Instruction for Using a Slide Rule

by W. Stanley

2. Multiplication and division.
Suppose we wish to do the following example:
Example 54: (4 * 15) / 2.5 = 24
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:
Example 55: (30/7.5) * (2/4) * (4.5/5) * (1.5/3) = .9
First set indicator over 30 on the D scale and move slider until 7.5 on
the C scale comes under the hairline. The intermediate result, 4,
appears under the right-hand index of the C scale. We do not need to
write it down but merely note it by moving the indicator until the
hair-line is over the right-hand index of the C scale. Now we want to
multiply this result by 2, the next factor in the numerator. Since two
is out beyond the body of the rule, transfer the slider till the other
(left-hand) index of the C scale is under the hair-line, and then move
the indicator to 2 on the C scale. Thus, successive division and
multiplication is continued until all the factors have been used. The
order in which the factors are taken does not affect the result. With a
little practice you will learn to take them in the order which will
require the fewest settings. The following examples are for practice:
Example 56: (6/3.5) * (4/5) * (3.5/2.4) * (2.8/7) = .8
Example 57: 352 * (273/254) * (760/768) = 374
An alternative method of doing these examples is to proceed exactly as
though you were multiplying all the factors together, except that
whenever you come to a number in the denominator you use the CI scale
instead of the C scale. The reader is advised to practice both methods
and use whichever one he likes best.
3. The area of a circle. The area of a circle is found by multiplying
3.1416=PI by the square of the radius or by one-quarter the square of
the diameter
Formula:
A = PI * square( R )
A = PI * (square( D ) / 4 )
Example 58: The radius of a circle is 0.25 inches; find its area.
Area = PI * square(0.25) = 0.196 square inches.
Set left-hand index of C scale over 0.25 on D scale. square(0.25) now
appears above the left-hand index of the B scale. This can be multiplied
by PI by moving the indicator to PI on the B scale and reading the
answer .196 on the A scale. This is an example where it is convenient to
multiply with the A and B scales.
Example 59: The diameter of a circle is 8.1 feet. What is its area?
Area = (PI / 4) * square(8.1)
= .7854 * square(8.1)
= 51.7 sq. inches.
Set right-hand index of the C scale over 8.1 on the D scale. Move the
indicator till hair-line is over .7854 (the special long mark near 8) at
the right hand of the B scale. Read the answer under the hair-line on
the A scale. Another way of finding the area of a circle is to set 7854
on the B scale to one of the indices of the A scale, and read the area
from the B scale directly above the given diameter on the D scale.
4. The circumference of a circle. Set the index of the B scale to the
diameter and read the answer on the A scale opposite PI on the B scale
Formula: C = PI * D
C = 2 * PI * R
Example 60: The diameter of a circle is 1.54 inches, what is its
circumference?
Set the left-hand index of the B scale to 1.54 on the A scale. Read the
circumference 4.85 inches above PI on the B scale.
EXAMPLES FOR PRACTICE
61: What is the area of a circle 32-1/2 inches in diameter?
Answer 830 sq. inches
62: What is the area of a circle 24 inches in diameter?
Answer 452 sq. inches
63: What is the circumference of a circle whose diameter is 95 feet?
Answer 298 ft.
64: What is the circumference of a circle whose diameter is 3.65 inches?
Answer 11.5 inches
5. Ratio and Proportion.
Example 65: 3 : 7 : : 4 : X
or
(3/7) = (4/x)
Find X
Set 3 on C scale over 7 on D scale. Read X on D scale under 4 on C
scale. In fact, any number on the C scale is to the number directly
under it on the D scale as 3 is to 7.
PRACTICAL PROBLEMS SOLVED BY SLIDE RULE
1. Discount.
A firm buys a typewriter with a list price of $150, subject to a
discount of 20% and 10%. How much does it pay?
A discount of 20% means 0.8 of the list price, and 10% more means
0.8 X 0.9 X 150 = 108.
To do this on the slide rule, put the index of the C scale opposite 8 on
the D scale and move the indicator to 9 on the C scale. Then move the
slider till the right-hand index of the C scale is under the hairline.
Now, move the indicator to 150 on the C scale and read the answer $108
on the D scale. Notice that in this, as in many practical problems,
there is no question about where the decimal point should go.
2. Sales Tax.
A man buys an article worth $12 and he must pay a sales tax of 1.5%. How
much does he pay? A tax of 1.5% means he must pay 1.015 * 12.00.
Set index of C scale at 1.015 on D scale. Move indicator to 12 on C
scale and read the answer $12.18 on the D scale.
A longer but more accurate way is to multiply 12 * .015 and add the
result to $12.
3. Unit Price.
A motorist buys 17 gallons of gas at 19.5 cents per gallon. How much
does he pay?
Set index of C scale at 17 on D scale and move indicator to 19.5 on C
scale and read the answer $3.32 on the D scale.
4. Gasoline Mileage.
An automobile goes 175 miles on 12 gallons of gas. What is the average
gasoline consumption?
Set indicator over 175 on D scale and move slider till 12 is under
hair-line. Read the answer 14.6 miles per gallon on the D scale under
the left-hand index of the C scale.
5. Average Speed.
A motorist makes a trip of 256 miles in 7.5 hours. What is his average
speed?
Set indicator over 256 on D scale. Move slider till 7.5 on the C scale
is under the hair-line. Read the answer 34.2 miles per hour under the
right-hand index of the C scale.
6. Decimal Parts of an Inch.
What is 5/16 of an inch expressed as decimal fraction?
Set 16 on C scale over 5 on D scale and read the result .3125 inches on
the D scale under the left-hand index of the C scale.
7. Physics.
A certain quantity of gas occupies 1200 cubic centimeters at a
temperature of 15 degrees C and 740 millimeters pressure. What volume
does it occupy at 0 degrees C and 760 millimeters pressure?
Volume = 1200 X (740/760) * (273/288) = 1100 cubic cm.
Set 760 on C scale over 12 on D scale. Move indicator to 740 on C scale.
Move slider till 288 on C scale is under hair-line. Move indicator to
273 on C scale. Read answer, 1110, under hair-line on D scale.
8. Chemistry.
How many grams of hydrogen are formed when 80 grams of zinc react with
sufficient hydrochloric acid to dissolve the metal?
(80 / X ) = ( 65.4 / 2.01)
Set 65.4 on C scale over 2.01 on D scale.
Read X = 2.46 grams under 80 on C scale.
In conclusion, we want to impress upon those to whom the slide rule is a
new method of doing their mathematical calculations, and also the
experienced operator of a slide rule, that if they will form a habit of,
and apply themselves to, using a slide rule at work, study, or during
recreations, they will be well rewarded in the saving of time and
energy. ALWAYS HAVE YOUR SLIDE RULE AND INSTRUCTION
BOOK WITH YOU, the same as you would a fountain pen or pencil.
The present day wonders of the twentieth century prove that there is no
end to what an individual can accomplish--the same applies to the slide
rule.
You will find after practice that you will be able to do many
specialized problems that are not outlined in this instruction book. It
depends entirely upon your ability to do what we advocate and to be
slide-rule conscious in all your mathematical problems.
CONVERSION FACTORS
1. Length
1 mile = 5280 feet =1760 yards
1 inch = 2.54 centimeters
1 meter = 39.37 inches
2. Weight (or Mass)
1 pound = 16 ounces = 0.4536 kilograms
1 kilogram = 2.2 pounds
1 long ton = 2240 pounds
1 short ton = 2000 pounds
3. Volume
1 liquid quart = 0.945 litres
1 litre = 1.06 liquid quarts
1 U. S. gallon = 4 quarts = 231 cubic inches
4. Angular Measure
3.14 radians = PI radians = 180 degrees
1 radian = 57.30 degrees
5. Pressure
760 millimeters of mercury = 14.7 pounds per square inch
6. Power
1 horse power = 550 foot pounds per second = 746 watts
7. Miscellaneous
60 miles per hour = 88 feet per second
980 centimeters per second

per second

= 32.2 feet per second per second
= acceleration of gravity.
1 cubic foot of water weighs 62.4 pounds
1 gallon of water weighs 8.34 pounds
Printed in U. S. A.
INSTRUCTIONS FOR USING A SLIDE RULE
COPYRIGHTED BY W. STANLEY & CO.
Commercial Trust Building, Philadelphia, Pa.