Part 1

Conventional mathematical notation requires specialized fonts and typesetting conventions. I have adopted modern computer programming notation using only ASCII characters. The square root of 9 is thus rendered as square_root(9) and the square of 9 is square(9). 10 divided by 5 is (10/5) and 10 multiplied by 5 is (10 * 5 ).

By the time I finished engineering school in 1963, the slide rule was a well worn tool of my trade. I did not use an electronic calculator for another ten years. Consider that my predecessors had little else to use--think Boulder Dam (with all its electrical, mechanical and construction calculations).

Rather than dealing with elaborate rules for positioning the decimal point, I was taught to first "scale" the factors and deal with the decimal position separately. For example:

1230 * .000093 = 1.23E3 * 9.3E-5 1.23E3 means multiply 1.23 by 10 to the power 3. 9.3E-5 means multiply 9.3 by 0.1 to the power 5 or 10 to the power -5. The computation is thus 1.23 * 9.3 * 1E3 * 1E-5 The exponents are simply added. 1.23 * 9.3 * 1E-2 = 11.4 * 1E-2 = .114

When taking roots, divide the exponent by the root. The square root of 1E6 is 1E3 The cube root of 1E12 is 1E4.

When taking powers, multiply the exponent by the power. The cube of 1E5 is 1E15.

INSTRUCTIONS for using a SLIDE RULE SAVE TIME! DO THE FOLLOWING INSTANTLY WITHOUT PAPER AND PENCIL MULTIPLICATION DIVISION RECIPROCAL VALUES SQUARES & CUBES EXTRACTION OF SQUARE ROOT EXTRACTION OF CUBE ROOT DIAMETER OR AREA OF CIRCLE

INSTRUCTIONS FOR USING A SLIDE RULE

The slide rule is a device for easily and quickly multiplying, dividing and extracting square root and cube root. It will also perform any combination of these processes. On this account, it is found extremely useful by students and teachers in schools and colleges, by engineers, architects, draftsmen, surveyors, chemists, and many others. Accountants and clerks find it very helpful when approximate calculations must be made rapidly. The operation of a slide rule is extremely easy, and it is well worth while for anyone who is called upon to do much numerical calculation to learn to use one. It is the purpose of this manual to explain the operation in such a way that a person who has never before used a slide rule may teach himself to do so.

DESCRIPTION OF SLIDE RULE

The slide rule consists of three parts (see figure 1). B is the body of the rule and carries three scales marked A, D and K. S is the slider which moves relative to the body and also carries three scales marked B, CI and C. R is the runner or indicator and is marked in the center with a hair-line. The scales A and B are identical and are used in problems involving square root. Scales C and D are also identical and are used for multiplication and division. Scale K is for finding cube root. Scale CI, or C-inverse, is like scale C except that it is laid off from right to left instead of from left to right. It is useful in problems involving reciprocals.

MULTIPLICATION

We will start with a very simple example:

Example 1: 2 * 3 = 6

To prove this on the slide rule, move the slider so that the 1 at the left-hand end of the C scale is directly over the large 2 on the D scale (see figure 1). Then move the runner till the hair-line is over 3 on the C scale. Read the answer, 6, on the D scale under the hair-line. Now, let us consider a more complicated example:

Example 2: 2.12 * 3.16 = 6.70

As before, set the 1 at the left-hand end of the C scale, which we will call the left-hand index of the C scale, over 2.12 on the D scale (See figure 2). The hair-line of the runner is now placed over 3.16 on the C scale and the answer, 6.70, 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.