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+The Project Gutenberg eBook of Instruction for Using a Slide Rule, by W. Stanley
+
+This eBook is for the use of anyone anywhere in the United States and
+most other parts of the world at no cost and with almost no restrictions
+whatsoever. You may copy it, give it away or re-use it under the terms
+of the Project Gutenberg License included with this eBook or online at
+www.gutenberg.org. If you are not located in the United States, you
+will have to check the laws of the country where you are located before
+using this eBook.
+
+Title: Instruction for Using a Slide Rule
+
+Author: W. Stanley
+
+Release Date: December 29, 2006 [eBook #20214]
+[Most recently updated: June 1, 2021]
+
+Language: English
+
+Character set encoding: UTF-8
+
+Produced by: Don Kostuch
+
+*** START OF THE PROJECT GUTENBERG EBOOK INSTRUCTION FOR USING A SLIDE RULE ***
+
+
+
+
+[Transcriber's Notes]
+
+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.
+
+[End Transcriber's Notes]
+
+
+
+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
+
+
+[Illustration: Two images of a slide rule.]
+
+
+
+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.
+
+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
+5:   85 * 2 = 170
+6:   45 * 35 = 1575
+7:   151 * 42 = 6342
+8:   6.5 * 15 = 97.5
+9:   .34 * .08 = .0272
+10:  75 * 26 = 1950
+11:  .00054 * 1.4 = .000756
+12:  11.1 * 2.7 = 29.97
+13:  1.01 * 54 = 54.5
+14:  3.14 * 25 = 78.5
+
+
+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:
+
+Example 15: (6.70 / 2.12) = 3.16
+
+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:
+
+Example
+16:    34 / 2    = 17
+17:    49 / 7    =  7
+18:   132 / 12   = 11
+19:   480 / 16   = 30
+20:  1.05 / 35   = .03
+21:  4.32 / 12   = .36
+22:  5.23 / 6.15 = .85
+23:  17.1 / 4.5  = 3.8
+24:  1895 / 6.06 = 313
+25:    45 / .017 = 2647
+
+
+THE CI SCALE
+
+If we divide one (1) 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:
+
+Example 26: 14 * (1/2) = 7
+
+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:
+
+Example 27: 4 * 4 = square( 4 ) = 16
+
+Set indicator over 4 on D scale. Read 16 on A scale under hair-line.
+
+Example 28: square( 25.4 )  = 646.0
+
+The decimal point must be placed by mental survey. We know that
+square( 25.4 ) must be a little larger than square( 25 ) = 625
+so that it must be 646.0.
+
+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:
+
+(a) 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.
+
+(b) 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.
+
+Example 29: square_root( 157 ) = 12.5
+
+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
+
+12 * 12 = 144, so that square_root(157) must be a little more than 12 or
+12.5.
+
+Example 30: square_root( .0037 ) = .0608
+
+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:
+
+square_root( .0037 ) = square_root( 37/10000 )
+                     = 1/100 square_root( 37 )
+
+The nearest perfect square to 37 is 6 * 6 = 36, so the answer should be
+a little more than 0.06 or .0608. All of what has been said about use of
+the A and D scales for squaring and extracting square root applies
+equally well to the B and C scales since they are identical to the A and
+D scales respectively.
+
+A number of examples follow for squaring and the extraction of square
+root.
+
+Example
+31: square( 2 ) = 4
+32: square( 15 ) = 225
+33: square( 26 )  = 676
+34: square( 19.65 ) = 386
+35: square_root( 64 ) = 8
+36: square_root( 6.4 ) = 2.53
+37: square_root( 498 ) = 22.5
+38: square_root( 2500 ) = 50
+39: square_root( .16 ) = .04
+40: square_root( .03 ) = .173
+
+
+CUBING AND CUBE ROOT
+
+If we take a number and multiply it by itself, and then multiply the
+result by the original number we get what is called the cube of the
+original number. This process is called cubing the number. The reverse
+process of finding the number which, when multiplied by itself and then
+by itself again, is equal to the given number, is called extracting the
+cube root of the given number. Thus, since 5 * 5 * 5 = 125, 125 is the
+cube of 5 and 5 is the cube root of 125.
+
+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.
+
+(a) 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.
+
+(b) 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:
+
+Example 41: cube_root( 185 ) = 5.70
+
+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.
+
+Example 42: cube_root( .034 ) = .324
+
+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:
+
+cube_root( .034 ) = cube_root( 34/1000  )
+                  = 1/10 cube_root( 34 )
+
+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:
+
+Example
+43: cube_root( 64 ) = 4
+44: cube_root( 8 ) = 2
+45: cube_root( 343 ) = 7
+46: cube_root( .000715 ) = .0894
+47: cube_root( .00715 ) = .193
+48: cube_root( .0715 ) = .415
+49: cube_root( .516 ) = .803
+50: cube_root( 27.8 ) = 3.03
+51: cube_root( 5.49 ) = 1.76
+52: cube_root( 87.1 ) = 4.43
+
+
+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.
+
+1. Multiplying several numbers together. For example, suppose it is
+desired to multiply 4 * 8 * 6. Place the right-hand index of the C scale
+over 4 on the D scale and set the indicator over 8 on the C scale. Now,
+leaving the indicator where it is, move the slider till the right-hand
+index is under the hairline. Now, leaving the slider where it is, move
+the indicator until it is over 6 on the C scale, and read the result,
+192, on the D scale. This may be continued indefinitely, and so as many
+numbers as desired may be multiplied together.
+
+Example 53: 2.32 * 154 * .0375 * .56 = 7.54
+
+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.
+
+
+
+
+*** END OF THE PROJECT GUTENBERG EBOOK INSTRUCTION FOR USING A SLIDE RULE ***
+
+Updated editions will replace the previous one--the old editions will
+be renamed.
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+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html>
+<head>
+  <meta content="text/html; charset=utf-8"
+ http-equiv="content-type">
+  <title>Instructions for using a Slide Rule</title>
+</head>
+<body>
+
+<div style='text-align:center; font-size:1.2em; font-weight:bold'>The Project Gutenberg eBook of Instruction for Using a Slide Rule, by W. Stanley</div>
+<div style='display:block; margin:1em 0'>
+This eBook is for the use of anyone anywhere in the United States and
+most other parts of the world at no cost and with almost no restrictions
+whatsoever. You may copy it, give it away or re-use it under the terms
+of the Project Gutenberg License included with this eBook or online
+at <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you
+are not located in the United States, you will have to check the laws of the
+country where you are located before using this eBook.
+</div>
+<div style='display:block; margin-top:1em; margin-bottom:1em; margin-left:2em; text-indent:-2em'>Title: Instruction for Using a Slide Rule</div>
+<div style='display:block; margin-top:1em; margin-bottom:1em; margin-left:2em; text-indent:-2em'>Author: W. Stanley</div>
+<div style='display:block; margin:1em 0'>Release Date: December 29, 2006 [eBook #20214]<br />
+[Most recently updated: June 1, 2021]</div>
+<div style='display:block; margin:1em 0'>Language: English</div>
+<div style='display:block; margin:1em 0'>Character set encoding: UTF-8</div>
+<div style='display:block; margin-left:2em; text-indent:-2em'>Produced by: Don Kostuch</div>
+<div style='margin-top:2em; margin-bottom:4em'>*** START OF THE PROJECT GUTENBERG EBOOK INSTRUCTION FOR USING A SLIDE RULE ***</div>
+
+
+<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>
+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&nbsp; <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 *&nbsp; 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 &amp; 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><img style="width: 894px; height: 199px;" alt=""
+ src="images/rule.jpg"><br>
+<br>
+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:&nbsp; 2 * 3 = 6<br>
+<br>
+<img style="width: 1166px; height: 388px;" alt=""
+ src="images/example01.jpg"><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:&nbsp;&nbsp; 2.12 * 3.16 = 6.70<br>
+<br>
+<img style="width: 1148px; height: 394px;" alt=""
+ src="images/example02.jpg"><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>
+<img style="width: 380px; height: 362px;" alt=""
+ src="images/example02B.jpg"><br>
+[This 6 inch rule uses fewer minor divisions.]<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>
+&nbsp; 2 + 1 major division + 1 minor division = 2 + 0.1 + 0.02 = 2.12.<br>
+<br>
+<img style="width: 568px; height: 368px;" alt=""
+ src="images/example02C.jpg"><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:&nbsp; 2.12 * 7.35 = 15.6<br>
+<br>
+<img style="width: 970px; height: 408px;" alt=""
+ src="images/example03A.jpg"><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>
+<code style="font-weight: bold;">a:&nbsp; &nbsp; 2.12 &nbsp;&nbsp; *
+&nbsp; 7.35 &nbsp; =&nbsp;&nbsp;&nbsp; 15.6<br>
+b:&nbsp;&nbsp; 21.2&nbsp;&nbsp;&nbsp;&nbsp; * &nbsp; 7.35 &nbsp;
+=&nbsp;&nbsp; 156.0<br>
+c:&nbsp; 212&nbsp;&nbsp;&nbsp; &nbsp;&nbsp; *&nbsp; 73.5 &nbsp;&nbsp; =
+15600.<br>
+d: &nbsp;&nbsp; 2.12&nbsp;&nbsp;&nbsp; * &nbsp;&nbsp; .0735
+=&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; .156<br>
+e: &nbsp;&nbsp;&nbsp; .00212 * 735&nbsp; &nbsp; &nbsp;
+=&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; .0156</code><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>
+<img style="width: 1076px; height: 392px;" alt=""
+ src="images/example02D.jpg"><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>
+<br>
+4:&nbsp;&nbsp; 20 * 3 = 60<br>
+<img style="width: 1038px; height: 390px;" alt=""
+ src="images/example04.jpg"><br>
+<br>
+5:&nbsp;&nbsp; 85 * 2 = 170<br>
+<img style="width: 806px; height: 404px;" alt=""
+ src="images/example05.jpg"><br>
+<br>
+6:&nbsp;&nbsp; 45 * 35 = 1575<br>
+<img style="width: 1002px; height: 400px;" alt=""
+ src="images/example06.jpg"><br>
+<br>
+7:&nbsp;&nbsp; 151 * 42 = 6342<br>
+<img style="width: 1166px; height: 388px;" alt=""
+ src="images/example07.jpg"><br>
+<br>
+8:&nbsp;&nbsp; 6.5 * 15 = 97.5<br>
+<img style="width: 1085px; height: 288px;" alt=""
+ src="images/example08.jpg"><br>
+<br>
+9:&nbsp;&nbsp; .34 * .08 = .0272<br>
+<img style="width: 1092px; height: 398px;" alt=""
+ src="images/example09.jpg"><br>
+<br>
+10:&nbsp; 75 * 26 = 1950<br>
+<img style="width: 1082px; height: 384px;" alt=""
+ src="images/example10.jpg"><br>
+<br>
+11:&nbsp; .00054 * 1.4 = .000756<br>
+<img style="width: 1067px; height: 296px;" alt=""
+ src="images/example11.jpg"><br>
+<br>
+12:&nbsp; 11.1 * 2.7 = 29.97<br>
+<img style="width: 1002px; height: 380px;" alt=""
+ src="images/example12.jpg"><br>
+<br>
+13:&nbsp; 1.01 * 54 = 54.5<br>
+<img style="width: 1051px; height: 312px;" alt=""
+ src="images/example13.jpg"><br>
+<br>
+14:&nbsp; 3.14 * 25 = 78.5<br>
+<img style="width: 932px; height: 386px;" alt=""
+ src="images/example14.jpg"><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>
+<img style="width: 946px; height: 394px;" alt=""
+ src="images/example15.jpg"><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:&nbsp;&nbsp; 34 / 2 = 17<br>
+<img style="width: 778px; height: 396px;" alt=""
+ src="images/example16.jpg"><br>
+<br>
+17:&nbsp;&nbsp; 49 / 7 = 7<br>
+<img style="width: 638px; height: 388px;" alt=""
+ src="images/example17.jpg"><br>
+<br>
+18:&nbsp; 132 / 12 = 11<br>
+<img style="width: 496px; height: 376px;" alt=""
+ src="images/example18.jpg"><br>
+<br>
+19:&nbsp; 480 / 16 = 30<br>
+<img style="width: 636px; height: 390px;" alt=""
+ src="images/example19.jpg"><br>
+<br>
+20: 1.05 / 35 = .03<br>
+<img style="width: 922px; height: 384px;" alt=""
+ src="images/example20.jpg"><br>
+<br>
+21: 4.32 / 12 = .36<br>
+<img style="width: 648px; height: 388px;" alt=""
+ src="images/example21.jpg"><br>
+<br>
+22: 5.23 / 6.15 = .85<br>
+<img style="width: 744px; height: 396px;" alt=""
+ src="images/example22.jpg"><br>
+<br>
+23: 17.1 / 4.5 = 3.8<br>
+<img style="width: 730px; height: 390px;" alt=""
+ src="images/example23.jpg"><br>
+<br>
+24: 1895 / 6.06 = 313<br>
+<img style="width: 598px; height: 382px;" alt=""
+ src="images/example24.jpg"><br>
+<br>
+25:&nbsp;&nbsp; 45 /.017 = 2647<br>
+<img style="width: 710px; height: 396px;" alt=""
+ src="images/example25.jpg"><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>
+<img style="width: 1013px; height: 323px;" alt=""
+ src="images/example26.jpg"><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 16 TO 25 OVER<br>
+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>
+<img style="width: 1160px; height: 374px;" alt=""
+ src="images/example27.jpg"><br>
+<br>
+Set indicator over 4 on D scale. Read 16 on A scale under hair-line.<br>
+<br>
+Example 28: square( 25.4 )&nbsp; = 646.0<br>
+<img style="width: 398px; height: 394px;" alt=""
+ src="images/example28.jpg"><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>
+<img style="width: 496px; height: 378px;" alt=""
+ src="images/example29.jpg"><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 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>
+<img style="width: 904px; height: 398px;" alt=""
+ src="images/example30.jpg"><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>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+= 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>
+<img style="width: 688px; height: 380px;" alt=""
+ src="images/example31.jpg"><br>
+<br>
+32: square( 15 ) = 225<br>
+<img style="width: 588px; height: 384px;" alt=""
+ src="images/example32.jpg"><br>
+<br>
+33: square( 26 )&nbsp; = 676<br>
+<img style="width: 844px; height: 374px;" alt=""
+ src="images/example33.jpg"><br>
+<br>
+34: square( 19.65 ) = 386<br>
+<img style="width: 742px; height: 380px;" alt=""
+ src="images/example34.jpg"><br>
+<br>
+35: square_root( 64 ) = 8<br>
+<img style="width: 552px; height: 366px;" alt=""
+ src="images/example35.jpg"><br>
+<br>
+36: square_root( 6.4 ) = 2.53<br>
+<img style="width: 824px; height: 386px;" alt=""
+ src="images/example36.jpg"><br>
+<br>
+37: square_root( 498 ) = 22.5<br>
+<img style="width: 746px; height: 388px;" alt=""
+ src="images/example37.jpg"><br>
+<br>
+38: square_root( 2500 ) = 50<br>
+<img style="width: 698px; height: 380px;" alt=""
+ src="images/example38.jpg"><br>
+<br>
+39: square_root( .16 ) = .04<br>
+<img style="width: 834px; height: 392px;" alt=""
+ src="images/example39.jpg"><br>
+<br>
+40: square_root( .03 ) = .173<br>
+<img style="width: 658px; height: 398px;" alt=""
+ src="images/example40.jpg"><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>
+<img style="width: 602px; height: 384px;" alt=""
+ src="images/example41.jpg"><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>
+<img style="width: 978px; height: 384px;" alt=""
+ src="images/example42.jpg"><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&nbsp; )<br>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+= 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>
+<img style="width: 842px; height: 396px;" alt=""
+ src="images/example43.jpg"><br>
+<br>
+44: cube_root( 8 ) = 2<br>
+<img style="width: 672px; height: 384px;" alt=""
+ src="images/example44.jpg"><br>
+<br>
+45: cube_root( 343 ) = 7<br>
+<img style="width: 582px; height: 382px;" alt=""
+ src="images/example45.jpg"><br>
+<br>
+46: cube_root( .000715 ) = .0894<br>
+<img style="width: 504px; height: 380px;" alt=""
+ src="images/example46.jpg"><br>
+<br>
+47: cube_root( .00715 ) = .193<br>
+<img style="width: 664px; height: 400px;" alt=""
+ src="images/example47.jpg"><br>
+<br>
+48: cube_root( .0715 ) = .415<br>
+<img style="width: 752px; height: 388px;" alt=""
+ src="images/example48.jpg"><br>
+<br>
+49: cube_root( .516 ) = .803<br>
+<img style="width: 500px; height: 384px;" alt=""
+ src="images/example49.jpg"><br>
+<br>
+50: cube_root( 27.8 ) = 3.03<br>
+<img style="width: 944px; height: 390px;" alt=""
+ src="images/example50.jpg"><br>
+<br>
+51: cube_root( 5.49 ) = 1.76<br>
+<img style="width: 596px; height: 374px;" alt=""
+ src="images/example51.jpg"><br>
+<br>
+52: cube_root( 87.1 ) = 4.43<br>
+<img style="width: 766px; height: 376px;" alt=""
+ src="images/example52.jpg"><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>
+4 to the 3/2 power is 8<br>
+8 to the 2/3 power is 4.<br>
+<img style="width: 694px; height: 380px;" alt=""
+ src="images/example52B.jpg"><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>
+<img style="width: 934px; height: 162px;" alt=""
+ src="images/example53A.jpg"><br>
+<img style="width: 968px; height: 158px;" alt=""
+ src="images/example53B.jpg"><br>
+<img style="width: 786px; height: 163px;" alt=""
+ src="images/example53C.jpg"><br>
+<br>
+2. Multiplication and division.<br>
+Suppose we wish to do the following example:<br>
+<br>
+Example 54:&nbsp; (4 * 15) / 2.5&nbsp; = 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: <br>
+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) *&nbsp; square(8.1)<br>
+&nbsp;&nbsp;&nbsp;&nbsp; = .7854 * square(8.1)<br>
+&nbsp;&nbsp;&nbsp;&nbsp; = 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>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 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:&nbsp;&nbsp; 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 X 0.9 X 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 X (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 <br>
+BOOK WITH YOU, the 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 </big><big>per second <br>
+</big><big>= 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 &amp; CO.<br>
+Commercial Trust Building, Philadelphia, Pa.<br>
+<br>
+</big>
+
+<div style='display:block; margin-top:4em'>*** END OF THE PROJECT GUTENBERG EBOOK INSTRUCTION FOR USING A SLIDE RULE ***</div>
+<div style='text-align:left'>
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+Project Gutenberg (https://www.gutenberg.org) public repository for
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+Project Gutenberg's Instruction for Using a Slide Rule, by W. Stanley
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
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+Title: Instruction for Using a Slide Rule
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+Author: W. Stanley
+
+Release Date: December 29, 2006 [EBook #20214]
+
+Language: English
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+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK INSTRUCTION FOR USING A SLIDE RULE ***
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+
+
+
+Produced by Don Kostuch
+
+
+
+
+[Transcriber's Notes]
+
+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 ).
+
+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.
+
+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.
+
+[End Transcriber's Notes]
+
+
+
+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
+
+
+[Illustration: Two images of a slide rule.]
+
+
+
+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.
+
+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
+5:   85 * 2 = 170
+6:   45 * 35 = 1575
+7:   151 * 42 = 6342
+8:   6.5 * 15 = 97.5
+9:   .34 * .08 = .0272
+10:  75 * 26 = 1950
+11:  .00054 * 1.4 = .000756
+12:  11.1 * 2.7 = 29.97
+13:  1.01 * 54 = 54.5
+14:  3.14 * 25 = 78.5
+
+
+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:
+
+Example 15: (6.70 / 2.12) = 3.16
+
+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:
+
+Example
+16:    34 / 2    = 17
+17:    49 / 7    =  7
+18:   132 / 12   = 11
+19:   480 / 16   = 30
+20:  1.05 / 35   = .03
+21:  4.32 / 12   = .36
+22:  5.23 / 6.15 = .85
+23:  17.1 / 4.5  = 3.8
+24:  1895 / 6.06 = 313
+25:    45 / .017 = 2647
+
+
+THE CI SCALE
+
+If we divide one (1) 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:
+
+Example 26: 14 * (1/2) = 7
+
+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:
+
+Example 27: 4 * 4 = square( 4 ) = 16
+
+Set indicator over 4 on D scale. Read 16 on A scale under hair-line.
+
+Example 28: square( 25.4 )  = 646.0
+
+The decimal point must be placed by mental survey. We know that
+square( 25.4 ) must be a little larger than square( 25 ) = 625
+so that it must be 646.0.
+
+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:
+
+(a) 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.
+
+(b) 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.
+
+Example 29: square_root( 157 ) = 12.5
+
+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
+
+12 * 12 = 144, so that square_root(157) must be a little more than 12 or
+12.5.
+
+Example 30: square_root( .0037 ) = .0608
+
+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:
+
+square_root( .0037 ) = square_root( 37/10000 )
+                     = 1/100 square_root( 37 )
+
+The nearest perfect square to 37 is 6 * 6 = 36, so the answer should be
+a little more than 0.06 or .0608. All of what has been said about use of
+the A and D scales for squaring and extracting square root applies
+equally well to the B and C scales since they are identical to the A and
+D scales respectively.
+
+A number of examples follow for squaring and the extraction of square
+root.
+
+Example
+31: square( 2 ) = 4
+32: square( 15 ) = 225
+33: square( 26 )  = 676
+34: square( 19.65 ) = 386
+35: square_root( 64 ) = 8
+36: square_root( 6.4 ) = 2.53
+37: square_root( 498 ) = 22.5
+38: square_root( 2500 ) = 50
+39: square_root( .16 ) = .04
+40: square_root( .03 ) = .173
+
+
+CUBING AND CUBE ROOT
+
+If we take a number and multiply it by itself, and then multiply the
+result by the original number we get what is called the cube of the
+original number. This process is called cubing the number. The reverse
+process of finding the number which, when multiplied by itself and then
+by itself again, is equal to the given number, is called extracting the
+cube root of the given number. Thus, since 5 * 5 * 5 = 125, 125 is the
+cube of 5 and 5 is the cube root of 125.
+
+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.
+
+(a) 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.
+
+(b) 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:
+
+Example 41: cube_root( 185 ) = 5.70
+
+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.
+
+Example 42: cube_root( .034 ) = .324
+
+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:
+
+cube_root( .034 ) = cube_root( 34/1000  )
+                  = 1/10 cube_root( 34 )
+
+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:
+
+Example
+43: cube_root( 64 ) = 4
+44: cube_root( 8 ) = 2
+45: cube_root( 343 ) = 7
+46: cube_root( .000715 ) = .0894
+47: cube_root( .00715 ) = .193
+48: cube_root( .0715 ) = .415
+49: cube_root( .516 ) = .803
+50: cube_root( 27.8 ) = 3.03
+51: cube_root( 5.49 ) = 1.76
+52: cube_root( 87.1 ) = 4.43
+
+
+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.
+
+1. Multiplying several numbers together. For example, suppose it is
+desired to multiply 4 * 8 * 6. Place the right-hand index of the C scale
+over 4 on the D scale and set the indicator over 8 on the C scale. Now,
+leaving the indicator where it is, move the slider till the right-hand
+index is under the hairline. Now, leaving the slider where it is, move
+the indicator until it is over 6 on the C scale, and read the result,
+192, on the D scale. This may be continued indefinitely, and so as many
+numbers as desired may be multiplied together.
+
+Example 53: 2.32 * 154 * .0375 * .56 = 7.54
+
+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.
+
+
+
+
+
+End of Project Gutenberg's Instruction for Using a Slide Rule, by W. Stanley
+
+*** END OF THIS PROJECT GUTENBERG EBOOK INSTRUCTION FOR USING A SLIDE RULE ***
+
+***** This file should be named 20214.txt or 20214.zip *****
+This and all associated files of various formats will be found in:
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diff --git a/old/20214.zip b/old/20214.zip
new file mode 100644
index 0000000..85c2639
--- /dev/null
+++ b/old/20214.zip
diff --git a/old/sliderule2.html b/old/sliderule2.html
new file mode 100644
index 0000000..a8d390b
--- /dev/null
+++ b/old/sliderule2.html
@@ -0,0 +1,734 @@
+<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html>
+<head>
+  <meta content="text/html; charset=ISO-8859-1"
+ http-equiv="content-type">
+  <title>Instructions for using a Slide Rule</title>
+</head>
+<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&nbsp; <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 *&nbsp; 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 &amp; 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:&nbsp; 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:&nbsp;&nbsp; 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>
+&nbsp; 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:&nbsp; 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--&nbsp;&nbsp; 2.12 * 7.35&nbsp; =&nbsp;&nbsp;&nbsp; 15.6<br>
+b--&nbsp;&nbsp; 21.2 * 7.35&nbsp; =&nbsp;&nbsp; 156.0<br>
+c--&nbsp;&nbsp;&nbsp; 212 * 73.5&nbsp; = 15600.<br>
+d--&nbsp;&nbsp; 2.12 * .0735 =&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; .156<br>
+e-- .00212 * 735&nbsp;&nbsp; =&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; .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:&nbsp;&nbsp; 20 * 3 = 60<br>
+5:&nbsp;&nbsp; 85 * 2 = 170<br>
+6:&nbsp;&nbsp; 45 * 35 = 1575<br>
+7:&nbsp;&nbsp; 151 * 42 = 6342<br>
+8:&nbsp;&nbsp; 6.5 * 15 = 97.5<br>
+9:&nbsp;&nbsp; .34 * .08 = .0272<br>
+10:&nbsp; 75 * 26 = 1950<br>
+11:&nbsp; .00054 * 1.4 = .000756<br>
+12:&nbsp; 11.1 * 2.7 = 29.97<br>
+13:&nbsp; 1.01 * 54 = 54.5<br>
+14:&nbsp; 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:&nbsp;&nbsp; 34 / 2 = 17<br>
+17:&nbsp;&nbsp; 49 / 7 = 7<br>
+18:&nbsp; 132 / 12 = 11<br>
+19:&nbsp; 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:&nbsp;&nbsp; 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 )&nbsp; = 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>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+= 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 )&nbsp; = 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&nbsp; )<br>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+= 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:&nbsp; (4 * 15) / 2.5&nbsp; = 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>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 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) *&nbsp; square(8.1)<br>
+&nbsp;&nbsp;&nbsp;&nbsp; = .7854 * square(8.1)<br>
+&nbsp;&nbsp;&nbsp;&nbsp; = 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>
+&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 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:&nbsp;&nbsp; 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 &amp; CO.<br>
+Commercial Trust Building, Philadelphia, Pa.<br>
+<br>
+</big>
+</body>
+</html>