Read Ebook: Instruction for Using a Slide Rule by Stanley W

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The DOC file and TXT files otherwise closely approximate the original text. There are two versions of the HTML files, one closely approximating the original, and a second with images of the slide rule settings for each example.

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:

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 . 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:

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 . 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:

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 . 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 , 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 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 of the major division, that is 0.02 of the whole interval. Therefore, the index is set above

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 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 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 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.

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:

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 , 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.

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:

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:

THE CI SCALE

If we divide one 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:

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:

Set indicator over 4 on D scale. Read 16 on A scale under hair-line.

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:

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.

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.

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

In this number we have an even number of zeros to the right of the decimal point, so we must set the indicator over 37 on the right-hand half of the A scale. Read 608 under the hair-line on D scale. To place the decimal point write:

A number of examples follow for squaring and the extraction of square root.

CUBING AND CUBE ROOT

To find the cube of any number on the slide rule set the indicator over the number on the D scale and read the answer on the K scale under the hair-line. To find the cube root of any number set the indicator over the number on the K scale and read the answer on the D scale under the hair-line. Just as on the A scale, where there were two places where you could set a given number, on the K scale there are three places where a number may be set. To tell which of the three to use, we must make use of the following rule.

If the number is greater than one. For 1, 4, 7, 10, etc., digits to the left of the decimal point, use the left-hand third of the K scale. For 2, 5, 8, 11, etc., digits to the left of the decimal point, use the middle third of the K scale. For 3, 6, 9, 12, etc., digits to the left of the decimal point use the right-hand third of the K scale.

If the number is less than one. We now tell which scale to use by counting the number of zeros to the right of the decimal point before the first digit not zero. If there are 2, 5, 8, 11, etc., zeros, use the left-hand third of the K scale. If there are 1, 4, 7, 10, etc., zeros, then use the middle third of the K scale. If there are no zeros or 3, 6, 9, 12, etc., zeros, then use the right-hand third of the K scale. For example:

Since there are 3 digits in the given number, we set the indicator on 185 in the right-hand third of the K scale, and read the result 570 on the D scale. We can place the decimal point by thinking of the nearest perfect cube, which is 125. Therefore, the decimal point must be placed so as to give 5.70, which is nearest to 5, the cube root of 125.

Since there is one zero between the decimal point and the first digit not zero, we must set the indicator over 34 on the middle third of the K scale. We read the result 324 on the D scale. The decimal point may be placed as follows:

The nearest perfect cube to 34 is 27, so our answer must be close to one-tenth of the cube root of 27 or nearly 0.3. Therefore, we must place the decimal point to give 0.324. A group of examples for practice in extraction of cube root follows:

THE 1.5 AND 2/3 POWER

If the indicator is set over a given number on the A scale, the number under the hair-line on the K scale is the 1.5 power of the given number. If the indicator is set over a given number on the K scale, the number under the hair-line on the A scale is the 2/3 power of the given number.

COMBINATIONS OF PROCESSES

A slide rule is especially useful where some combination of processes is necessary, like multiplying 3 numbers together and dividing by a third. Operations of this sort may be performed in such a way that the final answer is obtained immediately without finding intermediate results.

First divide 4 by 2.5. Set indicator over 4 on the D scale and move the slider until 2.5 is under the hair-line. The result of this division, 1.6, appears under the left-hand index of the C scale. We do not need to write it down, however, but we can immediately move the indicator to 15 on the C scale and read the final result 24 on the D scale under the hair-line. Let us consider a more complicated problem of the same type:

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