THE CI SCALE
If we divide one (1) by any number the answer is called the reciprocal
of the number. Thus, one-half is the reciprocal of two, one-quarter is
the reciprocal of four. If we take any number, say 14, and multiply it
by the reciprocal of another number, say 2, we get:
Example 26: 14 * (1/2) = 7
which is the same as 14 divided by two. This process can be carried out
directly on the slide rule by use of the CI scale. Numbers on the CI
scale are reciprocals of those on the C scale. Thus we see that 2 on the
CI scale comes directly over 0.5 or 1/2 on the C scale. Similarly 4 on
the CI scale comes over 0.25 or 1/4 on the C scale, and so on. To do
example 26 by use of the CI scale, proceed exactly as if you were going
to multiply in the usual manner except that you use the CI scale instead
of the C scale. First set the left-hand index of the C scale over 14 on
the D scale. Then move the indicator to 2 on the CI scale. Read the
result, 7, on the D scale under the hair-line. This is really another
way of dividing. THE READER IS ADVISED TO WORK EXAMPLES 16 TO 25 OVER
AGAIN BY USE OF THE CI SCALE.
SQUARING AND SQUARE ROOT
If we take a number and multiply it by itself we call the result the
square of the number. The process is called squaring the number. If we
find the number which, when multiplied by itself is equal to a given
number, the former number is called the square root of the given number.
The process is called extracting the square root of the number. Both
these processes may be carried out on the A and D scales of a slide
rule. For example:
Example 27: 4 * 4 = square( 4 ) = 16
Set indicator over 4 on D scale. Read 16 on A scale under hair-line.
Example 28: square( 25.4 ) = 646.0
The decimal point must be placed by mental survey. We know that
square( 25.4 ) must be a little larger than square( 25 ) = 625 so that
it must be 646.0.
To extract a square root, we set the indicator over the number on the A
scale and read the result under the hair-line on the D scale. When we
examine the A scale we see that there are two places where any given
number may be set, so we must have some way of deciding in a given case
which half of the A scale to use. The rule is as follows:
(a) If the number is greater than one. For an odd number of digits to
the left of the decimal point, use the left-hand half of the A scale.
For an even number of digits to the left of the decimal point, use the
right-hand half of the A scale.
(b) If the number is less than one. For an odd number of zeros to the
right of the decimal point before the first digit not a zero, use the
left-hand half of the A scale. For none or any even number of zeros to
the right of the decimal point before the first digit not a zero, use
the right-hand half of the A scale.
Example 29: square_root( 157 ) = 12.5
Since we have an odd number of digits set indicator over 157 on
left-hand half of A scale. Read 12.5 on the D scale under hair-line. To
check the decimal point think of the perfect square nearest to 157. It
is 12 * 12 = 144, so that square_root(157) must be a little more than 12 or
12.5.
Example 30: square_root( .0037 ) = .0608