1952
Staebler,
George R.
Calculator interpolations,
394.
May.
Journal of Forestry--Notes 50(5):
Notes Calculator Interpolations
A most tedious and exacting job
is the making of wholesale inter­
polations
intermediate
of
values
from standard tables of one sort or
anothet·.
In logarithm tables the
process is simplifie1l by a column of
differences and a table of propor­
frequently, the following calculator
method
prove
will
helpful.
Suppose, for example, a standard
volume taLle for Douglas-fir shows
the following board foot volumes
for trees of indicated d.b.h. and
total height:
120
appendages on a standard volume
17
JS
table?
The usual method of making ex­
pencil pushing and continual men­
tal calculations-all very tiring and
charged with the possibility, even
probability, of error. If the process
coul<l be carried out in one con­
tinuous operation on a calculator,
prolonged interpolation would still
be a boring task but uot so tiresome
It can be
nor subject to error.
done.
As an example of simple, one­
way interpolation, suppose tables
show that 14-inch tt·ees have a mer­
chantable height of 41 feet; and
15-inch trees, 46 feet.
want
something
in
As usual, we
between,
say
Simply subtract 41
14.7 inches.
from 46, multiply by .7 and add to
41 to get 44.5 feet.
Symbolicall ',
this might be written i=a+x(b­
a) where i is the interpolatrd value,
a is the value belonging to the
smaller independent variable and b
to the larger, 1111 <1 x is the frac­
tional value
of
the
ind<•pendent
variable (in this case .7 of the way
from 14 to 15). Rearranged in a
form for solution on the calculator
the equation is: .
i=(l-x)a+xb
or
i=(.3)(41)+(.7)(46)
=44.5
The products are accumulated in
the calculator- nothing need be
written down-and the answer ap­
pears d ire ctly .
This is a simple process and, un­
less one bas more than a few inter­
polations to make, the calculator
may not appear to be such a boon,
But in two-way interpolation the
case is quite different, and if one
has a series of calculations to make,
or even inakes single interpolations
administering,
in
conjunction with the Iranian gov­
ernment, a program designed to
standards of living
raise
the Iranian people.
among
It hopes that
to the satisfaction of all concerned;
370
410
ing to extend aid, flirectly and im­
but in the meantime it is endeavor­
tional method is to find the volume
of a 128-foot tree 17 inches d.b.b.
and the volume of a 128-foot tree
18 inches d.b.h., then interpolate
between these values for a 17.4-inch
tree. Altogether this requires nine
separate calculations, and the an­
swer for each must be recorded
The interpolated
or remem bered.
value is 377.88.
The equation below g-ives the in­
tr.rpolated value, i.
i=a(l+xy)+bx+&y+dxy- a(x+y)
-bxy-cxy
li'or the example given, x=.8,
y=.4; interpolated value would be:
i=(331)(1.32)+(370)(.80)+(367)(.40)
+(410)(.32)- (331)(1.20)- (370)(.32)
-(367)(.32)=377.88
This sum of products is most easily
accumulated on a calculator, add­
ing the first four terms and sub­
tracting ( negat ivr multiplication)
the last three terms.
No interme­
diate answers need be recorded.
membered and, if made often, be­
A small card mav
.
be prepared and kept handy' to the
come routine.
calculator for easy reference.
A
good form is:
keyboard
b
tl
+
-
r
{(a)
(b)
c)
tl)
(b)
(o)
Accumulate products
for interpolated value,
multiplier
(l+xy)=
(x)
=
11)
""'
my)
(x+y) =
(xy)
-
impoverished
of the population.
to
Projrcts
aid
these
people
must be planned in terms of their
desires and traditions. The former
are somewhat less complex
than
those which worry most Americans,
and are therefore easy for us to
understand.
'rhe Iranian peasant
does not wish to become blind from
trachoma or suffer from malaria.
lie wants to be literate himself, or
at least he wants his rhildrcn to
so.
be
He wants water for his
fields, fnel for his pot, and some­
thing to put into the pot.
On the other hand his traditions
are more difficult fo1· Americans to
grasp because thr.'·
stem from a
social history and strnl'tnre that is
not our own. For this reason proj­
ects which at·e well conceived from
the point of view of basic human
nreds
often
rnro1mtrr
the
most
smprising difficulties for reasons
that are inexplicable to Amel'icans.
Point IV in I ran, the forestr? pro­
gram will give first, though not ex­
clusive, attention to the question
of fuel snpply in the villages near
which trees have either heen de­
stroyed or do not g-row naturally
on account of low
{,
Puget Sound Research Center,
Olympia, Wash,
often
Too
mannrr
prrcipitation.
and
desert
shrubs are burnr<l in a search for
fuel that somr>time consnmN! ono·
third of the villagPr 's working
days.
There is however usually avail.
(xy)
GEORGE R. STAEBLER,
394
the
peasantry which forms BO percent
Because of the basic pnrposc of
The calculations are easily re­
.:t
to
luediatel ',
If the volume of a 17.4-inch tree
II a I
I
·I' II
II o I
The Technical Cooperation Ad­
ministration is
130
128 feet tall is desired, the conven­
II
Point IV Forestry in Iran
the problem of oil will be solved
tional parts, but who ever saw such
tensive interpolations requires much
exceedingly
able to him an abundant supply
of
water
for
winter
irrigation,
months of farming. Could they be
waste land, and leisure in the off­
put to work growing trees, the fuel