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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<title>Instructions for using a Slide Rule</title>
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<body>
<big>[Transcriber's Notes]<br>
<br>
Conventional mathematical notation requires specialized fonts and<br>
typesetting conventions. I have adopted modern computer programming<br>
notation using only ASCII characters. The square root of 9 is thus<br>
rendered as square_root(9) and the square of 9 is square(9).<br>
10 divided by 5 is (10/5) and 10 multiplied by 5 is (10 * 5 ).<br>
<br>
The DOC file and TXT files otherwise closely approximate the original<br>
text. There are two versions of the HTML files, one closely<br>
approximating the original, and a second with images of the slide rule<br>
settings for each example.<br>
<br>
By the time I finished engineering school in 1963, the slide rule was a<br>
well worn tool of my trade. I did not use an electronic calculator for<br>
another ten years. Consider that my predecessors had little else to<br>
use--think Boulder Dam (with all its electrical, mechanical and<br>
construction calculations).<br>
<br>
Rather than dealing with elaborate rules for positioning the decimal <br>
point, I was taught to first "scale" the factors and deal with the <br>
decimal position separately. For example:<br>
<br>
1230 * .000093 =<br>
1.23E3 * 9.3E-5 <br>
1.23E3 means multiply 1.23 by 10 to the power 3.<br>
9.3E-5 means multiply 9.3 by 0.1 to the power 5 or 10 to the power -5.<br>
The computation is thus<br>
1.23 * 9.3 * 1E3 * 1E-5<br>
The exponents are simply added.<br>
1.23 * 9.3 * 1E-2 =<br>
11.4 * 1E-2 =<br>
.114<br>
<br>
When taking roots, divide the exponent by the root. <br>
The square root of 1E6 is 1E3<br>
The cube root of 1E12 is 1E4.<br>
<br>
When taking powers, multiply the exponent by the power.<br>
The cube of 1E5 is 1E15.<br>
<br>
[End Transcriber's Notes]<br>
<br>
<br>
INSTRUCTIONS<br>
for using a<br>
SLIDE<br>
RULE<br>
SAVE TIME!<br>
DO THE FOLLOWING INSTANTLY WITHOUT PAPER AND PENCIL<br>
MULTIPLICATION<br>
DIVISION<br>
RECIPROCAL VALUES<br>
SQUARES & CUBES<br>
EXTRACTION OF SQUARE ROOT<br>
EXTRACTION OF CUBE ROOT<br>
DIAMETER OR AREA OF CIRCLE<br>
<br>
<img style="width: 701px; height: 420px;" alt="" src="images/01Pic.jpg"><br>
<br>
<br>
<br>
INSTRUCTIONS FOR USING A SLIDE RULE<br>
<br>
The slide rule is a device for easily and quickly multiplying, dividing<br>
and extracting square root and cube root. It will also perform any<br>
combination of these processes. On this account, it is found extremely<br>
useful by students and teachers in schools and colleges, by engineers,<br>
architects, draftsmen, surveyors, chemists, and many others. Accountants<br>
and clerks find it very helpful when approximate calculations must be<br>
made rapidly. The operation of a slide rule is extremely easy, and it is<br>
well worth while for anyone who is called upon to do much numerical<br>
calculation to learn to use one. It is the purpose of this manual to<br>
explain the operation in such a way that a person who has never before<br>
used a slide rule may teach himself to do so.<br>
<br>
</big><big>
DESCRIPTION OF SLIDE RULE<br>
<br>
</big><big>The slide rule consists of three parts (see figure 1). B is
the body of<br>
the rule and carries three scales marked A, D and K. S is the slider<br>
which moves relative to the body and also carries three scales marked B,<br>
CI and C. R is the runner or indicator and is marked in the center with<br>
a hair-line. The scales A and B are identical and are used in problems<br>
involving square root. Scales C and D are also identical and are used<br>
for multiplication and division. Scale K is for finding cube root. Scale<br>
CI, or C-inverse, is like scale C except that it is laid off from right<br>
to left instead of from left to right. It is useful in problems<br>
involving reciprocals.<br>
<br>
<br>
MULTIPLICATION<br>
<br>
We will start with a very simple example:<br>
<br>
Example 1: 2 * 3 = 6<br>
<br>
To prove this on the slide rule, move the slider so that the 1 at the<br>
left-hand end of the C scale is directly over the large 2 on the D scale<br>
(see figure 1). Then move the runner till the hair-line is over 3 on the<br>
C scale. Read the answer, 6, on the D scale under the hair-line. Now,<br>
let us consider a more complicated example:<br>
<br>
Example 2: 2.12 * 3.16 = 6.70<br>
<br>
As before, set the 1 at the left-hand end of the C scale, which we will<br>
call the left-hand index of the C scale, over 2.12 on the D scale (See<br>
figure 2). The hair-line of the runner is now placed over 3.16 on the C<br>
scale and the answer, 6.70, read on the D scale.<br>
<br>
<br>
METHOD OF MAKING SETTINGS<br>
<br>
In order to understand just why 2.12 is set where it is (figure 2),<br>
notice that the interval from 2 to 3 is divided into 10 large or major<br>
divisions, each of which is, of course, equal to one-tenth (0.1) of the<br>
amount represented by the whole interval. The major divisions are in<br>
turn divided into 5 small or minor divisions, each of which is one-fifth<br>
or two-tenths (0.2) of the major division, that is 0.02 of the<br>
whole interval. Therefore, the index is set above<br>
<br>
2 + 1 major division + 1 minor division = 2 + 0.1 + 0.02 = 2.12.<br>
<br>
In the same way we find 3.16 on the C scale. While we are on this<br>
subject, notice that in the interval from 1 to 2 the major divisions are<br>
marked with the small figures 1 to 9 and the minor divisions are 0.1 of<br>
the major divisions. In the intervals from 2 to 3 and 3 to 4 the minor<br>
divisions are 0.2 of the major divisions, and for the rest of the D (or<br>
C) scale, the minor divisions are 0.5 of the major divisions.<br>
<br>
Reading the setting from a slide rule is very much like reading<br>
measurements from a ruler. Imagine that the divisions between 2 and 3 on<br>
the D scale (figure 2) are those of a ruler divided into tenths of a<br>
foot, and each tenth of a foot divided in 5 parts 0.02 of a foot long.<br>
Then the distance from one on the left-hand end of the D scale (not<br>
shown in figure 2) to one on the left-hand end of the C scale would he<br>
2.12 feet. Of course, a foot rule is divided into parts of uniform<br>
length, while those on a slide rule get smaller toward the right-hand<br>
end, but this example may help to give an idea of the method of making<br>
and reading settings. Now consider another example.<br>
<br>
Example 3a: 2.12 * 7.35 = 15.6<br>
<br>
If we set the left-hand index of the C scale over 2.12 as in the last<br>
example, we find that 7.35 on the C scale falls out beyond the body of<br>
the rule. In a case like this, simply use the right-hand index of the C<br>
scale. If we set this over 2.12 on the D scale and move the runner to<br>
7.35 on the C scale we read the result 15.6 on the D scale under the<br>
hair-line.<br>
<br>
Now, the question immediately arises, why did we call the result 15.6<br>
and not 1.56? The answer is that the slide rule takes no account of<br>
decimal points. Thus, the settings would be identical for all of the<br>
following products:<br>
<br>
Example 3:<br>
a-- 2.12 * 7.35 = 15.6<br>
b-- 21.2 * 7.35 = 156.0<br>
c-- 212 * 73.5 = 15600.<br>
d-- 2.12 * .0735 = .156<br>
e-- .00212 * 735 = .0156<br>
<br>
The most convenient way to locate the decimal point is to make a mental<br>
multiplication using only the first digits in the given factors. Then<br>
place the decimal point in the slide rule result so that its value is<br>
nearest that of the mental multiplication. Thus, in example 3a above, we<br>
can multiply 2 by 7 in our heads and see immediately that the decimal<br>
point must be placed in the slide rule result 156 so that it becomes<br>
15.6 which is nearest to 14. In example 3b (20 * 7 = 140), so we must<br>
place the decimal point to give 156. The reader can readily verify the<br>
other examples in the same way.<br>
<br>
Since the product of a number by a second number is the same as the<br>
product of the second by the first, it makes no difference which of the<br>
two numbers is set first on the slide rule. Thus, an alternative way of<br>
working example 2 would be to set the left-hand index of the C scale<br>
over 3.16 on the D scale and move the runner to 2.12 on the C scale and<br>
read the answer under the hair-line on the D scale.<br>
<br>
The A and B scales are made up of two identical halves each of which is<br>
very similar to the C and D scales. Multiplication can also be carried<br>
out on either half of the A and B scales exactly as it is done on the C<br>
and D scales. However, since the A and B scales are only half as long as<br>
the C and D scales, the accuracy is not as good. It is sometimes<br>
convenient to multiply on the A and B scales in more complicated<br>
problems as we shall see later on.<br>
<br>
A group of examples follow which cover all the possible combination of<br>
settings which can arise in the multiplication of two numbers.<br>
<br>
Example<br>
4: 20 * 3 = 60<br>
5: 85 * 2 = 170<br>
6: 45 * 35 = 1575<br>
7: 151 * 42 = 6342<br>
8: 6.5 * 15 = 97.5<br>
9: .34 * .08 = .0272<br>
10: 75 * 26 = 1950<br>
11: .00054 * 1.4 = .000756<br>
12: 11.1 * 2.7 = 29.97<br>
13: 1.01 * 54 = 54.5<br>
14: 3.14 * 25 = 78.5<br>
<br>
<br>
DIVISION<br>
<br>
Since multiplication and division are inverse processes, division on a<br>
slide rule is done by making the same settings as for multiplication,<br>
but in reverse order. Suppose we have the example:<br>
<br>
Example 15: (6.70 / 2.12) = 3.16<br>
<br>
Set indicator over the dividend 6.70 on the D scale. Move the slider<br>
until the divisor 2.12 on the C scale is under the hair-line. Then read<br>
the result on the D scale under the left-hand index of the C scale. As<br>
in multiplication, the decimal point must be placed by a separate<br>
process. Make all the digits except the first in both dividend and<br>
divisor equal zero and mentally divide the resulting numbers. Place the<br>
decimal point in the slide rule result so that it is nearest to the<br>
mental result. In example 15, we mentally divide 6 by 2. Then we place<br>
the decimal point in the slide rule result 316 so that it is 3.16 which<br>
is nearest to 3.<br>
<br>
A group of examples for practice in division follow:<br>
<br>
Example<br>
16: 34 / 2 = 17<br>
17: 49 / 7 = 7<br>
18: 132 / 12 = 11<br>
19: 480 / 16 =30<br>
20: 1.05 / 35 =.03<br>
21: 4.32 / 12 =.36<br>
22: 5.23 / 6.15 =.85<br>
23: 17.1 / 4.5 = 3.8<br>
24: 1895 / 6.06 = 313<br>
25: 45 /.017 = 2647<br>
<br>
<br>
THE CI SCALE<br>
<br>
If we divide one (1) by any number the answer is called the reciprocal<br>
of the number. Thus, one-half is the reciprocal of two, one-quarter is<br>
the reciprocal of four. If we take any number, say 14, and multiply it<br>
by the reciprocal of another number, say 2, we get:<br>
<br>
Example 26: 14 * (1/2) = 7<br>
<br>
which is the same as 14 divided by two. This process can be carried out<br>
directly on the slide rule by use of the CI scale. Numbers on the CI<br>
scale are reciprocals of those on the C scale. Thus we see that 2 on the<br>
CI scale comes directly over 0.5 or 1/2 on the C scale. Similarly 4 on<br>
the CI scale comes over 0.25 or 1/4 on the C scale, and so on. To do<br>
example 26 by use of the CI scale, proceed exactly as if you were going<br>
to multiply in the usual manner except that you use the CI scale instead<br>
of the C scale. First set the left-hand index of the C scale over 14 on<br>
the D scale. Then move the indicator to 2 on the CI scale. Read the<br>
result, 7, on the D scale under the hair-line. This is really another<br>
way of dividing. THE READER IS ADVISED TO WORK EXAMPLES <br>
16 TO 25 OVER AGAIN BY USE OF THE CI SCALE.<br>
<br>
<br>
SQUARING AND SQUARE ROOT<br>
<br>
If we take a number and multiply it by itself we call the result the<br>
square of the number. The process is called squaring the number. If we<br>
find the number which, when multiplied by itself is equal to a given<br>
number, the former number is called the square root of the given number.<br>
The process is called extracting the square root of the number. Both<br>
these processes may be carried out on the A and D scales of a slide<br>
rule. For example:<br>
<br>
Example 27: 4 * 4 = square( 4 ) = 16<br>
<br>
Set indicator over 4 on D scale. Read 16 on A scale under hair-line.<br>
<br>
Example 28: square( 25.4 ) = 646.0<br>
<br>
The decimal point must be placed by mental survey. We know that <br>
square( 25.4 ) must be a little larger than square( 25 ) = 625 so that <br>
it
must be 646.0.<br>
<br>
To extract a square root, we set the indicator over the number on the A<br>
scale and read the result under the hair-line on the D scale. When we<br>
examine the A scale we see that there are two places where any given<br>
number may be set, so we must have some way of deciding in a given case<br>
which half of the A scale to use. The rule is as follows:<br>
<br>
(a) If the number is greater than one. For an odd number of digits to<br>
the left of the decimal point, use the left-hand half of the A scale.<br>
For an even number of digits to the left of the decimal point, use the<br>
right-hand half of the A scale.<br>
<br>
(b) If the number is less than one. For an odd number of zeros to the<br>
right of the decimal point before the first digit not a zero, use the<br>
left-hand half of the A scale. For none or any even number of zeros to<br>
the right of the decimal point before the first digit not a zero, use<br>
the right-hand half of the A scale.<br>
<br>
Example 29: square_root( 157 ) = 12.5<br>
<br>
Since we have an odd number of digits set indicator over 157 on<br>
left-hand half of A scale. Read 12.5 on the D scale under hair-line. To<br>
check the decimal point think of the perfect square nearest to 157. It<br>
is<br>
<br>
12 * 12 = 144, so that square_root(157) must be a little more than 12 or<br>
12.5.<br>
<br>
Example 30: square_root( .0037 ) = .0608<br>
<br>
In this number we have an even number of zeros to the right of the<br>
decimal point, so we must set the indicator over 37 on the right-hand<br>
half of the A scale. Read 608 under the hair-line on D scale. To place<br>
the decimal point write:<br>
<br>
square_root( .0037 ) = square_root( 37/10000 )<br>
= 1/100 square_root( 37 )<br>
<br>
The nearest perfect square to 37 is 6 * 6 = 36, so the answer should be<br>
a little more than 0.06 or .0608. All of what has been said about use of<br>
the A and D scales for squaring and extracting square root applies<br>
equally well to the B and C scales since they are identical to the A and<br>
D scales respectively.<br>
<br>
A number of examples follow for squaring and the extraction of square<br>
root.<br>
<br>
Example<br>
31: square( 2 ) = 4<br>
32: square( 15 ) = 225<br>
33: square( 26 ) = 676<br>
34: square( 19.65 ) = 386<br>
35: square_root( 64 ) = 8<br>
36: square_root( 6.4 ) = 2.53<br>
37: square_root( 498 ) = 22.5<br>
38: square_root( 2500 ) = 50<br>
39: square_root( .16 ) = .04<br>
40: square_root( .03 ) = .173<br>
<br>
<br>
CUBING AND CUBE ROOT<br>
<br>
If we take a number and multiply it by itself, and then multiply the<br>
result by the original number we get what is called the cube of the<br>
original number. This process is called cubing the number. The reverse<br>
process of finding the number which, when multiplied by itself and then<br>
by itself again, is equal to the given number, is called extracting the<br>
cube root of the given number. Thus, since 5 * 5 * 5 = 125, 125 is the<br>
cube of 5 and 5 is the cube root of 125.<br>
<br>
To find the cube of any number on the slide rule set the indicator over<br>
the number on the D scale and read the answer on the K scale under the<br>
hair-line. To find the cube root of any number set the indicator over<br>
the number on the K scale and read the answer on the D scale under the<br>
hair-line. Just as on the A scale, where there were two places where you<br>
could set a given number, on the K scale there are three places where a<br>
number may be set. To tell which of the three to use, we must make use<br>
of the following rule.<br>
<br>
(a) If the number is greater than one. For 1, 4, 7, 10, etc., digits to<br>
the left of the decimal point, use the left-hand third of the K scale.<br>
For 2, 5, 8, 11, etc., digits to the left of the decimal point, use the<br>
middle third of the K scale. For 3, 6, 9, 12, etc., digits to the left<br>
of the decimal point use the right-hand third of the K scale.<br>
<br>
(b) If the number is less than one. We now tell which scale to use by<br>
counting the number of zeros to the right of the decimal point before<br>
the first digit not zero. If there are 2, 5, 8, 11, etc., zeros, use the<br>
left-hand third of the K scale. If there are 1, 4, 7, 10, etc., zeros,<br>
then use the middle third of the K scale. If there are no zeros or 3, 6,<br>
9, 12, etc., zeros, then use the right-hand third of the K scale. For<br>
example:<br>
<br>
Example 41: cube_root( 185 ) = 5.70<br>
<br>
Since there are 3 digits in the given number, we set the indicator on<br>
185 in the right-hand third of the K scale, and read the result 570 on<br>
the D scale. We can place the decimal point by thinking of the nearest<br>
perfect cube, which is 125. Therefore, the decimal point must be placed<br>
so as to give 5.70, which is nearest to 5, the cube root of 125.<br>
<br>
Example 42: cube_root( .034 ) = .324<br>
<br>
Since there is one zero between the decimal point and the first digit<br>
not zero, we must set the indicator over 34 on the middle third of the K<br>
scale. We read the result 324 on the D scale. The decimal point may be<br>
placed as follows:<br>
<br>
cube_root( .034 ) = cube_root( 34/1000 )<br>
= 1/10 cube_root( 34 )<br>
<br>
The nearest perfect cube to 34 is 27, so our answer must be close to<br>
one-tenth of the cube root of 27 or nearly 0.3. Therefore, we must place<br>
the decimal point to give 0.324. A group of examples for practice in<br>
extraction of cube root follows:<br>
<br>
Example<br>
43: cube_root( 64 ) = 4<br>
44: cube_root( 8 ) = 2<br>
45: cube_root( 343 ) = 7<br>
46: cube_root( .000715 ) = .0894<br>
47: cube_root( .00715 ) = .193<br>
48: cube_root( .0715 ) = .415<br>
49: cube_root( .516 ) = .803<br>
50: cube_root( 27.8 ) = 3.03<br>
51: cube_root( 5.49 ) = 1.76<br>
52: cube_root( 87.1 ) = 4.43<br>
<br>
<br>
THE 1.5 AND 2/3 POWER<br>
<br>
If the indicator is set over a given number on the A scale, the number<br>
under the hair-line on the K scale is the 1.5 power of the given<br>
number. If the indicator is set over a given number on the K scale, the<br>
number under the hair-line on the A scale is the 2/3 power of the given<br>
number.<br>
<br>
<br>
COMBINATIONS OF PROCESSES<br>
<br>
A slide rule is especially useful where some combination of processes is<br>
necessary, like multiplying 3 numbers together and dividing by a third.<br>
Operations of this sort may be performed in such a way that the final<br>
answer is obtained immediately without finding intermediate results.<br>
<br>
1. Multiplying several numbers together. For example, suppose it is<br>
desired to multiply 4 * 8 * 6. Place the right-hand index of the C scale<br>
over 4 on the D scale and set the indicator over 8 on the C scale. Now,<br>
leaving the indicator where it is, move the slider till the right-hand<br>
index is under the hairline. Now, leaving the slider where it is, move<br>
the indicator until it is over 6 on the C scale, and read the result,<br>
192, on the D scale. This may be continued indefinitely, and so as many<br>
numbers as desired may be multiplied together.<br>
<br>
Example 53: 2.32 * 154 * .0375 * .56 = 7.54<br>
<br>
2. Multiplication and division.<br>
Suppose we wish to do the following example:<br>
<br>
Example 54: (4 * 15) / 2.5 = 24<br>
<br>
First divide 4 by 2.5. Set indicator over 4 on the D scale and move the<br>
slider until 2.5 is under the hair-line. The result of this division,<br>
1.6, appears under the left-hand index of the C scale. We do not need to<br>
write it down, however, but we can immediately move the indicator to 15<br>
on the C scale and read the final result 24 on the D scale under the<br>
hair-line. Let us consider a more complicated problem of the same type:<br>
<br>
Example 55: (30/7.5) * (2/4) * (4.5/5) * (1.5/3) = .9<br>
<br>
First set indicator over 30 on the D scale and move slider until 7.5 on<br>
the C scale comes under the hairline. The intermediate result, 4,<br>
appears under the right-hand index of the C scale. We do not need to<br>
write it down but merely note it by moving the indicator until the<br>
hair-line is over the right-hand index of the C scale. Now we want to<br>
multiply this result by 2, the next factor in the numerator. Since two<br>
is out beyond the body of the rule, transfer the slider till the other<br>
(left-hand) index of the C scale is under the hair-line, and then move<br>
the indicator to 2 on the C scale. Thus, successive division and<br>
multiplication is continued until all the factors have been used. The<br>
order in which the factors are taken does not affect the result. With a<br>
little practice you will learn to take them in the order which will<br>
require the fewest settings. The following examples are for practice:<br>
<br>
Example 56: (6/3.5) * (4/5) * (3.5/2.4) * (2.8/7) = .8<br>
<br>
Example 57: 352 * (273/254) * (760/768) = 374<br>
<br>
An alternative method of doing these examples is to proceed exactly as<br>
though you were multiplying all the factors together, except that<br>
whenever you come to a number in the denominator you use the CI scale<br>
instead of the C scale. The reader is advised to practice both methods<br>
and use whichever one he likes best.<br>
<br>
3. The area of a circle. The area of a circle is found by multiplying<br>
3.1416=PI by the square of the radius or by one-quarter the square of<br>
the diameter<br>
<br>
Formula: A = PI * square( R )<br>
A = PI *
(square( D ) / 4 )<br>
<br>
Example 58: The radius of a circle is 0.25 inches; find its area.<br>
<br>
Area = PI * square(0.25) = 0.196 square inches.<br>
<br>
Set left-hand index of C scale over 0.25 on D scale. square(0.25) now<br>
appears above the left-hand index of the B scale. This can be multiplied<br>
by PI by moving the indicator to PI on the B scale and reading the<br>
answer .196 on the A scale. This is an example where it is convenient to<br>
multiply with the A and B scales.<br>
<br>
Example 59: The diameter of a circle is 8.1 feet. What is its area?<br>
<br>
Area = (PI / 4) * square(8.1)<br>
= .7854 * square(8.1)<br>
= 51.7 sq. inches.<br>
<br>
Set right-hand index of the C scale over 8.1 on the D scale. Move the<br>
indicator till hair-line is over .7854 (the special long mark near 8) at<br>
the right hand of the B scale. Read the answer under the hair-line on<br>
the A scale. Another way of finding the area of a circle is to set 7854<br>
on the B scale to one of the indices of the A scale, and read the area<br>
from the B scale directly above the given diameter on the D scale.<br>
<br>
4. The circumference of a circle. Set the index of the B scale to the<br>
diameter and read the answer on the A scale opposite PI on the B scale<br>
<br>
Formula: C = PI * D<br>
C = 2 * PI * R<br>
<br>
Example 60: The diameter of a circle is 1.54 inches, what is its<br>
circumference?<br>
<br>
Set the left-hand index of the B scale to 1.54 on the A scale. Read the<br>
circumference 4.85 inches above PI on the B scale.<br>
<br>
EXAMPLES FOR PRACTICE<br>
<br>
61: What is the area of a circle 32-1/2 inches in diameter?<br>
Answer 830 sq. inches<br>
<br>
62: What is the area of a circle 24 inches in diameter?<br>
Answer 452 sq. inches<br>
<br>
63: What is the circumference of a circle whose diameter is 95 feet?<br>
Answer 298 ft.<br>
<br>
64: What is the circumference of a circle whose diameter is 3.65 inches?<br>
Answer 11.5 inches<br>
<br>
5. Ratio and Proportion.<br>
<br>
Example 65: 3 : 7 : : 4 : X<br>
or<br>
(3/7) = (4/x)<br>
Find X<br>
<br>
Set 3 on C scale over 7 on D scale. Read X on D scale under 4 on C<br>
scale. In fact, any number on the C scale is to the number directly<br>
under it on the D scale as 3 is to 7.<br>
<br>
<br>
PRACTICAL PROBLEMS SOLVED BY SLIDE RULE<br>
<br>
<br>
1. Discount.<br>
A firm buys a typewriter with a list price of $150, subject to a<br>
discount of 20% and 10%. How much does it pay?<br>
<br>
A discount of 20% means 0.8 of the list price, and 10% more means<br>
0.8 * 0.9 * 150 = 108.<br>
<br>
To do this on the slide rule, put the index of the C scale opposite 8 on<br>
the D scale and move the indicator to 9 on the C scale. Then move the<br>
slider till the right-hand index of the C scale is under the hairline.<br>
Now, move the indicator to 150 on the C scale and read the answer $108<br>
on the D scale. Notice that in this, as in many practical problems,<br>
there is no question about where the decimal point should go.<br>
<br>
<br>
2. Sales Tax.<br>
<br>
A man buys an article worth $12 and he must pay a sales tax of 1.5%. How<br>
much does he pay? A tax of 1.5% means he must pay 1.015 * 12.00.<br>
<br>
Set index of C scale at 1.015 on D scale. Move indicator to 12 on C<br>
scale and read the answer $12.18 on the D scale.<br>
<br>
A longer but more accurate way is to multiply 12 * .015 and add the<br>
result to $12.<br>
<br>
<br>
3. Unit Price.<br>
<br>
A motorist buys 17 gallons of gas at 19.5 cents per gallon. How much<br>
does he pay?<br>
<br>
Set index of C scale at 17 on D scale and move indicator to 19.5 on C<br>
scale and read the answer $3.32 on the D scale.<br>
<br>
<br>
4. Gasoline Mileage.<br>
<br>
An automobile goes 175 miles on 12 gallons of gas. What is the average<br>
gasoline consumption?<br>
<br>
Set indicator over 175 on D scale and move slider till 12 is under<br>
hair-line. Read the answer 14.6 miles per gallon on the D scale under<br>
the left-hand index of the C scale.<br>
<br>
<br>
5. Average Speed.<br>
<br>
A motorist makes a trip of 256 miles in 7.5 hours. What is his average<br>
speed?<br>
<br>
Set indicator over 256 on D scale. Move slider till 7.5 on the C scale<br>
is under the hair-line. Read the answer 34.2 miles per hour under the<br>
right-hand index of the C scale.<br>
<br>
<br>
6. Decimal Parts of an Inch.<br>
<br>
What is 5/16 of an inch expressed as decimal fraction?<br>
<br>
Set 16 on C scale over 5 on D scale and read the result .3125 inches on<br>
the D scale under the left-hand index of the C scale.<br>
<br>
<br>
7. Physics.<br>
<br>
A certain quantity of gas occupies 1200 cubic centimeters at a<br>
temperature of 15 degrees C and 740 millimeters pressure. What volume<br>
does it occupy at 0 degrees C and 760 millimeters pressure?<br>
<br>
Volume = 1200 * (740/760) * (273/288) = 1100 cubic cm.<br>
<br>
Set 760 on C scale over 12 on D scale. Move indicator to 740 on C scale.<br>
Move slider till 288 on C scale is under hair-line. Move indicator to<br>
273 on C scale. Read answer, 1110, under hair-line on D scale.<br>
<br>
<br>
8. Chemistry.<br>
<br>
How many grams of hydrogen are formed when 80 grams of zinc react with<br>
sufficient hydrochloric acid to dissolve the metal?<br>
<br>
(80 / X ) = ( 65.4 / 2.01)<br>
<br>
Set 65.4 on C scale over 2.01 on D scale.<br>
Read X = 2.46 grams under 80 on C scale.<br>
<br>
<br>
In conclusion, we want to impress upon those to whom the slide rule is a<br>
new method of doing their mathematical calculations, and also the<br>
experienced operator of a slide rule, that if they will form a habit of,<br>
and apply themselves to, using a slide rule at work, study, or during<br>
recreations, they will be well rewarded in the saving of time and<br>
energy. ALWAYS HAVE YOUR SLIDE RULE AND INSTRUCTION BOOK WITH YOU, the<br>
same as you would a fountain pen or pencil.<br>
<br>
The present day wonders of the twentieth century prove that there is no<br>
end to what an individual can accomplish--the same applies to the slide<br>
rule.<br>
<br>
You will find after practice that you will be able to do many<br>
specialized problems that are not outlined in this instruction book. It<br>
depends entirely upon your ability to do what we advocate and to be<br>
slide-rule conscious in all your mathematical problems.<br>
<br>
<br>
CONVERSION FACTORS<br>
<br>
1. Length<br>
<br>
1 mile = 5280 feet = 1760 yards<br>
<br>
1 inch = 2.54 centimeters<br>
<br>
1 meter = 39.37 inches<br>
<br>
<br>
2. Weight (or Mass)<br>
<br>
1 pound = 16 ounces = 0.4536 kilograms<br>
<br>
1 kilogram = 2.2 pounds<br>
<br>
1 long ton = 2240 pounds<br>
<br>
1 short ton = 2000 pounds<br>
<br>
<br>
3. Volume<br>
<br>
1 liquid quart = 0.945 litres<br>
<br>
1 litre = 1.06 liquid quarts<br>
<br>
1 U. S. gallon = 4 quarts = 231 cubic inches<br>
<br>
<br>
4. Angular Measure<br>
<br>
3.14 radians = PI radians = 180 degrees<br>
<br>
1 radian = 57.30 degrees<br>
<br>
<br>
5. Pressure<br>
<br>
760 millimeters of mercury = 14.7 pounds per square inch<br>
<br>
<br>
6. Power<br>
<br>
1 horse power = 550 foot pounds per second = 746 watts<br>
<br>
<br>
7. Miscellaneous<br>
<br>
60 miles per hour = 88 feet per second<br>
<br>
980 centimeters per second per second <br>
= 32.2 feet per second per second<br>
= acceleration of gravity.<br>
<br>
1 cubic foot of water weighs 62.4 pounds<br>
<br>
1 gallon of water weighs 8.34 pounds<br>
<br>
<br>
<br>
Printed in U. S. A.<br>
INSTRUCTIONS FOR USING A SLIDE RULE<br>
COPYRIGHTED BY W. STANLEY & CO.<br>
Commercial Trust Building, Philadelphia, Pa.<br>
<br>
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