I slan d s , 83
Fath o m , length o f , 3 10
Fij i I sl and s , 96 , 100, 103
Fisk e , J o h n , 14 5, 2 6 8
Fixed st ars, 10, 108, 109, 2 65,
26 6
Flo ren ce , I t al y, 88
Flo rid a, 90, 91
—
Fo rm o f th e earth , 24 44
Fo rm o sa, 84
Fo rm u l as , 307 309
’
Fo u c au lt ( f o o k o ) expe rime n t ,
w it h gyro sc o pe , 155
with pend u l u m , 54 57
Fran ce , 32 , 6 4 , 83 , 88, 89, 130,
136 , 139, 187
’
Frank lin s al m an ac , 137
Fun d y, B ay o f , 189
.
.
.
.
.
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.
.
.
.
.
.
E ll ip se ( see Gl ossary , p
308
20 22 ,
Ell ip so id o f ro t atio n (see Glo s
36
sary , p
Nic a
El Oc o t al (61 6 k 6
ragu a , 85
El P as o , Tex , 6 8 , 75, 76
E n c yc lop ae d ia B ritan n ic a, 102
98, 101 ,
En gl and , 9, 80,
136 , 139,
’
E p he m eris ( e f em é ris) ,
Nau tical al m an ac
Epic u rean s , 272
E u ad or, 83
E q u at io n of tim e (see Glossary,
2
1
3
7
12
p
-
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—
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G
.
q
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-
.
.
Gainesville , Ga , 75
'
Galile o
Galile i ,
(gal 1 16 6
2
277
7
8
a
l
g
.
.
.
328
I ND E
Gal veston , Tex , 75, 90
Gann ett, Garriso n an d Ho u s
to n s Co mm ercial Geo grap h y,
.
.
’
X
Gravity o n Me rc ury , 260
o n m oo n , 19, 20, 26 1
o n Ne p t u ne , 259
o n S atu rn , 258
.
.
.
.
Gauss, 52
Ge m ini , 295, 2 98
Genesis, 14 1
Gen o a, I taly, 76
Geo cen t ric , latit u d e ,
.
.
t
.
.
La ti
s ee
.
t h eory (see
.
.
.
t u de
1 9, 2 6 4 , 2 6 5
o n Uran u s , 259
on V en us , 256
Great B ri ain , 64 , 6 8, 77 80,
182 , 233
Gre at circle sailing, 203 , 204 ,
212
o n su n ,
.
Glo ssary, p
.
.
.
Gree ce , 84 , 88
Gree nlan d , 2 18
'
Greenwich (Am p ron , grén
’
wi ch ; E n g p ron , grin l j or
’
4
r
n
l
E
n
l
n
1
42
é
a
d
,
,
)
g
,
g
j,
6 4 , 6 7, 68, 73 , 77 , 78, 80,
82 , 84 , 86 91 , 96 , 100, 124
.
Geo de sy (see Glo ssary, p 3 1 6 )
.
275
Geodetic Asso c iatio n , I n te rn a
tio n al , 289
Kin g o f E n glan d ,
Geo rge I I
227
Geographi cal co n stan t s , 3 10
Geo id
33 3 7, 2 75
Ge o m etry , o rigin o f , 22 6
Georgia, 68, 75, 80, 89, 91
Germ an E ast Af rica, 84
Germ any , 6 8 , 77, 83, 84 , 88, 89,
97, 136 , 2 33
Gibraltar, S p ain , 82 , 88
Glasgo w , S c o tland , 88
Glo b u lar p ro j e c tio n , 198 201 ,
2 11
Glo ssary, 3 14 322
’
Gn o m o ni c ( n 6 m 6 n 1k ) , c ylin
drical p ro j e c tio n , 209 2 1 1
Gn o m o n ic pro j ec tion , 201 204 ,
21 1
Goo de , J P au l , 302
Go o d se ll Obse rv ato ry, No rt h
field , Min n , 6 9
Gravim e tric lin es, m ap s h o w
in g, 34
Grav it atio n , 1 6 18, 178, 1 79,
2 72 , 3 17
Gravi t y, 18, 25, 2 8, 2 9, 183
185, 2 79 282 , 2 90, 304 , 305,
.
.
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.
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.
—
.
-
.
.
.
.
.
.
.
Grego rian calen d ar, 135 138
Gu am , 73 , 87
Guaym as , Mex ico , 85
Gu iana , Fren c h , 88, 273
Gul f o f Mex ico , 37 , 189
Gu n n is o n , Utah , 2 4 3
Gu th rie , Ok la, 90
’
Gyro sc ope ( ji r6 sk 6 p ) , 154 , 155
—
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.
.
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.
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—
H
.
—
.
—
.
-
.
.
.
.
.
.
-
.
—
Hagu e , Th e , Ho llan d , 84 , 88
Ham b u rg Germ an y, 88, 125
Hark ness , William , 2 75, 3 10
.
.
’
arpe r s
.
Week ly
,
on
J u pite r
Mars ,
19, 2 56
2 53
,
.
.
16 3, 16 4
.
Harte , B re t , 92
Hartf o rd , Co nn 90
Harv ard As t ron o m ical S tatio n
.
.
(P eru )
.
4
6
1
,
Havan a , Cu ba, 83 , 87, 88
Haw aiian ( S and wich ) I slan ds ,
87, 101
Hayde n , E E , 5, 73 , 77
Hayf o rd , J F 36 , 3 7, 245
Hegira, 140
He liocen tric th eory (see Glos
sary, p
277,
.
.
.
.
.
.
.
.
on
.
.
.
.
330
I ND E X
Lansing, Mich ,
Lapland , 274
Larkin , E L , 265 267
Latitu de (see Glo ssary, p 3 17)
astrono m ical , 282
celestial , 2 83 , 284
.
.
.
.
.
.
.
.
.
.
.
t
n
r
i
e
oce
c
,
g
.
.
—
.
Longitu de , origI n of te rm , 40
Lo s An ge les , Calif , 90
Lo ui siana , 90, 230
Lo u isv ille , Ky
Lo ui s X I V , King o f Fran ce , 28
Lo well , Mass , 90
Lowell , Pe rcival ,
Lu xe m burg,
Lu z on , 90
.
.
282
l
4
h
r
i
2
a
a
eo
c
g g p
,
determ ined by altitu de o f
circ u m po lar s tar, 58 6 1
d eterm ined b y Fo u cau lt
e xp erim en t , 55, 56
determi ned by altitu de o f
n o o n su n , 170 175
lengt h s o f degree s , 4 2 4 4
o f p rin cipal c ities , 88 91
o rigin o f term , 4 0
Law No te s, q u o ted , 8 1
Layard , E L 101
Le ave n w o rth , Fran c is R , 5
.
.
.
-
.
M
.
-
.
-
.
—
.
.
'
.
.
.
.
.
Le o ,
Le gal aspe ct o f stan dard tim e ,
76 81
Leip z ig, Ge rm an y , 89
Le n gt h o f d ay, 155 158
Le wis , E rne st I 145
Le xing to n , Ky , 90
Le yde n , Ho llan d , 84 , 2 72
Libra
Lick Obse rv ato ry,
’
Lim a (le m a) , P e ru , 86
Lin c oln , Ne b , 90
’
Link o f s urve yo r s c h ain , 3 10
Lisbo n , P ort u gal , 4 1 73, 86 , 8 9
Litt le D ippe r, 9
Lit tle R o c k , Ark , 90, 2 33
Live rp o o l , E nglan d , 89
Lo n d o n , E n gland , 4 1, 6 3 , 6 4 ,
—
.
.
—
.
.
.
.
.
.
.
.
.
.
.
Macaulay s History o f En glan d ,
’
138 , 139
Mc Nair, F W
.
.
Madiso n , Wis
Madras ( m a
.
.
,
5, 52
6 7, 90
.
.
I ndia , 73,
82 , 89
Madrid , S pain , 73
Magnetic com pass, 152 , 153 , 226 ,
.
.
Magnetic p ole , 152, 153
Mage llan s fl ee t, 92
Maine , 32 , 37
Malta, 82
’
Managu a ( m a n a gu a) ,
.
’
.
.
.
ragu a ,
Nic a
85
.
Manitob a, Can ada , 82
Manila, P h ilippine I s
.
.
73, 90,
101 103
ch an ge o f date at , 101
Map , 4 1 4 2 , 230, 2 36
Map pro j e c tio ns , 190 225
Mare I slan d Naval Obse rvato ry ,
—
.
.
.
—
.
.
.
.
.
93 96 , 99, 137
Lo nd o n Tim e s , 139
Longit u de (8 66 Glo ssary , p 3 18)
an d tim e , 6 2 91
ce le s t ial , 2 84
h ow de term ined , 6 3 6 5, 12 8
lengths o f de gree s , 44
of p rin c ip al c i tie s , 88 91
—
.
.
.
—
.
.
—
.
.
—
.
Mariane I slan ds, 83
Mark h am , A H 153, 164 , 165
Mars , 253 255, 26 6 , 285, 306
Marseilles, Fran ce , 89
Marylan d, 89
Mas sac h usett s , 89, 90, 227
'
Mau ri tiu s (m a rish I 6 8 ) I slan d ,
.
.
.
.
,
—
.
.
.
.
73
.
Me an so lar day (see D ay)
Measu rin g diameter of moo n,
.
24 0:
I ND E X
Measuring distan ces
o b ec ts ,
of
j
237, 24 1
h eigh ts o f obj ects, 238
Measu res o f lengt h , 3 10
Medite rran ean , 102
Melbo u rne , Australia, 80
Mem phis, Ten n , 90
Mercator proj ectio n , 204 , 2 1 1
2 19, 22 1
Merced oni u s, 134
Merc ury, 183,
Meridian , 2 3,
95
100,
188, 19
0 225, 283 ,
3 18
celes tial , 283, 284, 3 18
c ircl e , 2 3
lengt h of degrees o f , 44
2
r
m
4
i
e,
1 4
p
r
i
n
i
a
l
c
f
p
p , or surveys , 230
236
rate f o r co nvergen ce , 2 33
stan dard ti m e , 6 6 6 8
,
77, 78, 81 87, 302
Merid io nal parts , table o f , 217
Mete o rs ,
Meter, len gt h of , 3 10
Me tes and bound s,
Mexico ,
Gu lf o f , 189
Michigan , 51, 6 8, 74, 76 , 80, 90
23 1
Co llege o f Mines, 52
Midnigh t sun , 163
Mile , I n vario us c o u n tries, 3 10
Milw au k ee , Wis , 90, 103
Mining and S cien tific Press ,
52 54
Minn eapo lis , Min
Minn esota, 90, 91, 23 1, 233
Mississipp , 90
River, 231
.
1
Mo bile , Al a 90
Mohammedan calendar,
.
.
.
.
.
.
.
.
.
—
.
.
.
.
.
.
.
—
—
.
.
.
.
Mollendo , Peru , 86
Mollw eide pro j ec tion , 207
Montana, 90
Montevide o , Uru guay, 87, 89
Mo ntgo mery Ala , 90
Month (see Glossary, p
.
.
.
.
,
.
.
.
133 , 134
sidereal , 177, 188
syn o di c , 177
Moo n or sate llite , 10, 1 1, 19, 16 1,
176 185, 240, 24 1, 246 , 255,
257 259, 26 1 264 , 26 6 , 2 78,
288 , 297, 298 , 308
Moo re , C B T 96
Morse, J F 303
Mosc ow , R ussia, 89
Mo tion in th e lin e o f sigh t , 106
109
Mo tio ns o f th e earth , 289
’
Mo tiorI s o f th e earth s axis, 286
2S9
Mo u lt on , F R
Mo u n tain time be lt, 6 7,
Mo u n t Diab lo m eridian , 2 30
Mu nich
Germ any , 89
Myt h s and su perstitions of the
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z odiac ,
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Misso u ri,
R iver, 2 27
Mitc h el l , Frank E 5
Mitch ell , S D , 90
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Miyak o (meya k 6 ) I slands, 84
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Nadir (see Gloss ary, p
38
Naples , I taly, 89
Nash , Geo rge W 4
Nash ville , Te nn , 90
Natal , Af rica, 82
Nau tical alm an ac , 1 18, 124 , 17 1
Neap tides , 185, 188
Nebras ka , 8 1, 90, 91, 227
Nebu lae , 248, 251
Nebu lar hyp o th esI s, 247 252
Nehemiah , 14 1
Ne ptu ne ,
Neu chate l , S witz erland, 86
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I ND E X
332
'
e vada ,
91
quity
Obli
.
Ne wark , N J , 90, 91
New B ru nswi ck , Canada, 82
Ne w Caled onia, 101
Newco m b , S im on , 1 18
New ch w ang, China, 83
Newf o u n dland , 82
New Gu inea, 83
New Hampshire , 90
New Haven , Co nn , 90
New Jersey, 32 , 78, 90, 91
New Mexico , 68 , 76 , 91, 230
New Orleans, La 59, 67, 90, 108
New S o u th Wal es, 82, 89
New S tyle, 137 140, 143
Ne wton , I saac , 15, 51, 138, 272
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76 , 78, 89 91, 96 ,
98, 99, 204
New ork S un , 55
New Zeal and , 82 , 96 , 97
Nicaea, Co u n cil of , 136
Nicaragu a, 85
Nile , 226
No rth America , 101, 185, 2 13,
2 19, 242 , 287
North Carolina, 91
North , line , 1 1, 6 1, 130
o n m ap , 2 1 1, 2 12, 2 17, 224
2
5
2
53
89
4
7
1
2
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2
1
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e
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p
star, 43 , 46 , 4 7, 49, 58,
North D ak ota, 89, 90, 234
Northfield, Minn , 6 9, 90
No rth S ea, 187
No rthwe st Territory, survey o f ,
228 230
Norway, 6 8, 85, 88
No rwoo d , R ich ard , 272
ov a S c o tia, Can ad a , 82
No u m e a, New Cale d o n ia, 101
Nu m a, 134
Nu tation o f poles , 288 , 3 18
o rk ,
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New
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the ecl ptic , 118;
147, 288, 3 10, 3 1
Observatio ns of stars , 9
Official Railway Gu ide , 73 75
den , Utah , 91
O o , 90, 230
Rive r, 228
Oklah o m a , 90
’
Old Farme r s Alm anac , 124
Old S tyle , 137 140, 14 3
Olympia , Was h 91
Omaha , Neb , 91
On tario , Canada 82
Oporto , P o rtu ga , 204
Oppo sitio n , 177, 178, 185
Orange Ri ver Co lony, 82
Orbit , o f e art h , 22 , 113, 1 14 , 1 16
1 19, 122 , 132 , 147, 152, 246 ,
251, 2 85, 304 306
o f m o o n , 177 , 1 78, 26 2 , 288
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Origin of geo m etry, 226
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Orion (o ri on ) , 1 1 1
Oroya, P eru , 86
Ork neys , Th e , 82
Orth ographi c p ro j ectio n , 190
195, 1 98 , 200, 2 1 1
Ou tloo k , Th e , 76 , 142 144
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P acific Oce an , 6 8, 96 , 97, 185,
2 2
P acific tim e bel t , 6 8
Pago P ago (p ro n pan go , pang o )
S am oa, 91 96
Pal estine , 89
Pallas , 293
Panam a, 69, 85, 87 89
Para, B raz il , 89
Parallax , 109, 24 1, 277, 3 19
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Parallelism o f earth s axis , 154
Parallel s, 23 , 190 225
Paris , Fran ce , 28, 29, 4 1 , 55, 64 ,
89, 274
Parliament , 77
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Oblate ne ss o f e art h , 2 8 33 , 3 7,
43 , 2 73 275
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I ND E X
334
R iche r (re
John, 28, 29,
273
Ri ch m o nd , Va 91
Ri o de Janeiro , B raz il , 89
Rh ode I sland , 91
Rh odesia, Af rica, 82
Ro c he ste r, N
91
Ro man cal endar, 134 , 138
Ro me , I taly, 73, 89
R o tatio n o f eart h , 2 3, 320
Ro tatio n , proo f s o f , 51 , 155
Ro tterdam , Ho llan d, 89
Ro m ani a, 68
R ussia, 32 , 86 , 89, 96 , 102 , 103 ,
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Scientific American , 26 7, 305
Scorpio , 296
Seas ons , 146
16 9
Seattle, Wash , 91
Sec tio n ,
Seo u l ( 86
Korea , 85
Servia,
Seven m o tio ns o f eart h , 28 9
Seven ranges o f Ohio , 2 2 9
Sex tant, 6 1
S hakespeare , 299
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S hangh ai ( sh ang bi ) Ch in a 83
S he tland I s , 82
S iam , 88
S iberia, 97, 99, 103
S icily, 289
S ide real , clo c k , 6 9, 70
day,
m o nth , 1 77, 3 18
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S
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Sac rame nto , Calif 91
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S agittarius ( sag It ta rl us) , 296
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S t Jo h n s , New fo u ndl and , 82
S t Lo ui s , Mo , 26 , 2 7, 6 7, 85, 9 1
S t P au l , Minn , 91, 96
S t Pete rsbu rg, R ussI a, 73, 86 ,
89,
Salvado r ( sal v ii
86
Sam o a, 84 , 88, 91, 96 , 97, 100
S an B ernardino , Calif , 2 30
S an Fran cisco , Calif , 93 , 173
San Jose ( h 6
Co sta R ic a, 83
S an J u an del S u r, Nicaragu a, 85
San J u an , P o rt o R ico , 91
S an Ra f ae l (ra f a
Mex ico ,
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85
San S al vad o r, S alvado r, 86
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Santiago ( S an t e a g6 ) , Ch ile , 82
Santa Fe , N M , 91
S anto D o min go , 86
S ask atc h ewan , Canad a, 82
Satelli te , see Moo n
Saturn , 30 248 253 , 257, 258, 266
Savannah , Ga , 91
S cale o f m ile s, 195, 2 16 , 22 4
S c h o tt , C A , 32 , 33
S co t lan d , 82 , 88 , 139, 187
Scrap B o o k , 6 5
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S ignals , tim e , 71 73, 8 1 87
S igns o f z odiac ,
Sines, natural , table o f , 31 1
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Siriu s ( sIr I us) , 4 7
S it ka, Al ask a , 73 , 91
S nell, Willebro rd , 2 72
So lar day, see D ay
S olar syste m , 24 6 26 7
table , 2 6 6
S o ls tice s,
’
So sigene s (so sIg e n e z ) , 134
So u t h Am eri ca ,
2 73
S o u th Au stralia, 82
S o u th ern Cro ss, 4 7
S o u th Carolina, 90
S o u th D ak o ta, 89 91 , 2 27, 233 ,
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S o u th , on m ap , 200, 2 11, 2 12, 224
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46 4 9, 58 , 59, 14 8, 151
S pai n , 6 8,
S pec tro graph , 10
s ar,
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9
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S pectro sco pe ,
S ph ere , defined , 20
S ph ero id , 2 2 , 28 33 , 320
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I ND E X
S pitz bergen , 32
S pring tides , 185, 188
S uare o f Pegasus , 48
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S tadi u m (sta ( 11 u m ) , 71
S tan dard p arallel , 233 , 234
S tan dard t im e , 6 5 88
S tar, distan ce o f a, 45, 24 6
m o tions o f , 108, 109, 265, 26 6
Th o m pson , A H , 244
'
Th u cydides ( th u sld l de z ) , 132
Tidal wave , bo re ,
Tides , 1 76 189, 280, 2 90 292
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Tien tsin ( te én tse n) , China , 83
Tiers o f to wn sh ip s , 23 1,
Tim e (sec Glo ssary , p 320)
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a
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265 26 7
S te reo graph ic pro j e c tio n , 195
198, 200, 2 1 1
S t o ck h ol m , S weden , 86 , 89
S t rabo
2 71
S trauss , N M 76
S u n , 10 12 , 19, 16 1 , 2 46 248 ,
250, 251, 26 4 2 6 7
app aren t mo tio ns o f , 113 2 94
a star, 2 6 5 26 7
declin atio n o f , 127, 171 174
f as t o r slo w , 6 2 , 123 130
S u n B o ard , 302 , 303
S u n dial , 6 2 , 65, 13 1, 300 302
S urve y, 3 1 3 2, 36 , 22 6 , 272
’
S urve yo r s ch ai n , 2 26 , 3 10
S wed en 32 , 6 8, 86 , 89, 2 77
S wi t z e rlan d , 6 8 86 , 136
S ydn e y, Au stralia , 89
S yen e , Egyp t , 270
S ym bo ls , 307
S yz ygy, 178 , 185, 3 20
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r
n
so
l
a
r
a
t
e
p
,
p
62
l 7 1 83
co nf us io n , 6 5, 73 76 , 144
in vario u s c o u n t ries, 8 1 87
local , 6 4
h o w de te rm ined , 6 9
signals, 6 9 73 ,
87
stand ard , 6 5 8
8, 1
Time s, Lo nd o n , 139
Titicaca , Lak e , Peru , 86
Todd , D avid, 106 , 289
To
I s , 84
To yo , J apan , 89
Toled o , O , 73
To nga I s , 100
Toscanelli, 2 12 , 2 13
To wn ship ,
Transit in st ru m en t , 6 9
Transvaal , 82
Tren t o n , N J , 91
Triangulatio n , 3 1 , 32 , 237, 2 75
Tropics , 150, 151 , 173 , 26 9, 32 1
Tu nis, 83
Tu rk ey, 87 88 142 144
Tu rkish c ale nd ar, 142 144
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Tut u ila ( too twe l a) , S a moa , 87
96 , 97
Twiligh t , 16 1 16 5
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Tab le s , lis t o f , 3 13
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Tac u baya ( ta k o6 b a ya) , Me x
ic o , 85
Tallah assee , Fla 91, 2 30
Tam arack m ine , 51 53
Tange nts , n atu ral , table o f , 3 12
Tas mania, 82
Tau ru s , 295, 2 98
Tegu cigalpa, Ho n d u ras , 84
Te fegrap hic tim e signals , 6 9, 8 1
Te nne ssee , 90
Te xas, 8 9, 90 2 43
Thales
270
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Une qual h eatin g,
United S tate s , 3 1 34 , 36 , 42 ,
4 8, 51, 6 5, 6 9, 71,
—
98, 101
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226 2 36 , 2 89, 293
United S tates Coast an d Geo
de t ie S u rve y , 3 1 , 32,
244 ,
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336
I NDEX
United S tates Geo logical S u r
3 1, 24 2, 243
Unite d S tates Governme nt La nd
S u rvey, 226 236
United S tates Naval Obse rva
to ry , 6 9 73 , 8 1
Unive rsit y o f Cali f o rnia , 155
Univ ersity o f Chicago , 250, 302
Ur, an c ie nt Ch alde an c ity, 14 1
Uru gu ay, 87, 89
'
Uran u s (u ra n us) , 2 53 , 258 ,
ve y,
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Ursa Maj or, 9
Utah , 91 243
.
Washingto n
Washington
,
.
D C , 35, 4 2 , 6 7,
71, 72, 85, 86 , 91 , 124 , 230
Was hingto n, Geo rge, 138, 139
Watch , to set by su n , 129
We igh t, see Gravity
Wellington , New Zealand , 73
We stern E u ropean time , 68
We st Virginia, 91
What k eeps the m em be rs o f the
so lar system in their or
,
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Wh eeling W Va 91
Wilh elm I I E mperor 77
Wilmington Del 91
Winona Minn 91
Winter conste liatio ns 1 1 1
Wisc onsin 6 7 89 90 103
Wood ward R S 5 35
World Alm an ac 123
Wyoming 90
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,
.
91
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,
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,
Valp araiso (val p a ri s6 ) Ch ile
82 , 89
V an de r Grinte n , Al ph o ns , 208
Vibrations , co lo r, 106 , 107
Vi cto ria, Au s t ralia, 82 , 89
V irgini a City, Ne v , 91
Virgo , 2 95
Velo c it y o f ro tatio n , 58
Vene z u e la, 87
Ven us 183 , 2 53 , 255, 266 , 2 77
Vernal e u i nox , see E u i nox
Vertical ray o f su n , 146 , 147,
152 , 155, 156 , 165, 166 3 13
'
Vin co c aya ( vIn k 6 k a ya) , Peru ,
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,
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,
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,
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,
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,
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,
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V
,
X
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X ico , Me xico , 85
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q
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q
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16 4
Virginia, 91
V oltai re , 2 74
V ol ume o f earth , 3 10
Ya
(ye ya m a) I s 84
Y aqui R iver, Mexic o , 85
eyam a
’
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.
.
Year, 132, 133 , 287, 3 10, 32 1
Y o u ng, C A , 16 3
You tl
Co mpani o n , 72 , 153 ,
1
'
76
sle ta (Is la ta) , Te x
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Y
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.
gg
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W
Wady Halfa
h al f a)
'
-
Egyp t , 83
Wallace , Kan , 35
Wandering of the poles, 288
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.
.
Zikawei (z ! k a we) , Chi na, 83
Zodiac , 1 16 , 1 17, 14 1 ,
Zones , 152 , 254 258, 260, 263
'
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