Instruction for Using a Slide Rule | Page 2

read on the D scale.
METHOD OF MAKING SETTINGS
In order to understand just why 2.12 is set where it is (figure 2), notice that the interval from 2 to 3 is divided into 10 large or major divisions, each of which is, of course, equal to one-tenth (0.1) of the amount represented by the whole interval. The major divisions are in turn divided into 5 small or minor divisions, each of which is one-fifth or two-tenths (0.2) of the major division, that is 0.02 of the whole interval. Therefore, the index is set above
2 + 1 major division + 1 minor division = 2 + 0.1 + 0.02 = 2.12.
In the same way we find 3.16 on the C scale. While we are on this subject, notice that in the interval from 1 to 2 the major divisions are marked with the small figures 1 to 9 and the minor divisions are 0.1 of the major divisions. In the intervals from 2 to 3 and 3 to 4 the minor divisions are 0.2 of the major divisions, and for the rest of the D (or C) scale, the minor divisions are 0.5 of the major divisions.
Reading the setting from a slide rule is very much like reading measurements from a ruler. Imagine that the divisions between 2 and 3 on the D scale (figure 2) are those of a ruler divided into tenths of a foot, and each tenth of a foot divided in 5 parts 0.02 of a foot long. Then the distance from one on the left-hand end of the D scale (not shown in figure 2) to one on the left-hand end of the C scale would he 2.12 feet. Of course, a foot rule is divided into parts of uniform length, while those on a slide rule get smaller toward the right-hand end, but this example may help to give an idea of the method of making and reading settings. Now consider another example.
Example 3a: 2.12 * 7.35 = 15.6
If we set the left-hand index of the C scale over 2.12 as in the last example, we find that 7.35 on the C scale falls out beyond the body of the rule. In a case like this, simply use the right-hand index of the C scale. If we set this over 2.12 on the D scale and move the runner to 7.35 on the C scale we read the result 15.6 on the D scale under the hair-line.
Now, the question immediately arises, why did we call the result 15.6 and not 1.56? The answer is that the slide rule takes no account of decimal points. Thus, the settings would be identical for all of the following products:
Example 3: a-- 2.12 * 7.35 = 15.6 b-- 21.2 * 7.35 = 156.0 c-- 212 * 73.5 = 15600. d-- 2.12 * .0735 = .156 e-- .00212 * 735 = .0156
The most convenient way to locate the decimal point is to make a mental multiplication using only the first digits in the given factors. Then place the decimal point in the slide rule result so that its value is nearest that of the mental multiplication. Thus, in example 3a above, we can multiply 2 by 7 in our heads and see immediately that the decimal point must be placed in the slide rule result 156 so that it becomes 15.6 which is nearest to 14. In example 3b (20 * 7 = 140), so we must place the decimal point to give 156. The reader can readily verify the other examples in the same way.
Since the product of a number by a second number is the same as the product of the second by the first, it makes no difference which of the two numbers is set first on the slide rule. Thus, an alternative way of working example 2 would be to set the left-hand index of the C scale over 3.16 on the D scale and move the runner to 2.12 on the C scale and read the answer under the hair-line on the D scale.
The A and B scales are made up of two identical halves each of which is very similar to the C and D scales. Multiplication can also be carried out on either half of the A and B scales exactly as it is done on the C and D scales. However, since the A and B scales are only half as long as the C and D scales, the accuracy is not as good. It is sometimes convenient to multiply on the A and B scales in more complicated problems as we shall see later on.
A group of examples follow which cover all the possible combination of settings which can arise in the multiplication of two numbers.
Example 4: 20 * 3 = 60