CONDENSED INTRO
TO
TESLA TRANSFORMERS
ERIC DOLLJI.RD
DISCLADmR:
This materia� was written ear�y
in the project and is in need of
e:tensive revision.
1-16
Pages
res�t from experiment�
investig­
ations and theoretica� considera-.
tions whi�e at my �ab in the
Marconi Wire�ess
at Bo�inas,
1980-1981.
Ca�ifornia,
22-25
(2) and
Pages
from reference
for re�ation to Tes�a
Pages
(3)
25-31
(R.C.A.),
Bui�ding
from
are
taken
adapted
Coi� waves.
are taken from reference
and serve as an i��ustration of
how the Tes�a Magnifying Trans­
mdtter can e:tract energy from the
Earth's
resonant e�ectric
Eric
March
fie�d.
P. Do��ard.
22, 1986
p.o. Box 220 * Bayside, California * 95524 USA
1
THE TESLA TRANSFORMER
©
11 e6 E,f� i)OU-ATl.."l;)
At the turn of the.century Tesla was
a means
of wirel es s
in the process of devis ing
The trans mis s ion involved
power transmiss ion.
the generation of long,itudinal ether waves .
this
is
not known,
but the idea
was
Whether Tesla accomplis hed
cons idered by
*
s uch as Kelvin a nd Maxwell.
Kelvin
generate "longitudinal \t?aves
in the luminiferous
phenomena of dis placement
on to indicate his
light,
as
greater
waves
curre nt
cons idered it pos s ible to
ether" thru the
He goes
(capacity current aD/at).
feeling that these waves
the longitudinal waves
other notables
in a s teel
velocity t han the trans vers e waves .
from his trans former propagate:.at. 'tr/2
must be faster than
rod move with much
Tes la claims
that the
the veloci.ty of
�ight.
It is interesting to note: that.:-the- veloc:;i.ty:measured .'-On.·:.the ·�e.sla
..
coiL is .a1:so.
.
"fr'!2. greater than·the·. vel.oc±ty "of:: light�'but�this ".
does. appear to be
a
phase velocity rather than a. group velocity .
Inhiswritings·Tesla.indicates
phenomena surroundthe e�nations
capacit y,
One is
and I
from the
s pherical terminal
have determined thes e to be true by experiment.
that the power
gradient
(poynting vector)
axis as the dielectric flux gradient.
is in the s ame
The other is the slow forma-
t ion of a conductive area surrounding the s phere that is
in nature
(in other words
is
not a s park
Contrary to popular relief,
W See reference 6.
not ionic
or glow discharge) .
the Tes la trans former is
not a
2
steady state device but i s a magnifier of transient phenomena.
Also it does not behave like a L.
c.
network nor a transmission
line, but more like a unique type of wave guide.
If all parts
of the system are designed properly the EMF and hence dielectric
flux jumps from zero to an enormous value a�ost instantaneously,
thereby producing an a�ost inc onceivable displacement current
The transformer is then
into space.
basically a device for rapidly
discharging the capacitor bank nearly instant � into free space,
producing
an
enormous dielectri c shock wave similar to
a
sonic boom.
Because the dissipation of the transformer is for all practical
purposes negligible, the energy k eeps increasing at a linear rate
per cycle of oscillation,
of electrical energy.
thereby accumulating a gigantic quantity
(A f
- orm
In order for the transformer to resonate with the planet the
energy storage in the active region that grows around the sphere
terminal must equal the conjugate energy storage of the earth,
a stiff requirement.
It is interesting
to note that dielectric -breakdown in this
active region grow into a log periodic form based on X2-X=1 as the
log base.
This will be recognised as the trancendental PHI or
the Golden Ratio.
In glow discharges the ions of metallic elements
form stable spheres of diameter inverse to the atomic weight of
the element involved.
as follows:
The transformer's principals of operation are
The first requirement is the
sudden coll apse of an energy field
thereby producing a sudden impulse of energy,
second is the
PI G-
.L C<.
TESLA
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transforming properties of the odd harmonic ordered single wire
delay
lin e
which
(coil)
E. M.F. and M. M.F.,
allow for the production of enormous
and third,
the die lectric phenomena s urrounding
the free s pace capacit y terminal.
1)
The formatio n of the energy
impuls e involves the discharge
of a capacitor with the highest practical stored energy into an
impedance
(inductive)
of the lowest practical value, and the dis charge
path is coupled to an energy s upp ly through a negative res istance
device.
This negative resistance is classically a spark d ischarge ,
but a superio r plasma device needs to be d evelop ed to enhance
efficiency.
Under optimal conditio ns the ex pon ent of os cillation
amplitude will be posit ive over a s u st ai ned period of time.
The net result of this sy stem is the production of an extreme
impulse of M.M.F.
of great d¢/dt.
An
alternate method is
the
dis charge of an inductor of t h e highest practical stored energy
into a circuit of the lowerst practical admi tta nce ,
thereby pro­
ducing an enormous impul se of E.M.F. of great d �/dt.
2)
The energy impulse generated by th e aforementioned methods
is then co upled into a pair of single wire transmis s ion s y s tems .
Thr ough induction a s trong travel lin g wave is formed.
Lropedance transforming properties of the odd
line,
the E.M. F.
Due to the
(A/4, 3�/4, etc)
order
of the wave is converted into lightning ma gnit udes ,
s till retaining the extreme d/dt of the initial discharge .
The capa citive discharge method of im p ulse generation is
Teslats faYorite, but Steinmetz s hows that inductive discharges will
also work.
6
The'capacitor contains the initial energy of the oscillating
system.
The buss from the capacitors to ,the primary loop
The capacitors should be
have a negligible transient impedance.
of the bolt on vacuum type,
however,
s hould
the unique dielectric properties
of water might be of advantage as capacitor plates.
The capacitors
must be in symmetrical arrangement with the primary coil.
The
primary must be of one turn only and exhibit the lowest practical
impulse reactance
S(P) P=di/dt.
Tesla indicates the proper length
of the prLmary conductor to be �/2=Kn,
w h er e n is a
harmonic
convenient for the size of the unit and K is unspeCified.
value is free osee
unspecified-is if this
capacitors or is
LC
number
Also
disconnected from the
dependent.
The transmission network consi sts of two X/4 single wire transmission
.
systems of negligible radiation loss.
.::the secondary
coil.
The
first of these is called
The next is cal�ed the
:.hencefort h w:i��-be':,ca�led.the: "�esla:CCJ±�·,�
_',
":is
.
"extra coil"
by Tesla,
This ,network.
typically,. absent' in: mast- uni.ts;', purport:inq. 'ta. be.-:Tes1a
..
The secondary coil,
serves
as
a:. match:ing ... ne'bt)rk,
generating primary' loop' and: the Tesla
factor·�· between the PRI and
co:iL.·
SEC' coils
is
.
0:
but
;'.'line
.trm:tsformers
between. the wave
The magnetic coupl:ing
typically
20%.
Negligible magnetic c o upl ing should exist between the secondary
and Tesla coils.
The function of-the secondary is three fold.
transforming of the primary M.M. F.
electric wave.
Second,
pulse into an
The first is the
abrupt travelling
to provide a constant potential constant
current transformat ion for good voltage regulation at the output·
terminal of the Tesla coil,
and third is to match the drive impedance
of the Tesla coil to the drive impedance of the ear t h.
•.
*
(
n e t page)
x
7
The secondary coil is of a low characteristic impedance of
�t.
the value Ss =
high s elf capacity.
s piral coils
This low impedance requires it to be of
This capacity is
of wide strip,
best
facilitated by flat
or by s hort coils
of wide s trip,
or by s hort coils of wide strip wound edgewise.
of the secondary must
3.
the
be very nearly. that of
The diameter
primary loop.
C onnected to this secondary coil is an additional coil,
the Tesla coil.
pronounced.
This
is where the magnification properties are mos t
This line or coil is also
�/4
possess the minimum possible s elf capacity,
highest pos sible characteristic impedance,
the greates t poss ible magnification of
long
however,
it mus t
resulting in the
thereby facilitating
E.M.F. by
the relation
Eo=�· Iin.
The s elf
capacity
of
the coil is
minimum
when
the diameter is
equal to length, roughly l� per centimeter of diameter.
of propagation alone. ·this.coll is ,"l2;times
due
to thedistributed.;shunt-":(:apacity�.
capacity
effects· whenthe coi..l
than resOnance
•
.
. .
The velocity
the'·veloci.ty."of
...
llght
This: .re.sul.ts.·�in:'�nolm.ced
.
is . operated; higher in. frequency
I.t wil.l discharge a rate .much
. .
faster
than the angular
velocity.·of free osc.i.llation, producing explosive phenomena.
The
self capacity 0·£ the t erminal s phere br ings the frequency of OSC
down to that of light velocity by acting as a shunt
the coil.
terminal.
capacitor load across
Tbere ::an be cons ,iderable e n:rgy radiation from the capacity
Steinmetz equations show a power factor as high as 40 %
is possible.
Dielectric radiation from the Tesla coil itself must be minimized .
*
It s hould be noted that the primary act s as a halfwave,
ng properti es .
exhibiting no impe dance trans formi
therefore
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This is achieved by concentric configura tio n with the primar y /
secondary system ther b y enclosi ng its dielectric flux.
The pote ntia l gradie nt along L�e Tesla coil is approximately a
step function due to the phase d i splacement of the. input impulse ' s
harmonics,
the velocity of the higher ordered overtones
however,
become propor tionate to frequency
s ign i f i c ant,
veloc ity
th er eby
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Fregue ncy
Coil
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900
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3Fo
2700
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Input Pulse Degrees
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(-900)
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(+900)
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The harmonics of the t�e function impulse are all in phase,
however,
the har.monics of the
and is theref o re a
space function are all out of phase
step f unc tion.
The
coil can be cons id er e d a form
of differentiator.
coil is a br up t at the last few
Hence the gr a dient along the
degrees of
coil length but
The last turns of
small
the coil mu st
elsewhere along coil
(see F ig.
be insulated ac c ordin gly ,
2).
it would
seem possible the gradient to cont inue to increase beyond the
dielectric terminal!
*
By fac i l i t a ting the last few de grees i n a
le a d from coil to terminal,
the gradient can be made to appear
along the lead rather than in the
coil,
min imiz i n g cap acity and flashove:
*EMF then also becQmes greater f arther from terminal,
reaching astronom�cal ma gnitudes.
possible
11
problems.
The dielectric radiation from this lead will be small
as it is Lmmersed in the sphere's flux.
No data exists as to the
ratio of the size of the s phere and earth.
The complete Tes1a transformer is shown in Fig.
3.
The
electrical length is 360 degrees at the fundamental of oscillation.
The earth connection must have negligible transient impedance,
star radial system preferred.
counterpart to the E.M.F.
terminal,
a
The earth terminal is the M.M.F.
capacity terminal.
Like the capacity
it is quite possible that the m agnetic gradient and force
will increase as the wave penetrates the earth.
Hence the 5 sections
of the Tes1a-transformer:
1.
Earth
2.
Primary ststem/ power supply
3.
Secondary wave coil
4.
Tes1a or magnification coil
'5.
Diel.ectric. antenna �:
It should'be:.born:- in mind: that
the. .tran-smission of. electric·waves:;.
lab.Work
as: .. severe'.
..
:' :Th:;is:.:is: .hardly dasi'rable for
damage to unprotected apparatus and electrical
interference can·re�t..
(1800 shift)
*
'resla:des.iqned:�thi:s,:,system for
To confine the energy an image coil
must be connected to the earth terminal.
Making this
arrangement in a horseshoe configuration produces intense dielectric
flux and displ a cement current that is quite usefu1l for plasma work.
Due to the immense difficulties surrounding the spark device,
a simple method and one of much greater control is shunt feed of the
primary network by an A.M. radio transmitter of special design such
as the unit at building number one.
Due to the high impedance
*The theories of ra dio at that time
considered transmission thru existing
lines of. force or
"ether tensions".
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offered by the primary resonator the �pedance effective of the
tubes must be high and therefore must operate at high anode
The el ec tro n emission however, must also be high,
voltages.
large cathodes and
necessitatins
High anode S and large electron emissic
teIr.peratu res.
are usually of inverse relation in available vacuum tubes.
pulse modulator vacuum tubes must be used.
Special
Hydrogen thyratrons might
operate satisfactorally at low frequencies where the�
d eionization time will not hind er commutation.
1 microsecond
The most effective
device for shunt feed may be the multipactor tube due to its stong
negative resistance effects,
l�eOKC
b ut it is not clear if it will operate belo�
with much efficiency.
By the utilization of the aforementioned devices a much �proved
field is devloped at the transformer output with regard to stability.
This
I have found desirable for the production of stable plasma
formations.
However,
I have not noticed the "j amm ing together of electrons""
unless the spark method is used
greater by the spark method.
as
the rate of ·rise of EMF
is much
Perhaps the multipactor will operate
comparatively but strong impulses d o not seem possible with shunt
methods.
For stability of certain plasma effects AFC may be required.
(See Fig.
5)
The image coil system exhibits strong discriminator
effects and thereby facilitates the formation of an error signal to
the V.C .O.
As to physical construction the primary should be sheet copper
of great conductor width and
large loop area.
Large surface is
required as the skin effect is total with impulses.
Large width
also min�izes inductance allowing for larger capacitors and more
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rapid discharge and hence high impulse strength.
In opposition
to this required �nductive reduction is the need for a large area
due to the flashover and coupling requirements.
Hence a balance
has to be established between the need for minimum inductance
for rapi d discharge and for a large magnetic field, resulting
in large inductance.
The formula fo r inductance
(rationalized)
is L=area/width.
Tesla indicates that the copper weight of the secondary
must equal that of the primary for maximum efficiency.
This
of . course goes along with:·.standard transformer theory but it must be
remembered that the depth .:of :pene.tration of waves into conductors
'. is microscopic forimpulses.
This coppe r requirement must be modif ied
to equal surface area rather than weight.
As to the use of water
for capacitor conductors Tesla gives no reason.
It would seem that
this is done for the sake of simplicity and/or is a holdover from
the Leyden jar.
(Remember he began this in 1890 ).
However,
water
has many curious dielectric properties that may be essential in
operation.
By theory,
for maximum discharge velocity the dielectric
must be a vacuum.
Analysis
(See Fig.
6)
The oscillating coil differs from the transmission line on
account of turn to turn capacity and distributed mutual induction.
The presence of series capacity causes the coil to respond
as a capacitor network
(with no inductive effect)
towards abrupt
impulses and ang�lar velocities greater than the angular velocity
of free . oscillation.
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The voltage distribution along the coil at the first instant
depends on the factor a=
capacity from end to end
�g/cs.
•
Cg= capacity to ground, Cs=
.
th � greater the concentration of voltage
The greater a,
The max�um voltage per unit length
at the feed end of the coil.
is equal to a t�es the voltage of uniform distribution.
a is a
small fractional value with Tesla coils.
The greater the d/dt or �
the greater the gradient of voltage.
If the impulse has a long tail the p henomena will be as
described but followed by a damped oscillation.
By impressing a sustained oscillation,
(OSC)
and if the coil
.has a small dissipation const"ant u, the voltage will
continue to increase indefinately.
capacitor ladder network
Initially the coil acts as a
7).
(See Fig.
The capacity elements a re
c har-ged to nearly twice the applied E.M.F.
capacity being charged is C=
�CgCs.
The effective
Because this netwwork contains
" impedance elements of only one type the voltage distribution is
hyperbolic rather than periodic.
If
%=distance/total length and
e is voltage to ground at the particular distance,
e= Eo COSH a %
COSH a
.
linear as possible
For Tesla coils this distribution should be as
(small a).
As the distribution goes from initial to fi nal the voltage
can be analyzed into a complex series of decremental waves at various
frequencies and wavelengths.
initial distribution
to the final
(DC)
This is accom plished by analyzing the
(hyperbolic)
distribution.
exists between frequency
into space harmonics with respect
If a is considerable, no linear relati o
and wave l ength.
( See Fig.
8)
When a n oscillating wave fol lows the initial impulse
(as is the
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case with the Tesla transformer)
the alternate positive and negative
voltages cause continuous increase in vol tage and energy.
The effect
of the alternations is to increase the amplitude o f the wave by twice
the applied voltage for each alternation.
voltage is 1. 24
times applied voltage.
Example - oscillating
(initial)
At each cy cle
this is multiplied by twice Ea, causing E to ground to increase in steps
At second cycle E is 4.72, at third E is 7. 20 ,
etc.
This effect is
reduced or suppressed by large u or �
The action of the spark gap has a multiplicative effect also.
Consider Steinmitz'
analy sis.
"Continual or cumulative oscillations
involve an energy supply to the system.
ener gy dissipation the e sc.
than
u.
do¥t1Ps
If the energy supply is less
as a trans ient with reduced
If the supply equals the dissipation the esc is continuous.
If supply is greater the esc is cumulative.
The esc represent energy and frequency transformation from
the L. F. or D. C.
supply to theH .F. esc system.
This transfer may
be brought about by the transient of energy readjustment resulting
from a change in circuit conditions, producing agairi a change in
circuit conditions and thereby an energy adjustment by transient,
etc.,
etc
•
.
•
Recurrent oscillations tend to run into each other and form
continuous esc.
When successive transients run in to each other
they tend to synch.
However, the formation of continuous esc is not the mere
overlap or running together of successive waves.
The recurrent
OSC c'annot start until the preceding esc has died out I
charg e time has elapsed for next arc a'er of gap.
and suffic ient
With overlap no dead
period occurs during which normal or supply frequency is supplied.
Energy then must be supplied by
a phase disolacement within arc
FIG
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dx
=
-
=
/V\=
L,
C,
KI
MI
/?')vT"r,.,lA'
/,A../T)Glc,A,/VCt-
-
L
?£R
/...vc;....t
-
C
rE"12
/;UCH
::I
a
I<
/V\
Pc�
IAJCH
�B2 ,INCh'
IN
(#G'",vny)
'U
-
1
-I
r�
;4 L.
L
+
G
-
C
]
22
Dur�
osci��ation, which gives a negative energy cyc�e or a reversed
hysteresis �oop. For continuous osci��ation then,
�oop nust be £ormed by the �ag o£ e££ect be£ore
a
hysteresis
cause."
(This is
negative resistance or the £ormation rather than the dissipation o£
energy. ) "For the cWDU�at:l.ve osci��ation,
depend
on
and increase
with
the
area o£ the loop
must
the stored vo�t amps o£ the osci��ating
system. II
Mathematic ana�ysis ( See Fig. 9) ( See re£erence 2)
e
=
E
to
ground
By lCircho£f's
es
=
gradient ( E/ inch )
E
Law
=
7.s
Let
Let
=
'7t
=
a/
/a�
a//
d t:
=
space operator
=
tae
( 23a )
0
operator
Then
Differentiation of
"'Ys')'�
These, ( 23a )
of
&
IL
-#-
(2)&)
'71t?'�
in time
Is
-
gives
"Ys"""'t
J,
:
0
( 23b )
(23b) are independent of initia� and £inal distributions
EMP' .
Equation (23b) must be expressed in one variab�eo
vo.ltage
C
g
and
current, the current density in capacity
per inch of coil times
the
rate of change of
e
to
In
terms of
grounc1
is
to ground.
( 26 )
R.�atiDg I
I
the
s
II
in
capacity
time rate
23
To �t a ge
aDd
turns equa�s capacity per inch times
between
of vo�tage
gradient.
IS :
?'� ?'"t
e
K
(28)
"I
I
(29)
Re�atiDg I� and vo�tages
The re�ation between magnetizing
( See
10).
defies
ana�ysis.
(t
)
the effeQtive inductance of
t
co s in e wave of current
wave
of the
times
the
cosine
opposes
norma�
wave
the
induction
of
Fig.
total
or
remaining
depending
the
and is
For the
the
IDUtua�
is
comp�ex
inductance
space integra�
equiva�ent
inductance
of
1/3
of
diminishment
of the
and
distribution
third harmonic,
1nductance resu�ting in
on the
�
coi� is the
of H.M.F.
H.M.F.
I
fundamental
For the
inductance.
current
current and
2/
to
3/4
the
coi�
of
se�f
bucking section
to the rest of the coi�o The process progre •• es simi�ar�y for the
7F,
rest of the harmonic series
(5F,
impedance for each harmonic
but effects
Capacitance of the
vo�tage dependent
conditions.
behaves in a
giving the
( Parametric
Denoting
the
coi�
coil
9F,
etc.
ten d
).
Thi s re s ul.t s in surge
to
cance�
for wave �ength.:>
simi�ar fashion and may be
vOltage gaiD under the proper
amp�ification
)
this residual inductance as l eaka ge inductance L,
dimensions of 1
-2
as
the
DlUtua�
induct ance M
(Henry- 1 )
,
aDd
then
(30a)
-
(30b)
24
r/� 10
(
s-
9
N
(�('--{-O
A
AI '/
h', ,/til.
13
c
F
l/'b
(')../�
L,,=
1,A/7)f./CTANCc
=
n
.
M .;AI1.�
-
1./7r
(hi."""".;: )
D.C.
+
':J./1t
)
/fI7./f'J.�
DC
r
•
(30b)
the
give.
va�ue of
..,,�
I".
whi�e (2)a)
,
in'Yo� 'Ye s ,.,..�
If we differe�tiate the former with respect to x and the
re spe ct to
25
I,
•
1atter with
substitution becomes possib�e.
t,
()1)
(31), (29)
Hence,
This
the
express
in terms of vo�ts
By
terms
of
(2)b).
�osses.
of the interaction between
the earth and various
possib�e by the use of ve10citymea sure .
comp1ex
the three
genera� equation:
equation n eg�e ct s
Ana1ysis
is
(27)
and
quantity
consisting of rea � and
coi1s
This in gene ra � is a
imaginary parts.
re 1a tion we1� known:
the
(34)
where v
time
is
the
to space.
f'mlctiona
Letting this
t
ve�o ci y be of unit �ue,
''''s =?'t'
2
become equiya�ent,
bstructions
Then ve�ocityis
ve�ocity of the wave.
2
•
stei.Dmetz gives
the ratio
time and space
the fo�1ovi.ng
for accomp�ishing this._
"Line constants are typica1�y given per unit �ength,
cent�etre"
mi�e,
1 000 feet,
in clistrubuted circuits,
unit
gives
is,
time,
v
or
1010
=
1
and therefore
C
=
L
-1
;
per
when dea�ing with transie�ts
is the ve�ocity unit v.
choosing as
3 times
as
etc.
The moet convenientvunit o� �ength,
Tbat
of
�e�gth the distance of propagation in
unit
em/sec
for transve rse waves
LC
=
=
1
�
in air,' this
26
That is,
the capacity per unit of length,
in velocity measure,
is inverse� y proportional to the inductance.
uni t of length,
In this velocity
distance will be represented by A. "
Substituting 6= I
to = ).o
F=l/Ao
Time angle � = 2nFt = 2�t/�o
Distance angle w = 2nF�= 2�A/�o
Analysis of the travelling wave along Tes la coil* utilizing
the light second.
,.
The equation for standing waves on a li ne are as follows:
i = io
e
=
eo
¥
COS
Jt
SIN
(e��)
(1)
(�:t�,.,,)
u is the power disSipation constant.
The power involved is:
( 2)
2
Because the sineterrn makes thi s symmetrical about zero
For the travelling wave:
the average power is zero.
i = io
e = eo
If
COS
�
COs
(� t:
."
(� ;�v)
The power involved is
eo i o
-
2
-l..,,-r
Eo
)
[1 + COS
(2)
(3)
:
(�:l'..
(4)
Power average is now :
2
*
Steinmetz's analysis modified.
(5)
27
Thus
two waves exist,
a.travelling steady power flow given by
and a standing wave given by
( 5)
s uch a
(2)
flow of power flows
along the different s ections
of the Tes la trans former,
of sections
For instance the
of different u.
primary
consisting
has very
u due to the large s urfaces and the negative u of the arc,
has a higher u due to no arc,
the small
the Tes la coil
conductor size of winding,
has a very
has
and the d ielectric antenna
high u due to radiation.
zero or negative.
to their higher u,
It then
follows
to antenna,
and by themselves their osc
tog ether,
so as
to have all
The power flow is
cons tant in the
s horter due
would dampen
all mus t dampen together.
s ections dampen together.
uniform,
general compound sys tem:
that is ,
the power remains
direction of propagation.
b)
The flow decreas es
c)
The flow of power increases in the direction of propagation.
This
as
u
that power must flow during transient from primary
Three conditions can occur in the
a)
very great as
The duration of coil os cillation is
Since all are connected
quickly.
the s econdary
higher yet due to
In the pr�mary the duration of oscillation is
is
low
last cas e is
in the direction of propagation.
of s pecial interest in the Tes la trans former
it increases the steepnes s
of the wavefront,
producing greater
displacement current.
If the flow of power increas es along
every
line element than enters
drained of its s tored
dies
it;
that is ,
not all the s tored energy of
power dissipated in the line elements ,
the
elements
in
more power leaves
the line element is
energy by the ?assage of the wave,
down with time at a faster rate than
That is ,
system,
increasing the flow of
by
its
the line
and
then
own diss ipation.
elements
supplies the
but part of the energy leaves
power
along the
line.
The
28
rate of dissipation thus is increased,
the equation.
and instead of u,
u+s enters
That is the time decrement is:
-(u+s)t
e
s is the power transfer constant.
But,
that is,
Eo
inversely,
along the line
the power flow increases,
the intensity of the wave increases, by the same factor,
+5).
or rather,
the wave decreases along the line at a slower rate than
that scattered by the power dissipation.
Therefore,
that taken from
the time domain is transfered to the space or distance domain.
i
.
=
io
Similar for e
�
P AVG is
2
E
-2 (u+s)t
E
+2s)'
The power transfer constant s determines the steepness of
-the wavefront.
To meet these requirements the u of the line
must exceed the average
Example
Uo
of system.
(See Fig. 11):
Transformer
=
"
Length
in light seconds
Dissipation
uo=
u AVG.
and s
=
=
1.OxlO
u
u�
100
0.1
�A
=
-3
1.5x10
-3
L:"",').
+ 700
=
Line
Load
-3
0.5xlO
900
1.35
1600
0.8
-100
-800
800
29
FIG- 11
XF,/IfR.
J./NE'
"1--11,1',
,-
F .
w
D
J.OAl)
•VW\
-
,
-
.
I
,
R
a
,
L
"Z<...
+/00
J./A/-
+w-OO
,
�
1)/'STAA..<;c
�__�____��__�__
•
'
,
..
•
•
-
-
--
""
" � nn"1sCS"'
•
,.
,
,
"
""
'P'
.
l./A/e
'X�;.fp.
�
?OIuCrl
-700
L.OAD u
,
,
}b���
�FM� �
,
,
,
,
-
"'
•
.lOAD
,�
,
,
,
•
,
,
,
-Jt13
'XJ:'MR u
J.IA/C
'k.
Leult)
""
- �3
-1"& 7
,
,
,
'
.
,
•
.,
#
_
•
•
rAAI ""
-I
c
7JAl1: CO,u�VlAI T
_
i
Tne transformer th us dissipates power at a rate u=lOO but
sends power at the rate of S=700,
dissipates by internal losses.
u -
or seven times as much as it
The load dissipates power at
that is � the power
1600 and rec eives power at the rate -S=800,
it d issipates is suppl ied from other sections,
in this case the
transf orner.
The transmission line dissipates power at the rate of u=900
only a l ittle faster than the system
power at -S=lOO,
transformer;
that is,
Uo
of 8 00;
and the line
receives
receives on�y 1/9 of its power from the
the rest comes from its stored energy.
For the special cond ition of waves increasing in magnitude
towards lead;
'). =
-3
lxlO
u
=
100
�=
1.0
u0 =
L oad
L ine
T ransformer
-3
0.5xlO
3
1.5xlO
1600
500
0.75
0.8
AVG u =
S = +433
-106 7
+33
That is the power transfer constant of the line has b ec ome
positive S=33 and the l ine now assists the transformer is supplyin g
power to the load
(See Fig. 12).
The preceeding paper has attempted to show the considerations
involved in the optimization of the Tes la tran sf ormer .
T he en o rmo us
number of fac tors involved make this a difficult task indeed!
The
authors of coil analy sis have come up with conflic ting results and
an attempt towards resolve has been. made.
equations
have not
been
given
due
to
lack
solutions to the differential
of
generality of
those
31
ava i l ab l e
a nd l ack o f s p a ce .
men t i o ne d
I t ha s been
i n papers on the
s ub j e c t o f coi l
o s c i l l a t i on s t ha t the ory doe s not ma t c h p r a c t i c e .
exper imenta t ion
)s
-- ?:
is ne c e s s a ry .
doe s not give
c la ims
that his
i n f o rma t ion
1.
2.
3.
4 .
5.
6 -.
i t a l so m i g h t be p o s s i b l e tha t
the proper ve l oc i t y ,
ve l o c i t ie s are
Much more
f a ster
re memb e r i n g
t ha n l i ght .
that Te s l a
For f ur t he r
see :
ABNORMAL VOLTAGE S INT RAN S FORMERS . J . M . Weed .
Ame r i c a n
I n s t i t ute o f El e c tr i c a l En gineer s .
S ep t . 1 9 1 5 , p . 2 1 5 7 .
ABNORMAL VOLTAGE S W I T H IN TruL� S FORMERS . L . F . B lume .
F eb . 1 9 1 9 , Am e r i c a n In s t i tute of E l e c tr ic a l En g in e r s
ELECTRI C WAVES ,
D I SC HARGE S AND IMPULSES .
TRAVEL IN G WAVE S ON TRANSMI S S I ON
1 9 3 8 , 1 9 5 1 . Dove r .
SY S TEMS .
C.
P.
D.
p.
S te inme t z
B ew le y ,
D IELECTRIC P HENOMENA IN H I GH VOLTAGE CABLE S .
Rob in son , 1 9 3 6 .
,
L.V.
M.
ROENTEEN . RAY S AND P HENOMENA OF THE ANODE AND CATHODE .
E . P . T ho mp s o n . 1 8 9 6 , Van Nos t r and Co. , p . 9 3 ( K e l vin ) ,
p . 1 36 ( 're s l a ) .
5 77 .
•
,2
Fl c;. .
1 1·...1111111 1"'on Lil1�
/�
Tl .... l�.!Urlllf"r
T.-anan",.!',,,, .. Lilt�
U - :IOO
u _�
I
U � - .00
_
Energy Dist rihution in C'ompound O!;rillat ion uf ()pen Circuit .
•
may come
Than Light !
By HUGO GERSS BA CK
�h()(k, to most 5tud .. nt� of scien.:e,
th .. r� art' �ti11 in tht' "'o rld some
�('i,.ntists who helie.. � thAt ther� li r e . pt't'ds llr,.ater
t han that of Jip:ht.
S i n('t' the advt'nt o r F.instein. ",osl �d-n t i � ts and
physicists have tRken i t rur Il'ranled thRt & peel\. jrr,.at,.r
than 1 86,800 mile� per s f'Con d art' impo.s i ble in t he
universe..
I n deed, one or the principal tenets of the
relativity theory is that the mass of a body in c reases
with ill lpeed, and would b�me Infinite at the yeloc­
ity of lip1.
Henre. a greater yelocity is impossible.
Among those who deny fhat this il true, there ia
Nllrol& Tesl&, well known for his bUDdreda of im­
portant Inventions. The inductknl motor and the ..,__
tem of distributing alternating narrent are INt & f_
of his creat contributions to modem 5Ci-. In 18n.
be made his historic nperimrntl in Colorado ; when
he _nufaetu� for the lint tirM. artificial lirbtning
bolts 100 reet long. and where he was abie. by mean l
of high-frequency cu rrents, to l ittht elt'Ctric lamp' at
& d is t a n C'e of three Dliles without the USe of any w i res
I
I
T
Faster
to
learn
as A
that
whatsoe"er.
•
Talking to me ahout the� exp,. riments recently. Dr.
Tesla revealed that he had made a number of 5ur­
prisintt diS«'o"eries in the high-frequency el,.ct ric field
and that. in the course or t� u periments, he had
become convinM that he pro"attat� frequencies at
speeds Nlher thaA the speed of li,ht.
In his patent No. '78'7,112. filed M ay 16, 1900, Tesla
ahowed that t� cu rren t of hil transmittu passed o ver
the earth', su rfaC'e .·ith • speed of 2!12,880 nl i l t'S per
�nd. while rad io wayes proceed "' i t h th,. - el'H'i ty
of litrht. Tl's la holds, ho..,,.v�r. that our vr�.en � "rRdio"
wa y ,.s are Dot trur H ,. rtzi.n "'awes. bUl r � 8 l 1 y so:.tr.d
w . v es�
H� i n forms
mt'.
furt!> .. r. t hu.t he k,WW, tlf sl' .... u �
s eve ra l times grrater I han that nf IiJrht, . . nd thllt he
hal
designed
a pp aratus w i t h "' hkh he ex pe('ts to
eled r Dn s ...· ith a sperd ,.. . u al tll t ", i " e
project so-<alled
t ha t of light.
Coming from
should be (iye
10
due
eminent a IDU I'Ce, the statftnmt
conllderation. A fter all, abstract
•
nll. th�mllti("s i< !'nr th' l' lr. and a("tual ex�r;men tation
j � a n o t h e r . Sut </'I :nan�'- years allo. o n e o f t h .. "' orld's
jrrrs t .. " t lO("ienti< t - of tl'", t i me r ro"rd �nath"""" t i ",.. l I y
t t .... t i t is im pt·;: . or. ! � : . • t!�- i< h,.a\· i e r - t h ,l n -, u r � I l .. (' h i n .. .
Yet "'e ar� t! y i r.i/ r ; " � " "f .. j rl'lan .. � l oday.
Te�IOl t·CH.. t rH u :('t. .. part ,,� t h.. :r l R t i \'it� th ... , n·
emph .. t kal l�·. ho I t1 i ."
th.t m L<. is u n . I ! " � R b ! e : ot�r­
",· ise. ene r ltY ('oul d I,e i'rn<l ..('� f rom �lothi nJr. "i n('e
t� kin e t ic ent'r;r�- II('quired in t he fall of a body would
be greater t ha n th"t n«f'!>5&ry to lift it at a small
veiO('it}',
It is
withlll
the bounas of posslhility that Ei nstein's
.peeck «""S ter than litrht ma�' �
wrong. Tesl& bas bee ript Ulany tirnes during thr
p.. t. and he _y � PI'09f'ft ript In the fatun,
III
any "ent. the Itaftmrnt tNt there . an s� fastrr
thaD lipt Is & tnmendou 0-. aDd. opeDI up elltirdy
new " ilt .. to 5Ci�.
\\'hil,. it is �!i,. .... d r\ !."&nt' St'ientists. t" da ,·. that
the (.. r(o,. of /travit .. I ••,,, · i:i In-�Iy another m.';i{esta­
t iun of .. h·,·t r"r' i&{". ' "
"' '' YI',:. I hrr� h,,,· ... a. ,·et.
h,."n no pr,oo(s of t his.
Tn.. rl' a re, of . ·t'u rsl'. n.:" n \·
oh" 'urp I h i n ,.... .. i"'ul frll \·i � .ti"n th a I we ha" e not, as
y,.t. f.t l:"llI ...d .
A t 0 1 , <, t i lll�, it ..... belie"ed h,' :nan \" <cie" I j .ts t h . t
'
t he s p ..ed of j[ r .l , i t a t inn i s ift5hn tan ;" u � th ro" �hou t
th,. u n ; ",.r",.. This is sin'ply &S'Icoth,.r way of putt i n g
i t that thei t' art' & � !I Ireater I h an Ii!!,hl.
Yet. from a s t rictlr M"il'ntific: Yie.·point. 110 " ne t�
day has Any ide. ho .. fast jtra"i t a t i,'nal wa" f"'-always
p ro \'idin!l' th"t tht' fo� is ill :tar .._tr ... .. l.
I f the
moon, fu r in<�ar.r .. , "·er,. to esplode at a jl'i';en morn,.n t.
h, · ..· I"n,l[ ,,· . . ,,!,I ; [ i·.. i ... r. • rt' thr � r" .. i t . l itJn"j d i � t u rb­
an .. '; ,,· ,, :.z ! d 1If' fel t , " ,,:.,t:' ··
Would �h .. j."TK d t a t :nnal
i m p u lse o r ,,· ,, ' ,.s [ � � \' <' ! .. I : 1 · ,. s' ..... d of l i ir h r -- t h a t is,
1 1<6,000 nult's r .. r . .. . · ' . n d · �r .. " ,, 1 1 t he e /fcC't I .., i ., ­
s t tl n t .n�ou.); : \\. ... d n fl" � :.o ..
The- f' n t i rf' ... u hj r(" t ..... 11 �o d.;n d , t :. " H.. ... .. It t r r : u r- uduu s
int .. rest in s,·i .. n l ific: c i rC'le",_
It i6 I"'ped that other
l('ienti�t5 ", i l l he ent'oura� to i n"'l"lIb,ate D r. Tesla 's
far-r..�hi ng a.swrtions ; either to definitely proye Dr
to disprove thenL
mathematic:a
of
'N o , 6 4 9 , 6 2 1 .
N. T E S LA.
P atented •• Y ,1 5 , 1900
A P P A R A T U S F O R TR AII S . ' S S I O N O F E L E C T R I C A L E II ER6Y.
( . . . . . . . ,)
c.
I.
UNITED STATES PATENT OFFICE.
N J K OLJ. TE� I . A , O . N E W 'iORI{ . N . Y
A P PA R A T U S F O R T R A N S M I S S I O N O F E L. E C T R I C A L E N E R G Y .
BPEClnC.A.TIOH
lol'lllo.lD� put or
Wt&en 1".....t Jfo. M8,81 U, datad Jla7 I ll, 1 800.
on,; ••1 ."Ii.. ti-u II.. �"r :, ll'7 , leriu ... laCi.'U. blYloIocI
••. e,710. I •• cod.l
5
10
15
10
'5
30
.15
40
45
50
eili' l
...
·
t"• • ,�II_t1 .. II.. r.� I t. 1 toO . leri.l
'Tn all u·h mn ,t ",all CD"""7'1I:
elevat ion sui table for tbe p u rposes 01 "·:ln�·
Be tt k nown that I, N I KOLA TaLA , a
m ission . Tbe ot.ber �rm i a31 of the secoodnry
zen of t.be l! n i loed Slales, rMidiD
At t.be bor·
A, is eon neeted II> _rt.b , and, if dell i red , to
the pri m ary al .. .. io o rder t h:\t th" latter m ay
ol\�h oC )f anlu ltlan , in the cit)" 0 New York .
be at " u ".. ta n li�I I ! t be same potential as lho 5 5
co u n ty a n u S ta t e of Ne- York , ha�e i n veDtf'd
eer ta i o n ew a n d useful IDl provemeou i D A p · adjaren l portioo!t or t he aecondarr, t b a!! i u ­
p:uatus {or tne Tranam iasion or Electrical s u r i nl: lla fety.
At the reee i viDg - lltation A
Energy, or .·h l cb the folJowing is a s pP.C i fi ca· Lraosformer or silll i lar �nstrncLjon is em ·
p l oyed ; but in thi. e.... tIM IODJrer coil A ' eQIt·
Lion , reference Uein� had 10 tbe d rawio.g ae ·
companyiag aud forlll ill2 a part oC the same. ati LoLes the primary, aad tbe shoneI' t!oil C' 60
Tbi. llpplicat.ion ia a d i v ision of an Applica· t.be eee O Ddaf'J', of the ttaDSformer. In t he cir·
\iOD flIed by me 0 1 1 September 2 , 1 1!97 , Se r ial c u i l of the laUer are coaDOCLed l alll p3 L, . " .
lio. 6SO,:U3, e o t l tled " Syatems of tl"1lDsm is· to" If , or oLher devle. for utiliziog t be cu r·
alons oC electrical energy , " And is baaed U POD
,"" o t.. Tbe "Jevated &.erminal O' cooneoc:u wit b
D e w and u N f u l reat.nree A"d combi natiolU of the ceD ter oC the coil A', aDd :ht' otber te r · ci S
appatat.as sbown aDd dfllC ri bed i n Aid a ppli - m l Dal oC saHi eoll is c oa D ec ted to Mrlh an.l
coaUoa for carryinr oa L the Dlethod t.berei n preferab l y , alao, too Lhe coi l C' for lh(' reuon s
diecloeed A a d clai med.
above I�ted .
The i n vent ion whicb forDis tbe I>nbject or
The leD1ti. of tb .. Lhio "' i re (,NI in each
my preseDt Applicat.ioD com prises a trAnsmil· trAII . Cor. n e r 8houl":' be appro x i m ately ODO· 7 "
l i o ; oo l i or eODd uctor in which elect rical e u r· qu arter of t h e .ave leD gt h of Lbe elt'ct rie d is·
r6D ,", or oecillatioos Are produced Alld wbiob to rbanc(' io the cireui t , thili .. t i m.�e boiDg
ill arrang.a to caUN laeb carreDta o r oac:ill a· baled 00 Lbe velocity of propaga .. ioD n( the
&.ioa to be propag"ted by cond uotioa through cllstllrbAnee tbroQgh the coi l ilL'tolf and tho
t.he D a la ral med i u lli from oDe poiDt. &a aDoUier e i rc u i t. w i th wbicb It is d .. igoed to be aeed. 7S
remo&.e tJ-erefrolll ADd a receivlDK coil or coo- By ""y at ilI ust.raUoD , if the rat e at wh ich
d llcfor a& Illoh d iAaDt poi n t ad"pLed too be es· t h e C U rTen t tra\'erMII t b e circuit i nc lu d iDg
clt.ed by the OIIc illaUoDI or CUn'eDta propa- Lbe coil be ODe h U Ddred aad eighty· Ii \'e t.bOD ­
pLed fro m tbe traDsmiUer..
&aad m il8l' per aec:ond theD a frequeDc)" of
Thil apparatUl ill lhoWD iD the acco m pa D Y · n i D e h U D d red aDd tweDty - 6 � � rer lecoad 80
Inr d raw iDg, which il A diarralli m at.ic m DS· woald mAi"at.aio DiDe hllodred aad t weoty.li,e
traUoD of t.he &ame.
ltat ionary moves in a oire.iL ODe ll u adred
A II a coil, :tiDerally of maDY tu TU aDd or aDd t' l rhl1 ' � \'e tbousand mil.. loag aad eaeb
A Te,.,. 1al'le diAmeter, woaDd ia �lra l forra wan w o u ld be two b U Dd red mllM ia leDgth •
either abO at. a magnetic eore or DOt, .. may
For IOcb a low freq uency, which woold be 15
be d .. lred. C II a aeeoDd eoll formed by a resorted to o D ly - bea il il l Ddi.a peuaable fo r
oaa hetor of III lIch larger aize aDd .maner the op8pal ion of motors of the ordi llAry k iD.I
leDrth 1tou.,d aro n ncl All d in prox i m ity to tbe UDder the cond i l.ion. abo" e .. u m ed , 1 would
eoll A.
aMI a �o n d a ry or li tty m il .. iD leogtb.
Jiy
TIM apl"'I'Atu. at' one polaL i.e used &I a aach aD adj usLment or proport.loo i D g of tbe 90
UaDallli lter, C.he coil A in tbis cue con s LiLot- leDgth o f w i re i D the seeond.ry &: o i l o r coila
iDC a hip·tea'i9n, MCOadal'1, ADd the eoil C tbe poi n u oC hi ghest . po:.ential are mad e k»
tbe primary, oC m uch lowe r teaaioD, of a trans· coiDcide "' itb the elevated term i nAl. 0 D',
fj)rmcr. I D lbe circlI il of the pri .D"ry l: ia i a ' ADd tt "boll hl be und�rst.ood tbJ\t whate ver
elueled a aui lAule aouree of eorreD t G.
One len::th be �l .. n too the w i res I bis rt'qu i rem "nt 9S
t.ermiDAl of t b e aeeo nlla ry A ia at t h e ceDt.er sbo u ld be eODl piied with i n ord t' r lC"" ooLAin
oC tho .plral coi l , and frow to ia term i Dal the i tbe bes t rea u l ,",.
cu rrellt Is led by a cond llctnr n to • tern d Dal
I L w il l be rt'ad ily u ntleratood tbAt w h e D t.i",
n, prt' Cerab ly of large sllrface , fo r m ed or abo\· o · p rMcr i bo!-d relation, es iat t b .. \.)oal {'nn · ·
mni D l n:aed by Buch me:\116 as a bal loon at aD : d i lioDS Co r reso Dan c e bet_MD tbe tr&n,m l ,· . o e
f
l
I
35
t
lj np; and recei v i n g ci rc u i ts Are AttAined, a n d t b e former case t h o t'oll l l ection of o n o terlD i ·
Ofl"i n ci to the taet th a t the poin� of h i gh est po­ nal o f the recei \' i n � apparat.us to the ground
l e n t illl i n the coi ll! or conductor.. A A' are - m i gh t n o t be permAnent, but m il!'bt be inter- 70
cO lucirie n t w i t h the elevated term i n Als the m itle n tly or i nd ucti vely est.a.bl isbed withou t
5 m a x i m u m ftow of cu rnm t will \.ake place in de parti ng from the spir i t of my i n veD tion.
It is to be noted thAt the phenomonon here
t h e t'll" O coi ls, and this , f u rther, neceSSArily
i m plies t h at th e cApacity a nd inductAnce in i n voh'ed i n t h e transm ission of electrical en­
each of the circni� have' linch vai lles as tG ergy is one or true cond uction and is not to 75
secure tbe m08� perfee, CODdition of syucb ro- be confouDded \vitb tbe phenomena of elec·
trical I'Ild i ation whicb have heretofore befon
10 nism witb the imp� oeclllaSions.
When the aouree of cnrreDt G is in opera­ observed and wh ich from the very nature and
tion And producee rapidly pulaat inl or oecil­ mode of propagation wonld render practiCAlly.
. lating curreate
in the circuit of coil C, oor­ i my.l88 ible tbe tnulam_ioo ot any appl"ft· lio
responding iDduoed c u rrentl! of very m uch eiable .moun � ot eDergy to auch d i slA n cM a.­
15 hieher pO\en Ual are gen erated in the aeoon d­ are of practical i m portAnce.
What I now claim AS my i n veDtion isary coil A, aud since the potential in the same
1 . The eom bination with A transm iLti ug coil
gradually increases wi th the n u m ber of turns
toward Lhe center and th e d i fference of poten­ or conductor connected t.o g ro u n d and to a n Ss
tial between the ad j ace n t t u rns is compara- elevAt.ed termi nal reapoctively, And means for
producing therein electrical c u rren� or oscil ,
10 tiyely smal f .a very high pdten tial i m practica­
ble with ord i nary coils may be successively l ati o n s, of A reeei l" i r. g coil or ccon d llctor si m i ·
larly con n ected to �roll ntl nnd to an ele\'''ttod
obtained .
As the mAiu object for w h i ch t h e appr.rll1 us term i n al , at a d istancs from tbe t r8 n s lD i " �I)
is designed ill to prod u ce a c u rre n t of es:ce&l' ti n g-eoi J -And Ild apterl to be esciled by cll r ·
2 5 · l \·ely·h igb poteu tial , tb is object is fllcilitAted re n ts CAused to be proPAPu·d ( ro m tb e fla m e
by "Usiug a pri mary c u rren t of \'ery consid· b y co n d u c tion throuL'h t h e i n lon-on i n !: D a t ·
e ra b l e treq uency ; bllt the freq uency of the u ral m ed i n m , A ! !Condary co u d u c to r i n i n ·
c u rrents i s in a large m el\"� l I r� a r b i t rary, fo r d u c ti v e relation to lhe r�c� i \· i l l � .co n d tl c t o r 9 5
i f the poten t ial be s n ttk i e n t l y h i gh R u d the And d et' i ce8 ro r u t i l i::ing t h e c U I're :! ! i n t h e
30 te rm l D als of the co i ls be ID A i n ta i ned at tbe c i rc u i t of s[. i d 3econd sry con ,.l t: ctor. AS set.
p roper e l e vatiou wbere t b e fl t m os p h e re is forth .
2. The com b i n ation w i t h a t l'ansm i ttl D g co i l
",relled the strat u m oC all' v; i l l se r,e Pol; � con ·
d ucti n g m ed i l l m fo r t h e c tl r r" n t prod u ced or conc uct o r bn.Yi cg i ts e n ds coo uected to 1 00
And the latter w i l l be t ra n s m i tted t h rongh tlJe r;,roc n d and to au el�t':.:.ed term i nal respec·
3 S air, with. i � may be, e ven less resist Ance �an ti vely, a p ri mAry coil in itul uctive relAtion
thereto SOC " sou rce 01 eloctrical oscillations
through an ordinary conduct.cr
Aa to tbe elevation of the termi nals D D', It in said pri mary circu it, of A receiving conducis ob�i01lS that this Is l\ mAtter w b i c h will be tor or coil having itB eods connected to grouDCl 105
de&enDlaed by " Dumber of things, AI' by the aDd to an ele\'atfd t.e:'1Dinal respectiveJy aac!
40 AIDOGDS aDd quality oC the wort to be p91'­ adapted to be excited by cnrte:!ta caused to
ronaed. by the condit ion of She atmosphere, bo pro� from tbe tranamitter tbroqb
and alao by the eharoiCter of the 8urroundiDg I.b natarat medium a.ad .. MCOQdary circuit
countl'y. Thu it there be h igh mountni[l!! in it!daetive relation to the receiving-circu i t 1 . 0
III the ,.ici1Jlity the termiuala IIho;J ld bo at A and rec::iviog devicee connected tberewith .
45 greater height, and generally they 8hould al· &II set Corth.
"'18 be -' au l!titude much greater than that
: 3. Tbe combi n&tion w i t b 'a tr&n s Ul i t ti nr I n'
of the highest oOjt!etB neAf them . S i ncII by stru mect com pris i ng A tran8f�rr::l e r· hat'i np: i ts
the meau deee ri bed practiCAlly aDY potE:n tial S8COOciAr.y cou nected to gro u n d e.nd to a D ele- I I S
that is desired may be prod u Ct!<! . the c u rrents vn.ted term i n al reapecti \'ely, a nd meanl Cor
So through tbe &ir atrata may be ve ry small. th ua . imp:-euiog eleetrical oeci !\Iltions u po n j t,a pM'
red uctng the 1088 in the air,
:nary. of a re-oei vinB i n stru m e n t comprisiDg
The apparatns at the receiving·atation J'&o a transformer hav iug i ts primary aimilarly
.panda to the c o rren ti! p ropagat.ed Crom the oonnecr.eci to grouud and to an elevat.d �r· J 10
transmit�r in a man:!er w hich ;rill be well m i aal. aDd a tranalaUDg device conDected
S S o nderstood froID the foregoI ng descripti o n . wi t h its NCOndary, the capao i ty and iDdue&­
T b e prim.". circuit of Lbe receiyer-tbAt is, ance of the two traneforme!'ll baving Inch
the thin wire coli A·-lit exei t.ed by the cur· val ues .. to leCure synenroniam with tbe i m ·
reDtA propagated by_ conduction th ro u gh the preued OIOmationa . .. se t forth.
I I�
1 :l �rVeD iDg lIatural m � i c m f ro m lhe tran&4 The combillation with . transmitting I n ·
M lII iUer, and theee currente i n d uce in tbe sec­ stru m 8 D t com priain� a D electrleal tran.e­
on dary coi l C' other c u rre c tA w h i ch aNI D tU ­ Co rm e r b�vlng itA eecGndAry �onnect.ed tc
ized for operati ng tbe d e v i CM i n c l uded i n t b e ground and to aD elevated termtnal respec·
C l rc ni t thereof.
tl vely, and meanl for i m preMlng electrical I .JO
ObYiously tbe ree8 1 v i ug-eoi ls. t rA D s form · osci llations Il po n It. p ri m A ry , or a recei v i ng
65 e n!! . or other apparaL Il8 may b! m ovabl e-All , instra m e n t comprtal ng a traneform t r bavlng
(or i nstance, wh en tIley are carried by a ves · ita pri mary aimllarly connected to grouDd
\el fto&t.in� in tho Air or by a sh i p At IleA. I II and to an ele,.. ted tel1ll1D&l , aDd a traulal-
I
649,6lJl
i og r. e �· i('e c c· n n ec ted w i th i : " sec o o d ary. tilt'
r.apac i ty aDd i nu u·:ta n r .. of the lIEl("onuary o f
tbe tra os m i ttinS IUl ll p r i m n ry o ( tbe rece i v ·
ing i ns t.r u m e n ts ha\' l n g s l I c h �':\ l u es s.!I t o �e ·
5 c u re synchron is n , w i t h t h e hn p ressed osc i l l/\·
Lions, aa eet fortb.
.
5. The coln bi n ation w i th a translD i Lti n g coi!
or coDd actor COn DtlCted to ground and An elevateeS armiaal respectively. and means for
10
.s
.
10
2S
30
I IEln s:-th
! furth .
I
produciag electric:al current. or osci llations
iD tbe eame, of a recel viu g coli or coad u ctor
almilarly Cf)Dneo&ec\ to grou Dd aDd to an elevatee! termiDal and lIynchronbed with t:le
tr8Umlttiag coil or coad actor, u s e t fort h .
8. The combination wit.h a t./'Ansmitting i n ·
etramen t com prisi ng an electrical traos·
former. baving ita secondary con nected to
ground and to an elevated t.erminal respec·
\i vely. of a rec:eivio[t iOIl\rament compr isi o g
a t.raaeformer, havlog Ita pri mary si m i larly
con nected to grouad aud to an elevated ter·
m inai , the rece l v i ng·coi l being sy �ch ronized
w i tb that of the tr"nsm i tter, as set fort.h.
7 . The combi DALioo 'Wit.h a \ransmitting coil
or conductor c o n n e c ted to groond and to an
e lc \' l\t8l1 te rll\ i n�l respecti vely. and m eaDS for
p rQd u c i u g e l ectrical corrents or oscillati ons
i n the sa c c , of a recei f' i n g coil or cou d uc!or
I
8l1n & 1 a rly con n ected to grou nd a n d t o a n e l e · I
va ted term inal, the slli d coi l or coils hllv i n � i
a le n gt h eq llal to o n c · q l l n r t ll r' v [ tl:a � :\ ',' O .
I
I
o f the d is t u rba n c e p r,'pRgated ,
.
a,. s t' t
8 . T h e cl l in h i nal ; o o ..:" i th a !. onn sm i tt i n !; co ! l
o r l� o o d u ct.or coo n ected to gro u n d anu to an 3 5
� l e va!.ed It· l' t n i u al respeet i . ely, snd a dap ted
to CA use thl: p rolJ"88ti on of cu rran ts or asc i i ·
latiGns b y c o u d u ctior. tbrousrll t.he natu ral
m ed i u m , of a recp.i \·ing,cLrcait sim ilArly Con­
nected to gro u n d and to an elevated term i · 40
nal, aad of a capacit.y and i n ducta n ce lIuch
Lhat ita period of vibration is t.he same as that
of thtl' transmitter, aa Bet forth.
9. The transmit,t.ing or ' roeeiving cfre u i t
h e re i n described, cODnected to ground and 4 5
an elef'&.Led te r m i n al respectively, and ar·
ranged i n su ch Ulanner that the elef'ated ter:
m i nal is chargftd to the mAXi mum potential
de\'eloped in the ci rcuit, as set forth.
10. The combiaAtion wit.b a transmitt i n g S o
cciil or cond nctor conoected to grouod an d to
an ele\·a!.ed termi nal respect! vel) of a racei v·
i og-ci rc u i t hAvi o g a period of vi brat.ion cor·
respoo d i n g to that of the traosru itting-ci rc 'l i t
and si m i lArly c on o ec ted t" ground and to an 5 !'
e le\·at.ed term i u al and so arra n ged thl\t tb(\
ele\' nted term iual i " ("harged t o the b i gh ",,!.
pote n tial oc\'el.)Def] in the C'i �C'l\ i t . l\s set fort h
N r K O I..-\ T E S L A .
�"' ; t n es5es :
P A R K ER W . P ,H' £ .
:,i .\ �':EL L t' :' :1 \ I !. r: y .
37
P-360
N. TESL A .
A r f A ii A T U S f O F. i R A S S M I TTINO E LECTRICAL EYERG'\. .
A p n I C A n o � r : u : ., J A W . l B . B 0 2 .
1 . 1 1 9,782 .
I � W t W t D . � t 4. I V O?
Patented Dec. I, 1 9 1 4.
..Pt::l!�� .E
i ;
"
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. )8
UNITED STATES PATENT OFFICE.
NIXOLA TESLA, OF NEW YOB.lt, N, y,
�pABATl1S FOB TBANSXITTING ELEC'l'lUcaI. ElfEBGY,
IpeC1acaUoll ot I.etten hteat.
t , 1 19.732.
Patented Dec. 1. 1 9 1 4.
AppllcaUolI tlell Jallury II. 1102, Sertal liD. 90.24$. llellewell .a� to 1107. Serial liD. 371 .117.
..
ID
Ja
20
26
:.n
36
40
46
110
66
To 1111 ,rJ, ll m it m fly ronurn :
Be it kno"'n t h :l t 1 . X I KOU TEsL.\ . Il ci t i '
7.t'n o f thl' F m ted !'Ot!ltl'l<. resi c.l i n � i l l till'
boron :;:h 4 . f M :Ul h a t t:J l I . I I I t h e Cl t�' . (·" u l l ty .
a n d :-; t a h' o f Xew Y .wk. ha \"(' i n n'lIh'l! I'el·'
ta i n 1 1 (, ,," :10.1 u!O!' fl J l l ru I"·')\ t·lIl1"nts I I I A ppa ·
ratll!'l for Tra n sm i t t i ng j·:I(,ct l"i (·:1 I E l ll' r:;:�' .
of " I I I I' ll t h.' fol lllw l I I g I S !l !ipt.'c i l ic:l t Ul U , ,·d
erclu·c 1 'I.' i n " h a d t . ) the tll-: I \' IIII! :1I.·COlII
p:III .\" I I I :;: a llt.i f�)rm : ng :1 P:I I·t o f t l lt.:- !'a m(',
In endea " ortng to :ul:l pt cn rl'('nts 01· eits ·
('ha rg('s of n!ry 11 1 gb tens!on to \"Iniou!> \·11 11 1 ·
Ilhle lISl'S, as the dist ribution of energ,"
through ,,· i res from Cf' n tra l pla n ts to dist:llt t
plAces of conslIm ptiun, or the trn nsmi sslOn
of po,,"erful d istll rham.�s to gl"t'3t d ista nces,
tlu-ough the- n3 t u I": I 01· non , a rt i ti c l a l me-d i 3 ,
I h 3 \"e ('ncount('r('. 1 . h lticl l i tics I n c o n fill ing
l'onsi d('ra hle 3 mollllts . . f (' I ectrit'i t \" to t he
cond llctol"S and pn'\\:n t i nJ; i ts 1(,:l k·!1 �c 0 \"(' 1"
thei r S l I p )Ol"t::: , 01" i t;; e"'l·:t l '� intn t l l (' :lIill .il'nt
a i r, "' h i l' 1 :l I n- a ,'·s takt.·" pl:H"C w itt'n t h e ('I(·c,
tlic s l l r fa c� dl'nsih' n·:I (: I I ,·s a re r t a i l l '·a l ll" .
ThE' i llll'm: l t y of thl' e !l t·l"t "f :I t I":I Il",m it·
ling c l r.-u i t w ii h a fret' or clc'· :l h·. J tt' n n i u:d
is proportitllla tl' to th e IJII:l Iltity o f (, I t.,('t ri("
ity displ:ll'(·d, w h i ch is d('lt'rm i ll" t l I ,.\" t h ('
product ot t h (' capal'ity of tilt.. c l I·c l l it. t h l'
pl'('!!!'lIrl'. and t ift' f r('(lul'ncy C l f t he l·lI ITClltS
em plon'd . To prOtl l1l:(' an ('\ecl rll":. 1 mo\"e·
ment of the I"t'll u i rt'd magnttUlle It is de,
si ra b l r to cha r�l' t he ternun31 :18 h i gh l �· :IS
pos.c: i h l l' . fCII· w h i l,' a great (ll1 a llt i t�, of ('Il'c,
tri('i t�, may :11 1'0 lx> di !'placl'd hy :1 l a rge
cn P:lci ly I'h:l r;:ed to low pl·l'SSl\ l"t', there Il re
d isud" ;l Iltagl"l' m e t ' n t h I n many ('ases w hen
t he form(" · i!' ma cll' tllO la rg�, The ch i d of
thl'S(' a n' ri l lr to the fart t h a l :I n i ncrease of
the cll pal" l t '; e-nl a l ls :1 l owering of the fre'
qllt"IIC"�· of t h l' I m p u l :;t·s or d i sch:lrges and a
d i m i n u ti on o f the ('nl'rg�' of ,· i hl·ation. This
W i l l be IInti(,l'!'tood whel) It IS bornc in m i nd ,
that a cm· u i t 't" ith a la rge caplicity bt>ho\'es
liS a ,;Iacksprmg, w herell s one "" j th a sma l l
Ca pll(· l t .\' a c ts hke n st i lf sprm;, vi brating
Therefore, I n order to
mOl? ' I gorously .
a tta i n thl' h l gl1l.·st poss, hle freq uency. w i l l ch
for certa t n pll rpo.c:es is a . h n n t a g!'llus and.
a pa rt fl·om t h a l, to dl'\"E·lop t h e gl·(':.tl'st
elle r�)" in sllch a t rD lIslIl . t l l llg l' l rcl l l t , I em ·
p l o," :1 I('rm i na l of reb l . H·I .,· sma l l 1':l p:1 (' i t�· ,
w h l ('h I (' I . :I I"/:e t o as i t i !!" :1 pl·ess l l rc ns prac ,
To n('('om p l i�h I I1 I s rCl'u l t I hnnl
t ic n!.lc .
found i t i m pera ti ,·e t o !'u const ... . ct the ell't"a tcd 1'0n.i l1l'lor. th:1t it� nllU>'· !i l l r C:lCt', on
1
/
which the electrical cha rge chiefl y accumu.
l a tes, hns Itsel f a la rge rA d i u s of c u n·nture,
or rs com posed o f sepnrnte e l c m f' n ts ,,"hich,
I rr·c"'pect, ,·e of thei r own rnd i us o f cur" u­
tu r(' . a rc 3 rra n g('d III close proxi mi ty to ench
oth('l· 31ld so, tha t the outside idc:11 surfllce
en wluptng them IS oC a large radi us. E"i-'
elt'ntly, t h e 5mnl 1er the radi us of cu rvllture
the g \"(� a tel·, (or II. � \"t'n e l ect ri c d ispl lll'c,
101.'1�t, w t l l be the surf3ce-densl Ly and, con ,
Sl'<1�ll'ntl�'. the I�\\"l'r the limiting pressu re to
wh ich the tennn�3 1 �3y be cha rged w i th out
elt'ctrl c l ty esca pmg IOto the Ill r.
Such a
ternn n3 1 I secUI"e to 3n insulating support
ente l·m g more or less into its interi or, and I
l i ke"·I5e connect the ci rcui t to it inside or,
general l�', Ilt po i n ts where the electric den.
sity is SID31l, This plan of constructing.ll nd
s u ppo rt in g Il high ly cha rged con du ctor I
hn " e fou n d . to be of gre3t practi cal im portanCt'. :l ft d i t m:1y be usefully Ilpplied i n many
ways.
UefelTinl; to the accompllnying dna wing .
t l l(' li�l I l·e IS 3 ,'it-w in eleution And pa rt
;-t>d i. n of :m imp ro,·oo free te rmi n a l nnd
" j r' · l I i t of I :l rgt' sUI·face ,,"ith supportin g
�t l·l Il·t l l rc ancl �n eralin g a pPll ratus.
The tl'rmin:ll D consists of a su it ahly
",ha P<",1 meta l l i c frame, in this case a ring of
r.l':l rly cir('u l 3 r cross section, ,," hich is ('0" ,
('1'('11 \\ ith hal f SJ'herica l metal piAtt's P P,
thl l S l'nnstituting a " ery large condll('ting
Sll rf:u:e,.SJnooth t.'n all places w here the elec,
tric chllrge princi pal l v accamlll :ates. The
frame is carried by a' strong plntform ez pressl y p rori ded for safety appl i nnces, in­
,;truments of obser"a tion , etc., wh ich in turn
rests on insul ating supports F F. These
!lh ou ld penetrate fllr into the hollow space
formed by the terminal, ADd i f the el ect r i c
density a t the po in ts where they a re bol ted
to the frame is still considerable, they may
be .specially pl"Ot«ied by conducting hoods
AS
H,
A part
flO
65
70
75
110
II�
!!Il
II !)
of tht! amprovemenu wh ich form ! 110
the subject of this specific a t i on , the trans,
!1litt i � g Ciz:c" it, in its seneral feot!lres, is
rde-nt ,,·;! l W i th that dt'SCn bed and c 1 a l meel in
m�· ( I!·igi n :l l Pnten ts !I: flS. 645,5 76 an-i fi49.62 1 .
Th£' c i rcu it comprises a coil A w h ich i s i n 1 p !)
I'lu!'l<" il1dlll't i ,·t' r d a t ion ,," i t h a pri mary C,
: md o n l.' e n d of ,,·hich i s connected t o a
wnllnrl · plAle E, ,,· h i le i t!l other en d is led
t h roll�h a l"I.'pAr':1tr S(>1 f . ind u('t ion roil B a n d
R ml'tll J l i � ('yl indl'r n ' to t.hc t.erminal 1>. ] t Q
.39
1.11D,'7U
Ii
10
15
20
2S
30.
:l b
4�
45
1>0
�5
60
iii
f i l l' ("f'nn<>d i on to the l n t ter sh ou l d al ways
I ,. . m n ; ) ,' a t . or n e a r t h ,' ("cnt er, In ord�r to
< · " " 1 1 1"\' : 1 � " lIImet n('a ) <.l i "t n l >u I j " l l .. f tllf' (" u r ,
n ' I I ! . a " ;,t ile nqSt', w h e n t h l' f !'l·q l l .'n (',v i l'
\ !'I'y h i /!,h a n d t he fl o \\' I O f ) a r:.!" \· " l l I m�, the
Pl'I' r"rJ l l n n re of the a p p:l l'a t ll " m l :.! h t he 1 m '
pa I red
Thl' pl'im a ry e m il Y I lt' " x " l t.. d I n
a l l Y t 1 l',;i l'l�<.l m n n n e r . f rom a sUIta ble sou rce
u ( "t1 l'renls ( i . w h ich nUl)' be lin a lternator
imp'>I"tant re<llI l rement
o r ("on deo ,;c r , the
Lein'" that t he n'son a n t ("ond ition is E'St:l h,
l i sh�J . t hat i l' t ei sa \' , that the term i n a l D IS
cha r:red to thE' Jll a x l m u lIl pressu rE' dE'\'el oped
in t l tc c i rclI i t . a s I h a \'e speci fied 10 my
ori l! i n a l p:l ten ts ) ,e fl l l'(' re fe rred to, The a u ,
j lL'otmc n ts shou l d I .IE' 1II:)(le w i th parti cular
c a re \\ hen the t J'nn�m i t t c r is (lne of I!rcat
p" ..' er. not only on nccou n t of ecun om.Ji , out
a l so in order to :lH,id " n n �E'r. I ha"e sho"' n
t h,a t i t is prad icllhle t o produce i n a resonnt,
in,z ('i ITlIit as E A n B ' D im menge electri ,
cal a cti" ities. measu red bv tens nnd evcn
hundl'c(ls of ihuusa nds of horse-power, and
in such a c:isc. i { the points of maximum
pressure should be �hift.ed below tbe ter,
Inionl D, :llong coil n. a ball of fire might
hren k out and destroy the 1lUppcB't F or auy'
thjn� el!>e in 'the ..ay. For � better ap'
precJotitJD of the 11.8tuft of tbia dUlF' it
shoul<.l be statE'd. that the destnH:ti ve aebCIII
rna v ' bke plare with inCODeei�te -rioleD�,
ThiS 'l\-ill ct'.:Lc;e to he surprising .. hen it is
hOnle In rn i n d , thllt the entire energy accu·
In n l nted in t h e exci ted c i rcuit. instend of re'
< J l I i 1'inl;!, as u n der n o rm al �orking condi ,
t i "n�, 1 ' 1 I t' ' i u a l't e r of the period or more for
ito; tra n s f o rm a t i on f re>m static to kinetic
(01'1 1 1 . m :l �' sp4'nd 1 tsE' l f in an mcompsrably
"1 I 1 :t l l l' r i nterv a l (I f time, at a rate of many
m i l l ion� of horse power
The aC'CideDt is
:' pt t o o('"cl l r w h�n . the transmittin g circuit
h<! l O g �t rongl,v t'Xcittod . the impl'essed (}Scil,
11I t i.>nt-l 1I1'0n It ore ('a ulled . in any ma nner
mC>l'e (lr I�� slId.len, til be more ra p i d than
the frP(> osci l l a t ions.
It is there fore ad,
\'isHhle t o I)('�i n t he o d j ustment.c; w i th feeble
and some,,' h a t slo't'er impressed osci llations"
strt'lI !!1.ht'n i n� llDd qui cken ing them grad ,
lIo l l y , u nti l t h e apparatus has been brought
l IndE'r p4' rfec't control
To increase the
'lll fet y , I pro,i de on a coDvenient pi li ce , p re f­
era oh- e>n terminal D, one or more elements
CI' p ln tes either of some,,'hat smaller radius
of ('n r \'a t u re or protruding more or less be·
YOlld the others ( in which c:a&e they may be
of !la rger rn dius of l'Urnture ) &0 tb.t, a�oul,d
the r_ rf"!'�lI re rise to a v a l ue, be�'ond w h i ch It
is not (\ " !'i red to go, the po w e r f u l discha rge
Ill n \' c\ ,, , t t l l l t t ill' re and lose itsE-1 f h .lrmlessly
S U l' h a p l :t te, per fllrm i . I g a f u n c ,
i n thl' a i r.
tio n si m i l a r t o thnt of a sa fety ,' n l ve on a
hil!h p re!'s l I re reSt'rvo i r . is indic:oted at V ,
�t1 l 1 f l l J,th('r E' xt e n d mg the princi ples
unue rl \' i n� my i n n·n t i on. �pt'Cia l re ference
is
The
made to coil B :JDd L�nduct or B'
I lI t tl' r i l' in thE' form of a cylinder with
smOOTh or polishf"d s l i r f a c :e o f II radius Tll u ch
):I I'�f> r t h n n t h a t o f tit .. ha l f spheri cal ele­
·n lf" n ts I' P. lind w l dl'ns out nt the boU',:, m
m t n :l / t oo c l I I , t\' h l ch "hol i i d be sl ottRd to 70
!1 \ ol d 11K" Il\' eo d v ('urn>nt.c; and the pur,
� of w h i .:h "' I i i be clrn r from the fore
,zoi ng
Thf> roi l R i" 't' olllld on a fra me 01
d ru m J ) ' , of i nsllla tlD� ma terial, with its
t u rnl> duse to�ether, I h a " e d i sc�\'(>red thnt 75
wh(>n so wOllno the E' /feet of the small ra d i us
of cnr\ ll tn rl' I I f t h (> w i re I L�I ! is O\'E'rl'.omt'
>I . u) thf> ('oi l bt-h n \ t·s li S a eond l l r l O I of l n r�
1',l d i l l S of (·u n a t u r....�Tespond
.
l ,,� t o thnt
Clf th (· rl n l ll l . TIl i s fea t l l rf> I l' o f consH iE'r, 80
II hle pr:lctil'n l I I l 1 pO I· lu IIM' a no IS :1 ppi i cA ble
n ot on l y i n thi" Sfle(" t . a l I nl't:lnce, but �n­
�ra l l.", For e:-:lI m ple, sl lch p l a tE's at l' P,
I I f te rm i n a l 1 > . thou:rh p re fer.l b l y of l n �
r:l Il i llS of ClI rY " t.u rc, I ll·ed not lw neccs'ls. ri l \' 85
so, for p r'''': l df>u oll l \' th:l t the indi\; d u:il
p i a tt'S or l'iE'n,pnt.<; (I f II hIgh potentilll con­
d uctor ()J t(,rJ l l i u fl l :I re 8 r rn n �d in pros­
'Ill u tv to ench other ond "' itb their outer
bollll d llnE'S .a long an ideal symmetrica l en- .
" eloping surface of a lar� radius of eun-a­
tUft, the .d,·.ntar;es of tHe m�enuon wm
be m<m! m- � fuJly ftIllized The tower
� of the coil �wbich, if desired. may
be enended up to tM tnrnma l D-shouM 15
be _"'hilt hf"low the uppermost turn of
coil A, Th i s, T fin d , I�ns the tendency of
the cha rge to b rt' n k Oll t from the ... irt' con­
nedj n� both and t.o pass along the sup.
- 100
port F '
H \l n n g dE'scribed m y in ,enti on, I cl lli m :
1 . :\ s II means for producing grea t elec·
tnt'RI actl \'i ties a n'SODllllt t'ircu i t ha \;ng
its outt'r l:()ndlJcti u� bou nda ries, 1l'hir.h nre
('ha r�t'd to a high pptential, arranged in 106
su r fn cE'S of large ra dii of cu r\'alu re so as
to pre" E'nt lea k li lre of the oscillating charge,
sll bstll nti a l ly as . 5(' t forth,
,
2, In appa ratus for the t.rnnsmission of
elect I'ir.n I energy a circl l i t conn ected to 1 1 0
g round a n d to 11 11 de\'oted terminal and
ha\'ing its oll ter conducting boundaries,
"" h i cb a re subject to high tension, n rra n �
III sur faces of Inr�e rndii of cll rt'ature sub­
stantiolly .s, lind for the purpose described, 1 1 5
3 . In n pla nt for the transmission of elec·
tricli l energy without wires, in combino tion
"'- i th a pri muy or exciting ci rcuit 0 second­
Il" connl'Cted to ground and to an ele;ated
Iotrmi n,,1 IUld ha,;ing · its outcr condu�t�ng no
boundllrif'S, " hich n re charged to • �
potf'ntinl, IIrrangt'd in surfoces of lnrge n dii
of cun'atu re for the purpose of pre" E'nt ing
lea k a ge a n d loss of energy, substan t i oll.V lIS
116
Sl't forth
� , As a m eR ns for tnnsmitt i n " electrical
t:nel·gv to a d i st a nce th ro u gh th e naturlll
m�u i lf 1\ gro l l n d r d rt'Son:t n t c i rc u i t, com­
prisi ll� u pa l1 u pon w h i ch oscilla tions a re
i m pressed ond :mothcr for raising the ten - 1 10
40
1,118,,"12
;;.
HI
15
::0
2'
� i (, n , h :l \' i n l! i t !' n u l.' r , 'on , l l l " t i l ; /! hOl l n c b ri O's
on w h i e- h :I h i gh u' l l " j un I ' h a rgo' IiCC 1 ! /l I U i a t t',.,
n rrn l l �I'd i n su da," '" of l a l'�I' rn d i i of c u rT :! ,
i : ; n ' , �Ill o:,ta llt i :l l l \' ns I kse-ribeod , '
'
;" The Im'ans for p rod ucing ex<.'essi \'e
t,l(,(,t r i c pott>nti a ls ('on�isting of a primary
exC' i t i n g c i rc u i t and a ",sonant secoodan'
h a v i n g 'i ts ouu-r cond�lcting \'!lements which
II "' suhject to h i gh t<'n"ion a r ra n ged i n proximi t�, to each ot he r and in surfaces of l ar/!t'
ra d i i of eun'ature so as to prevent leaka ge
o f tht" cha rge : m d a tten dan t lo\\'ering 'of po­
unti a l . suh"t a n t i a l h' as dt's('!'ibed,
G, .\ ci rcu it com, ; rising a pa rt II pon w h i ch
osc i l l a t i on s a rl' i ll l p l,t'��d all.1 I I n otlu,'r part
for ra isin$!' the �n;:ion hy r('son a nct' , the
l a tter p a rt lx- i n g supportl'd on places of low
elect ric densit:" and ha " i n$!' i t s outermost
cond ucti n g boundaries arran/!ed iJi su rfaces
of 13 r/!e radii of ,cur\'ature. as set forth,
i, In apparatus for the ,t �nsmis.."ion of
eleetriC:ll energy without wires a �ounded
circll it the outer conducting element..'" of
which have & grat �g:lu area and are
a
ill sun:u:es of large l':ldi i of curva­
ture BO as to pennit t.he storing of a high
ebl 1"g'e at a small electric density and pre·
" ent 1035 through le3kage, substanti a l ly as
described,
rranged
Copies ot WI patellt
ma,.
8
8, A "'irelcss transm i tter c(\m prisin� in a r
com b i n a t i on a sou rc� of os.� i I l :l t i ons as a
cOIl . ] t'nser. a p ri m a ry e�!:'iti ng ri re- n i t n n d ::.
.5('('ondary grounded a nd elp\'at�d con d l lct o :'
t h e ollter conducting bounda ries of w h i ch
are i n proximity to each other and arranged :: �
i n surfae-es o f large radii o f cur\'ature. sub·
stanti a l ly as described,
9. In apparatus for the transmission of
t'\P<'t rical energy ".. i thout wires an ele\'ated
cond uctor or nntenna h:l \:ing its outer high 4 ('
potential conducting or capacity e\l'mt"nts
Ilrrangt"d in proximity to each other and in
slI rfa c('s of la rge ra d i i of cuC"'atn re !IO as to
Q\'ercorne the e ffect of the sma l l radius of
cur\'ll t ure of the indi,;du3 t element!! and 4 ',
\t'ak:rgc of the charge, liS set forth.
1 0, A grounded resonant transmitting
circu i t ha,·ing i ts outer conductic/Z bound­
a ril'S arranged in sn r faees of lar� radii
of ctll"" ature in combination "'ith a n ele. :' 0
" attod termiWlI of great surface supported
at points of low electric density, substan·
tially
as
described.
Witnesses :
'
NIKOLA TESLA.
.
M, L\JlIION Dna,
DoNOV.:K.
RrCIlAIlD
l:c obt.a1lle4 for lYe cellts each, b,. lL44resJillC tlae U C_aiwoln ef h-.sta,
Wa5l1!llctDa, D, c....
CAPACITI ES ·
By
FRITZ LOWENSTEIN
� rl£e r�1..
As the seat of energy of an electri c31 field is in the space
outside of the charged bodies we will consid<:>r the shnpe :wcl
concentration of the field only, but not thut of the body i t�elf.
This di sti n ct i on il' necessnry
bec3u�e .cnpacities nre
i" . occupied
usunl ly
attributed to the bodies cha rged , whereas the energy is exclucled
from that space w h i eh
by the body.
a�
the space between t wo cha rged bodies
Consi dering
the only seat of enC'rgy ,
t h e expression " c ha rgC'd body " is b(':<t rC'plncl'd by " term i n31
surface " of the fiel d .
Comparing
g<:>omet ri c;l l ly
portional to l i nea l
similar
Ext<:>ndinj!; t h i� 1 3 \\'
elem C'llts
of
th<:> elemC'nt ary capacit ies
(SC'l'
dimC'n;:ioll;:.
metrically similnr fipl d ,.: .
oyer
Figure
1 .)
two
g('O­
arC'
pro­
th(> <:>nt i Te fidel hy th<:> i n t egrat i n g
procl'>';;:. we fi n d th a t geom<:>t rica lly silll i ln r fi("ld� have c3paci t i es
proport iollnl to t h e lin ea l d i me ns i o n s of t he terminal surfaces.
It i� to be expect<:>d . o t h erefore, t h a t cn pacities expressed in
d i mC'll;;ion;: of terminal ;:urfa ces �hould he of li neal dimensions.
That the ca p n c i t �· i " by r,o mean;; a funct ion of the " ol u m e of
the field or of the t er m i n a l hody may hC' easi ly seen from F i gure 2
"'herl:'
IJf'
r
a
fidd <:>lement i;; i n c reased to dOUble t h <:> volume hy
• PI'l'l'ented before
1 , 1915.
The I nstitute
of Radio Engineers,
17
xc\\"
York,
adding
Decem-
volume in t h e direction of the field lines and in a direction per­
pendicular to the lines.
In the first case the ca pa ci ty has been
decreased whereas in the latter case increased, altho In both
ca..c;es the volumetri c in crease
is the same.
FIGt:RE 2
I t is �een , therefore . t hftt i n s t ea d of being dependent on the
volu m e , the rapacity i� rather a function of lineal dimension
and therefore the m ftx i m um li neal dimension predominates.
An interesting example of this predominating lineal dimension
or "maximum reach " is given by the composite capacity of two
wires joining at one end under various angle�, as shown in
Figure 3.
FlGl'RE 3
When t he :m�le i" "mall the com posite capacity is practically
that of t h e ,,:ingle wire, since the addition of the
second wire hfts not i ncreas('d the maximum reach.. . If the
s('cond wire B he jOillf'd to A. 'at an angle of 1 80 degrees, ' which
me:ms in straight ('ontinuation of wire A the tota! " capacity has
the �ame
a�
18
oubled , as the maximum reach now is twice that of the single
wire.
\Ve noti ce also that by de v i a ti n g wire B slightly from the
traight continuation of wire A , t h e maximum reach of the
system is not m ater i al l y altered , from which one may co rrectly
�
c nclude that turning the wire B thru an appreciable angle b
does not materially change the capacity of the system .
On the
other hand a great chanJ!:e of maximum rE'a c h is pro<i lw('ti by
va ri at i o ns of the anJ!:lE.' whE'n the two wircs a rc approximately
perpendicular, and i n fact t hc ca paei t y of the total �tructure i�
most sensitive to changE'$ of angle bet ween thE' two ('ll'ID('nts at
ahout 90 degrees.
In Figure 4 , I haw /ti wn a tal>ll' of {'a paciti('� per ( ( n t i mE't e r
of the greater lineal dimension o f t he diff('rE'n t ('onfi�urntions .
' '
()
c =.'10 1
c-.}Z.t
o
C-.l01
(-.I0 l
F 1 G r n F. 4
I n Fig:uf(' ;) t he WIrE.' A. B i s a""umed t o he m o vp d I", the
variahl(, ah:-ci,,"ae x , t lwreby gCIH'ra t ing: a conducting sh;et S,
I t is i nstruet i " e to follow the yariati o n of the capaeity Cz•
10
At x = tI the c a p ac i ty is that of t h e wire Ca b ; as long as x
is small the capacity is practically constant because the width
of t he sheet is small c o mpared to the length A B and a change
of x does no t invol ve a change of the pre d om inating lineal
d i mcn s i o n ; however, as x increases and finally becomes greater
than .-1 B, it a...�umes the part of t he predominating di mension ,
and , indeed, the graph shows the capacity then to be propor­
tional to x.
I
"
"""-_
_
'- _ _ _
FIGt.:RE .'i
_ _ _ _ _
J
Com purin!-t t hc capncities of a s p he re and of a wire, i t is
found t hnt the c:l pn c i t y of the sphere is only three or four t i mes
as grcnt al"
t ht' ('npacity of the wire in sp i t e of the mill i o n times
greater v o l u m e .
I ha\'c !':poken of the eapacities of a wire and of other bodies
inste:l<l of thr cap:lcity of the field si m pl y because I do not wish
to distr:lct uttentioll from the f:lmiliar co nce ptions .
Let me
an:llyze t hr field �hown in FiJ1;ur(' 6, ha vi ng two co ncent ri c
�pll('re,; ;' ''' tf'rminal �u rf:\('e�, and defining :lS "volumetric energy ·
dcn",i t y " t hl' enerl?:Y ('ont:lillcd in one cu bic c(' n t i m eter . As the
encrl!y I)f a fi el d (·I(,01('nt is mmle up of the product of potential
alor./! t h e linl'''' of fon'(' w i t h i n t hat ('l('ment and of the number
of l i r. I'''' t ra nr"in/! i t . t h E' I'nerl?:Y of :l cuhic cen t i m et er of ele ctri c
field i", proport iomtl to t hl' squa re of the field de ns ity . Since the
field d(,ll "ity diminishes as th e square of the distance from the
center of ficld, the volumetric energy dens it y diminishes with
t he fourt h power of the dist anee fro m the eenter. The diagram
to the ll·(t in Figure 6 ;:: h o\\'8 the de c rease of volumetric energy
dE'o"it y .
O f /!rc'a t l' r i ntcrl'",t t h:ln t h e v o l um et r i c energy density i s the
lim':l l ('ll('r/!y clt·nsit y . w h i c h may be defi ned as the energy contained
20
of on!' ("('nt i uwtl'r radia l t h ieknf':<:< : n nd a"
iaYl'r in('n':I:« '" w i t h t he :<qlJare of t he di,.;tnlll'f'
from t hE.' eentC'r, t llf' la w fol l o \\' ", f ro l l l t h i " f:1 <,t , a n d from t h(·
\'ol l l lllf't ri(' r n ('r�y dl'n",i t y I:t \\" t h:1 t t I l ( ' l i l H' n l ( ' n l' r�:' d l ' l l " i t y
cl('erea � es inyersely a s t il(' squnr(' of t h l' t i i :<t a n('(' from t hr (,l'nt t·!" ,
:'Udl d epel:drn('r i" gm p h i l':l l Iy ,, 1 10\\' 11 t u t i ll' right ill Fj �Il J"(' 0 ,
T h r !'had('d surfa ce belo\\' t h i:< e u n'l' n' pn':'l' n t :< t he t ot a l 1'Ill'I'I!:Y
of t hr fil'leI and it is ea�ily l"een t h e re from t h a t t h e mnxim u rn
enerl!y of the field is con ct,'nt rnted nea r t h e smaller of thc two
in
a
spherica l iayC'r
t h e yolume of such
:<ph('re!' ,
I hn n� t ak e n
a
simplf" e:lSe of
a
field wi t h �phE'ricnl term i n n l
"lIrf:l('(>:o: t o r;how that the conccntrntion " of cne�- lie::; l!ear the
..01:111('1" tf'rminal � urfa ('e , �imilar l'on�id<'rntion'" C3.n he a ppli<'tl
",hf'n :-ouh�titutinl! for t h i i< firl< l r: uliatinl! thr('('-(Iimf'n ,.iort :ll l�' ,
:t fi(,ld of hi-diml'n"ionnl rndiation (�:-o t h n t oe("urrinj!; in til(' ('ase
of IHul! <,yl i ndric3.1 t erminnl surfnc'(';') : wit<'rt>, a:-o in this inst a m'(· ,
til!' blJk of the enNj!;:' of t h (' fi('ld is t o l w fou n( l llenr t h e :-om:t l l('r
on' of t II(' two t crm inal ",urf:H'l':<,
I n Figur(' I, I haw' sh own !I fi ('l d w i t h ('OIl ('l' n t r i (" t (' I'JI l i r :t I
,. u rf:U'l ',. ( · i t l H'r :<plH'ri ('a l o r ey l i n d ril':I U , and h a n' illf"l'l':I"'('d t l . . .
" " " p,. of t ill' fi('ld by J'('d u("i n g t h e "iz(' of t ht' :<lll a ll e r t t'rlll i l l a l
!<urfa ,·(' w i t hou t , ho\\"('\'(>r, changinl!: ('it her t h e t o t a l n um i Jpr o f
. fi(·le I lines o r t h e la rger terminal surfaee, A s t h e linenl clwrgy
den:<it y i:< \"('ry !tren t near till' �mall('r t e rm i n n l surfa c('. ",urh
acltli t ion of t il(' fi e l d a t t hnt point m u�t hnn' materi a l ly incf('a:« ,d
t il(' ('n('rgy of t lw fi C' l d nnd t h t' eh:mge in c a p :l (' i t y to be ex p<'e t (,t l
l'hould h(, ('oll"itl('ra bll', I n fact , a consid l'ra bll' e hnng(' in ea p:l ('i t y
of a "ph l'rt· i,.: o l Jt a i n ('d hy a changc of i t ... d iamct er,
I f, in Fij.!Ufl' I t h(' l a r gl' r t erm i r. a l surfaet' a lone i ... changl'd,
21
even mate-rinlly, the total energy of the field will be increased
very sli ghtl y o nl y ;
due to the fa ct, as we have seen, th at the
energy density near .the larger terminal surface is very small .
Such a small change in energy corresponds to only a small
change in the capa c i t y of the field, from which we concl ude :
FIGCRE i
In
fidd
:l
hn\'ing: t wo t prminal s u rfa c es of g re a tl y different
I'iz('. a ch:m g:e of the �1l11111er surface pro d u ces a great change in
capacity, w h ere as a cha n�e of the larger terminal surface affects
the- capacity of th(' fiplel only very slightly.
The capacity of a
field is, there-fore, almo:>t ent i rply determined by the shape of
t he smaller termin al �urface.
That is · why
we
may with rorrectI!.ess speak of the capacity
of a �ph(·r('. or any ot h('r hody , without ment i on in g the size and
l'ha p(' of t ilt' ot h('c t " rmi r :ll surface, as l o n g as the as sum pt ion
is
(·
occ('( t that I'Ul"ii ot lwc t('rmir.al s\lrface is of greatly l arger
·
diuu'nsi.,nl'.
It may not he ami"" t o ('all your att ent ion to the fact that
t hl' in(·cpa,.. , ' of fiplll (,llI'CltY al' illul'trnted in Fig u re 7 is accom­
pani('t1 hy :1 del'r(':!",' in (':l pal'ity. This relat ion may easily
he t\t'lhll'(·t\ from phy"jC:1I considerations, as well as, from con­
sid('ration of t he m a t hpmat ical expression for the capacity
C. =
f/J�
32 ::-� lJ'
wh e re f/J = total field lines
Jr = energy,
w h ('r('in t l l f' " :l pa('ity j" expc�sell aR a property of the field alone.
I
to i n t rodul'p h('re t he re c i p rocal " alue of capacity
i
and a pply t o t t lH' t {'rm " st iffness of the field," as an i�crease
of ('n('r�' would hI' fol lowed hy an in cre a se of sti ffness. I am ,
am
h'mptf'tl
22
however, l o at h to mar a ny
add i ti o n
al insight which may be
gain ed from t h es e explanations by deviation from so familiar
a. term as capacity .
For
a
better conception of the slight change of capacity
c au s ed by a considerable in crease of the larger terminal s u rfac e ,
I refer to Figure 7 , where the difference of capacity is only
1 per cent in spi t e of the diameter of the larger te rmi n al surface
It appears, therefore, that that
part of the capa c it y of an :mh'\ul a w h i c-h i" d u (' to t he flat top is
not ma.terially changed · by its hei�ht aho ve ground.
being increMe<i 1 00 per cent.
While considering the capacity of
a
fl at t.op antenna to
ground, it m ust have o('currf'cl to many cngi neen; , as it did to
me, that the statement t o be found in many text books on electro­
statics is rat h er m i sleading :
"That the free capa('ity of a body
considered alone in space must not he confoUluh'd wit h t h ('
capacity t h e body may have again:o;t another hody t"ol: "i<1('I"('<I
as a pl a te conden�er. "
Thil' stat ement i" quit(' erroneou:o;.
As
the stren gt h :md diredion in any point of a field i:o; of sinp;\" : m d
definite val ue, only one electric field can exist in
at
a
:t
gi" en "p:H"e
gi\"(m mom ('nt . :111 <1 . t lH'rdol"e. onl�' one vahl(, of e:l p:l!'i t y .
It i!O i n c o rr (' c L t hen·forl', t o d i"t ingui�h \)et\\'('('11 fr('e ra )1a ('ity
:md
c on d en ser
('aparity.
This c la ri fyi n g stat('mellt is de(,llled
ndvimble, or at least permil'I'ihle, in vjew of the quot('d errors . .
By spea king of the capacity of the field instt'ad of t h a t of t h e
body, no such erroneous thought is possihle, and it is c lear that
by free capacity of a body is mt>:lnt tht> capacity of the field
whose smaller terminal surface is the ,;ven body and whose
largrT terminal . surfncl' is olle of \-:lstiy greatrr dimensions.
It is not essential t h at thi! ; grt'nt eT tt'rminal surf:u.'(' be 1000000ted
at infinite di st a n c e , berau!:'(' of t ilt' fact that ('ven if construt'd
a!' of t en t i m es the l i neul dim('n:-::i on" of. the smal l :<urface th('
('ha nJt(, e:msed by r('mo"in� it to an infinite d i s t an ('e would
rt·,.. u h in a l"han�e ill ea p:l C' i t y of not more t h a n on('-t ('n t h of
1 I ll'r l'l'nt .
"\ t a t i m e whell I hMI not rl'a lizf'<1 t h l' "inp;ly determ illrd
\'alue of a fi(,ld caparity, I ('on:< i liere d a (' om p a riso n between free
an<l plate eapacity as shown in Fi�ure 8, wherein to an upper
di",(· ( of whi ch t h e free capacity is
�r) ,
was
added anot her lower
dil"c, th'�n·by form i n� a platl' cond � nser. The problem aro se in
my m i nd t o determ i n e the di:;ta nce of separa t ion of thl' t wo
pb t t·,. "0 t h at t h e plate ('apaC'ity would equal t h e free eapaeity
of t h(' :<i ngle dii'(,. From the well-known formula.., for the d i :<c
23
FIeURE 8
capncity nnd plnte capacity, it would appenr thnt the two were
equnl at n d i st a n ce equal to d
=
�r,
and I must confess that
I hn d quite n struggle to decide whether in spe aki ng of the
capacity of thE' upper plate I would not hnve to ndd the t wo
c3pn(·it ie,<. While such n mistnke need hardly be cnIled to the
nttention of fhl' majority of engineers, I do not hesit3te t o make
m ent ion of it fo r t he henefit of even the few students who might
gnin t lwrefrom .
The adyent of the 3 e rop l an e has opened another field, for
radio communic3tion. Whereas in the static field of an antenna,
one terminal surface is art·ificial and the other provided by the
surroundin� �o u n d both terminal surfaces in an aeroplane
outfit hnye to he nrtificinl an d are, therefore, open to design.
The qu(>�tion nri,.es in such a radio oscillator as to how mu ch
may be �:lin('d in ("ner�y for ench single charge by increasi ng
that Olll' of t Ill' t wo t("rmin:ll surfn ces which consists of a d ro p ped
wirE'. Tlw :trrn nj!t'mt'nt i:o; :o;hown in Figure 9. It is evident that
,
FIGCR£ 9
2-1
as long as the d ropped wire is of smaller dimensions than the
electrostatic counterpoise provided on the aeroplane, an increase
in length of such dropped wire will materially . increase the
capacity of the field and , therefore, the energy per charge (as
we may conclude by analogy from Figure 7 ) .
As soon, however,
as the dropped wire is m ateri ally longer than the conductor
on the aeroplane it assumes the role of the larger terminal
surface of the field, and any further increase of its length will
not materially contribut e to
an
increase of electrostntk capacity
nor of the energy p<'r unit charge.
Figure 1 0 shows the function of the volumetric and lineal
energy density in a field whose smaller terminal surface is a long
cylinder.
Such
a
field, radiating bi-<lim<,nsionally only, shows
an energy conC'entration not
so
ncccntuated as that found in the
FIGURE 10
tri-dimensionnlly r:uiint ing field ;
termin31 sUrfn ('e of
n
l Iu. ('onsidt>riulr the largt>r
diameter ten time� that of t h c smal ler
surf3('e, the (·:tp:wity ""{' \lId only be ehangl'cl 1
per cent
by
increasing the larger t erminal surfact' i nfinit ely.
I n all C3;;:es, t h erefore, where the larger · t erminal surface
does not come closer nt any point than (say) ten times the
corresponding dimension of the smaller terminal surface, we
need not be concerned with the actual shape of the larger terminal
surf:!cc when we determine the seat of energy, the capacity and
the ('onfi guration of t h e field lint>S emanating from the smaller
surface. It will be seen , therefore, that from the fiat top of an
anten n a, line ;;: emanate almost symmetrically both upwards and.
dow nw ard�
a"
th ough the larger terminal surface were one25
s u r ro u nding the a ntenna symmetrically on all sides, in spite of
t he fact that the ground is l ocat ed entirely at the bo ttom of the
antenna.
This is clearly illustrated in Fi gure 1 1 .
By integ ra ti n g the l i neal energy density of a three-dimen­
sio nal ly radiating field between the radius of the smal l er s phere
FIGtTRE 1 1
and t hat o f t h e I:t r�er �phf're . we can fi nd t h e enerity o f :;uch a
fiE'ltl : wherE'hy th£- l'apacity is d lO'termi ned .
dE'n:oity fol io\\",.; t h .. I:\\\" of
to
:
;
-�.
,..
The lineal e n ergy
and its i n te�l is proportional
and ("on:-;C'qupntiy th� (:apacity of the field varies
as
r.
We h:l\·e deduted. therefore, the capacity . of a sph e re from
prorwrti(':': of thc' til·I(1 :l l on e , ('Ori:-;idering the spht.>re a.., a terminal
surfal'e only.
In d cd ueinJr l"i mihlrly tilt' ('apacity of the "ire from properties
of t he fiC'lll :ll one. \\'l' hu\"(' to start with the bi-dimensionally
radi:l t inp: fi(·le I t lU' linenl energy density of which follows the
law
..! a::;
we
han ;;cell.
The int egml of su c h function is of
lup:arithmic' llatun'. !l" i ndeNI i:o; t h e ('apacity of the wi re .
r wi"h to cal l your attent ion to t he fact that in a sphere
segments of t he same p ro j e ct ed axial length contribute equally
to t he capndty o f the sp here , as shown in Figure 1 2.
If n ('hn rlre \\"{'/',. made' to e nt er a sphere and traverSe the
splll're in t h e d i rec·t ion of a diameter, the s ph ere as a conductor
r
\\"oul<l hcha\'e l i kt> a straigh t piece of wire of uniform lineal
capaeity.
Thi" fatt wu" fi rst recognized, to my knowledge, by
2G
F I G (-Rl: 12
Mr. Nikol:l Tesl:l , and [ l'Xlwd to euml:' ba ek t o t he hdlD.vior of :l
sphere as a cond uctor of radio fn·queney ('ur:r('uts at !o'om e
later date.
The study of capal:'iti(';. of compo�it(' hodies i!o' most in­
structive and c o n d u c i v(' to a clear COIl('('ptiOll of capacity.
ut. as in Figurf:;' 1 3 , a num h('r of !o'mall !o'plwre,.: of rndi ll": b(' �o
3rra. nged :1 5 to ('o Y('r (·o m p h·h·ly t hl:' !o'urf: H'(, of t lw hlrJ,{pr
I f (':l eh Oi l (' of t h e
sph('re, t he ra d i ll:< R (If ,," h i i' l l hp 1 00 _
3 1 ,4()U "1Jl:t 1 l er ,.pherp� ('oti ld hI' l'lmuf <'d : I t i t s full value of
('3J 1:11·i t y . t he e:l paeity of t h t' I'om po;:ite hody would be 3 1 ,400 ;
a... a mat t �r of fact , howe\"('r. it is not mon' tb:lll rad i u s R of
tilt- l:lr�{'r ;:;.phere , t ha t is 1 00_ Indeed , t he confi�urat.ion of
tlK- (·I(·et ric fiE'l d F cou l d not ha ve chan�('d materially by the
arr:lnJ!{'Dl{,ll t of t h e small " pheres, and t he ca p a ( i t y clearly
pr�nt ,.: itself as a property of the confiJ!urnt ion of t he fieJd
lyin� outside of thE' eun- loping surfa('(' of t he com posite
'
f'tnu-t ure.
Capacity may pl ay a part in the conduction of el e ctric i ty
Let us assu me a series of spheres in
lineal a rran gem en t as shown on Figure 14.
thru liquids and gases.
As long
as the distance between the spheres is great com­
full {'apacity as gi v e n by its radius.
pared to the diameter of the spheres, each s p here will retain i ts
By decreasing the distance
q) 4 $ 0
OOcPc1?ooooo
0
� c5'<1 o o o
I-'IGt:RE 1 4
bet\n'('n :;pheres t h e indi\"idual {'apaeities o f the
because of t he negati\"E:-
!."
spheres decrease,
a pa c i t y coefficients. If such approxima­
tion he {'arri ed to the point of contact between the spheres, the
capacity of ea c h individual sphere would be redu{'ed to ap-
proximately !
were
t
of the original capacity.
If such
a
ruw
uC �lJhl'n:"
coneeh..ed as freely mo\'able, so as to enable each sphere to
make contact with a p l ate P, which is kept charged to a certain
potential , t hen the {'harges carried away by the spheres after
{'ontact wit h the plate would he proportional to the f':lll capacity
of each :-;phere as long as the spheres are far apart, and would
he onl\"
-
!
�
=
!"pht'rel' arc
1
- _
lh p�,rt of su{'h maximum charg-e when the
2.7 1 8
i n cont act . A s w e a!"�umed the plat� P to be main­
__
tai ned at n {'ertain potential hy an outside
sOurce
of electricity,
of t h e spht'res would Yary a pproximately in a ratio of 2.71 to 1:
the ('om'('et ion current represented by the departing -{'harges
J n t h e passage o f e l ectri city thru a n electrolyte, the molecular
conci uctivity has been found to be the same for all electroJytes ,
ancl \'aryin� only with t he concentration
of
the solution ; - the
moll'{'ul ar ('onduct i\"ity being approximately 2.5 times as great
in the yery dil ute so l ut i o n as in the concentrated solution.
1 wi:-;h to {'all your attent ion to t h e striking similarity between
th e rat io of ('oncl u{'ti\"ity experimentally determined in
28
elec-
trolytes of small and large concentrn.tion and th e ratio of con­
ductivity of the row of spheres where the spheres are far apart
or close together.
I do not pretend at this moment that a
ALCOHOLS
N
c;.!04,;;. o H
WATER
o
H-OH
C H,�H
C; ,,\-0..
, c,,,\-oH
" c;.��ti
� c.,H,.-oH
I
2
�Z.7
MnlII'L ALCOHOL
ETHYL
Z2.&
PROP'fl
BUTYL
I�NTVL AL.COMOL I '
o
I
FIGURE ] .5
plaul'ible modification of the theory of ('on d u ct ion thru elec­
and gases can be based on slleh a c:oincidence ; and in
fact , asswnptions would havc t o 1)(' lll:l de. For exam ple, a
lineal arrangement of the ion:; in t h e di n·(·t ion of t il(' static field
impressed on the electrolyte or on the gas mu�t · he assumed.
trolytes
f'DRMIC AGIO
METHYL FORMlATI:
ETHYL
150SUTYL.
•
....MVL.
"CEnC 'ACID
E�YL ACETATE
PROPY\.
o
2
:3
4
�
N
I+- COO -l-l
I+- coo -.c:
t\
H-COO �,,\
H- COO -C.w, .
M-COO -q+"
C� COO _
CHj COO-Cz"\
eM; COO- C;H,
-�
I
Z.
...
,
�
:3
or ""I. AL."�
FIGURE 1 6
But t he fact that su ch rat i o i n t h e case of the spheres is deduced
from gf' o m ct r i c n l considera t ions alone , ('ou pled ",ith the fact
that in clcetrolytcs the sam e rat i o follow:< from purely ge om etri cal
eon."ide'rnt ion!', i s sufficient to warra nt further t hough t . I do not
�itate t o bri ng this i nt eresting coin ei<iellce t o yo�r knowledge ,
1rJth the' hope that other physicists ma y carry on investigations
2'J
9.9
�
T.T
D
�
in the same di recti on .
I h ave said that the m o l e cul ar con­
ductivity of e l ectro lytes arose from geometrical considerations
only, and I think it advisable to call your attention to the founda­
tion of such a statement.
While it is true that the conductivity
of different electrolytes varies considerably, it has bee:p. found
that the · molecular conductivity is the same for all electrolytes.
The s i m i lar behavior, of the same number of m olecul es, in­
de pen dently of the.> weight of the moit·(·u){'. t herefo re reduces the
phenomenon to
a
purE'ly geometric ha.",i�.
SUMMARY : Considering that electrostatic energy is actually in the space
surrounding a charged body. the latter is called a "terminal surface." It is
shown that capacity is predominantly a function of the maximum lineal
dimension of the terminal surface. The volumetric and lineal energy den­
sities in the field are defined and studied in a Dumber of cases . It is proven
that the capacity between two terminal surfaces is greatly affected by chang­
ing the lineal dimensions of the smaller terminal surface. but not so for
changes of the larger.
Certain current errors in cxmnection with "mutual
-capacity" are considered.
The practical appli cations to a radio antenn a and to aeroplane counter ­
poises are given .
When a charge traverses a sphere. entering parallel to a diameter. the
sphere beh aves as a conductor of uniform lineal capacity.
Applications of the theoretical considerations are also given in connec­
tion with the conduc..:ivity of con centra ted and dilute electrolytes.