Instruction for Using a Slide Rule | Page 3

5: 85 * 2 = 170 6: 45 * 35 = 1575 7: 151 * 42 = 6342 8: 6.5 * 15 = 97.5 9: .34 * .08 = .0272 10: 75 * 26 = 1950 11: .00054 * 1.4 = .000756 12: 11.1 * 2.7 = 29.97 13: 1.01 * 54 = 54.5 14: 3.14 * 25 = 78.5
DIVISION
Since multiplication and division are inverse processes, division on a slide rule is done by making the same settings as for multiplication, but in reverse order. Suppose we have the example:
Example 15: (6.70 / 2.12) = 3.16
Set indicator over the dividend 6.70 on the D scale. Move the slider until the divisor 2.12 on the C scale is under the hair-line. Then read the result on the D scale under the left-hand index of the C scale. As in multiplication, the decimal point must be placed by a separate process. Make all the digits except the first in both dividend and divisor equal zero and mentally divide the resulting numbers. Place the decimal point in the slide rule result so that it is nearest to the mental result. In example 15, we mentally divide 6 by 2. Then we place the decimal point in the slide rule result 316 so that it is 3.16 which is nearest to 3.
A group of examples for practice in division follow:
Example 16: 34 / 2 = 17 17: 49 / 7 = 7 18: 132 / 12 = 11 19: 480 / 16 = 30 20: 1.05 / 35 = .03 21: 4.32 / 12 = .36 22: 5.23 / 6.15 = .85 23: 17.1 / 4.5 = 3.8 24: 1895 / 6.06 = 313 25: 45 / .017 = 2647
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