diff options
| author | Roger Frank <rfrank@pglaf.org> | 2025-10-15 01:19:54 -0700 |
|---|---|---|
| committer | Roger Frank <rfrank@pglaf.org> | 2025-10-15 01:19:54 -0700 |
| commit | 355e0032620ad931e7edba139564f1d51858f79a (patch) | |
| tree | df9ce171ce677112284d7cfd1253345980c25733 /old | |
Diffstat (limited to 'old')
| -rw-r--r-- | old/20214-doc.doc | bin | 0 -> 1930752 bytes | |||
| -rw-r--r-- | old/20214-doc.zip | bin | 0 -> 1827739 bytes | |||
| -rw-r--r-- | old/20214.txt | 1113 | ||||
| -rw-r--r-- | old/20214.zip | bin | 0 -> 16378 bytes | |||
| -rw-r--r-- | old/sliderule2.html | 734 |
5 files changed, 1847 insertions, 0 deletions
diff --git a/old/20214-doc.doc b/old/20214-doc.doc Binary files differnew file mode 100644 index 0000000..b680667 --- /dev/null +++ b/old/20214-doc.doc diff --git a/old/20214-doc.zip b/old/20214-doc.zip Binary files differnew file mode 100644 index 0000000..8a7eedf --- /dev/null +++ b/old/20214-doc.zip diff --git a/old/20214.txt b/old/20214.txt new file mode 100644 index 0000000..64359fa --- /dev/null +++ b/old/20214.txt @@ -0,0 +1,1113 @@ +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 +with this eBook or online at www.gutenberg.org + + +Title: Instruction for Using a Slide Rule + +Author: W. Stanley + +Release Date: December 29, 2006 [EBook #20214] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK INSTRUCTION FOR USING A SLIDE RULE *** + + + + +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: + http://www.gutenberg.org/2/0/2/1/20214/ + +Produced by Don Kostuch + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +http://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +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 +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH F3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need, is critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at http://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +http://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at http://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit http://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including checks, online payments and credit card donations. +To donate, please visit: http://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart is the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + http://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. diff --git a/old/20214.zip b/old/20214.zip Binary files differnew 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 <br> +1.23E3 means multiply 1.23 by 10 to the power 3.<br> +9.3E-5 means multiply 9.3 by 0.1 to the power 5 or 10 to the power -5.<br> +The computation is thus<br> +1.23 * 9.3 * 1E3 * 1E-5<br> +The exponents are simply added.<br> +1.23 * 9.3 * 1E-2 =<br> +11.4 * 1E-2 =<br> +.114<br> +<br> +When taking roots, divide the exponent by the root. <br> +The square root of 1E6 is 1E3<br> +The cube root of 1E12 is 1E4.<br> +<br> +When taking powers, multiply the exponent by the power.<br> +The cube of 1E5 is 1E15.<br> +<br> +[End Transcriber's Notes]<br> +<br> +<br> +INSTRUCTIONS<br> +for using a<br> +SLIDE<br> +RULE<br> +SAVE TIME!<br> +DO THE FOLLOWING INSTANTLY WITHOUT PAPER AND PENCIL<br> +MULTIPLICATION<br> +DIVISION<br> +RECIPROCAL VALUES<br> +SQUARES & CUBES<br> +EXTRACTION OF SQUARE ROOT<br> +EXTRACTION OF CUBE ROOT<br> +DIAMETER OR AREA OF CIRCLE<br> +<br> +<img style="width: 701px; height: 420px;" alt="" src="images/01Pic.jpg"><br> +<br> +<br> +<br> +INSTRUCTIONS FOR USING A SLIDE RULE<br> +<br> +The slide rule is a device for easily and quickly multiplying, dividing<br> +and extracting square root and cube root. It will also perform any<br> +combination of these processes. On this account, it is found extremely<br> +useful by students and teachers in schools and colleges, by engineers,<br> +architects, draftsmen, surveyors, chemists, and many others. Accountants<br> +and clerks find it very helpful when approximate calculations must be<br> +made rapidly. The operation of a slide rule is extremely easy, and it is<br> +well worth while for anyone who is called upon to do much numerical<br> +calculation to learn to use one. It is the purpose of this manual to<br> +explain the operation in such a way that a person who has never before<br> +used a slide rule may teach himself to do so.<br> +<br> +</big><big> +DESCRIPTION OF SLIDE RULE<br> +<br> +</big><big>The slide rule consists of three parts (see figure 1). B is +the body of<br> +the rule and carries three scales marked A, D and K. S is the slider<br> +which moves relative to the body and also carries three scales marked B,<br> +CI and C. R is the runner or indicator and is marked in the center with<br> +a hair-line. The scales A and B are identical and are used in problems<br> +involving square root. Scales C and D are also identical and are used<br> +for multiplication and division. Scale K is for finding cube root. Scale<br> +CI, or C-inverse, is like scale C except that it is laid off from right<br> +to left instead of from left to right. It is useful in problems<br> +involving reciprocals.<br> +<br> +<br> +MULTIPLICATION<br> +<br> +We will start with a very simple example:<br> +<br> +Example 1: 2 * 3 = 6<br> +<br> +To prove this on the slide rule, move the slider so that the 1 at the<br> +left-hand end of the C scale is directly over the large 2 on the D scale<br> +(see figure 1). Then move the runner till the hair-line is over 3 on the<br> +C scale. Read the answer, 6, on the D scale under the hair-line. Now,<br> +let us consider a more complicated example:<br> +<br> +Example 2: 2.12 * 3.16 = 6.70<br> +<br> +As before, set the 1 at the left-hand end of the C scale, which we will<br> +call the left-hand index of the C scale, over 2.12 on the D scale (See<br> +figure 2). The hair-line of the runner is now placed over 3.16 on the C<br> +scale and the answer, 6.70, read on the D scale.<br> +<br> +<br> +METHOD OF MAKING SETTINGS<br> +<br> +In order to understand just why 2.12 is set where it is (figure 2),<br> +notice that the interval from 2 to 3 is divided into 10 large or major<br> +divisions, each of which is, of course, equal to one-tenth (0.1) of the<br> +amount represented by the whole interval. The major divisions are in<br> +turn divided into 5 small or minor divisions, each of which is one-fifth<br> +or two-tenths (0.2) of the major division, that is 0.02 of the<br> +whole interval. Therefore, the index is set above<br> +<br> + 2 + 1 major division + 1 minor division = 2 + 0.1 + 0.02 = 2.12.<br> +<br> +In the same way we find 3.16 on the C scale. While we are on this<br> +subject, notice that in the interval from 1 to 2 the major divisions are<br> +marked with the small figures 1 to 9 and the minor divisions are 0.1 of<br> +the major divisions. In the intervals from 2 to 3 and 3 to 4 the minor<br> +divisions are 0.2 of the major divisions, and for the rest of the D (or<br> +C) scale, the minor divisions are 0.5 of the major divisions.<br> +<br> +Reading the setting from a slide rule is very much like reading<br> +measurements from a ruler. Imagine that the divisions between 2 and 3 on<br> +the D scale (figure 2) are those of a ruler divided into tenths of a<br> +foot, and each tenth of a foot divided in 5 parts 0.02 of a foot long.<br> +Then the distance from one on the left-hand end of the D scale (not<br> +shown in figure 2) to one on the left-hand end of the C scale would he<br> +2.12 feet. Of course, a foot rule is divided into parts of uniform<br> +length, while those on a slide rule get smaller toward the right-hand<br> +end, but this example may help to give an idea of the method of making<br> +and reading settings. Now consider another example.<br> +<br> +Example 3a: 2.12 * 7.35 = 15.6<br> +<br> +If we set the left-hand index of the C scale over 2.12 as in the last<br> +example, we find that 7.35 on the C scale falls out beyond the body of<br> +the rule. In a case like this, simply use the right-hand index of the C<br> +scale. If we set this over 2.12 on the D scale and move the runner to<br> +7.35 on the C scale we read the result 15.6 on the D scale under the<br> +hair-line.<br> +<br> +Now, the question immediately arises, why did we call the result 15.6<br> +and not 1.56? The answer is that the slide rule takes no account of<br> +decimal points. Thus, the settings would be identical for all of the<br> +following products:<br> +<br> +Example 3:<br> +a-- 2.12 * 7.35 = 15.6<br> +b-- 21.2 * 7.35 = 156.0<br> +c-- 212 * 73.5 = 15600.<br> +d-- 2.12 * .0735 = .156<br> +e-- .00212 * 735 = .0156<br> +<br> +The most convenient way to locate the decimal point is to make a mental<br> +multiplication using only the first digits in the given factors. Then<br> +place the decimal point in the slide rule result so that its value is<br> +nearest that of the mental multiplication. Thus, in example 3a above, we<br> +can multiply 2 by 7 in our heads and see immediately that the decimal<br> +point must be placed in the slide rule result 156 so that it becomes<br> +15.6 which is nearest to 14. In example 3b (20 * 7 = 140), so we must<br> +place the decimal point to give 156. The reader can readily verify the<br> +other examples in the same way.<br> +<br> +Since the product of a number by a second number is the same as the<br> +product of the second by the first, it makes no difference which of the<br> +two numbers is set first on the slide rule. Thus, an alternative way of<br> +working example 2 would be to set the left-hand index of the C scale<br> +over 3.16 on the D scale and move the runner to 2.12 on the C scale and<br> +read the answer under the hair-line on the D scale.<br> +<br> +The A and B scales are made up of two identical halves each of which is<br> +very similar to the C and D scales. Multiplication can also be carried<br> +out on either half of the A and B scales exactly as it is done on the C<br> +and D scales. However, since the A and B scales are only half as long as<br> +the C and D scales, the accuracy is not as good. It is sometimes<br> +convenient to multiply on the A and B scales in more complicated<br> +problems as we shall see later on.<br> +<br> +A group of examples follow which cover all the possible combination of<br> +settings which can arise in the multiplication of two numbers.<br> +<br> +Example<br> +4: 20 * 3 = 60<br> +5: 85 * 2 = 170<br> +6: 45 * 35 = 1575<br> +7: 151 * 42 = 6342<br> +8: 6.5 * 15 = 97.5<br> +9: .34 * .08 = .0272<br> +10: 75 * 26 = 1950<br> +11: .00054 * 1.4 = .000756<br> +12: 11.1 * 2.7 = 29.97<br> +13: 1.01 * 54 = 54.5<br> +14: 3.14 * 25 = 78.5<br> +<br> +<br> +DIVISION<br> +<br> +Since multiplication and division are inverse processes, division on a<br> +slide rule is done by making the same settings as for multiplication,<br> +but in reverse order. Suppose we have the example:<br> +<br> +Example 15: (6.70 / 2.12) = 3.16<br> +<br> +Set indicator over the dividend 6.70 on the D scale. Move the slider<br> +until the divisor 2.12 on the C scale is under the hair-line. Then read<br> +the result on the D scale under the left-hand index of the C scale. As<br> +in multiplication, the decimal point must be placed by a separate<br> +process. Make all the digits except the first in both dividend and<br> +divisor equal zero and mentally divide the resulting numbers. Place the<br> +decimal point in the slide rule result so that it is nearest to the<br> +mental result. In example 15, we mentally divide 6 by 2. Then we place<br> +the decimal point in the slide rule result 316 so that it is 3.16 which<br> +is nearest to 3.<br> +<br> +A group of examples for practice in division follow:<br> +<br> +Example<br> +16: 34 / 2 = 17<br> +17: 49 / 7 = 7<br> +18: 132 / 12 = 11<br> +19: 480 / 16 =30<br> +20: 1.05 / 35 =.03<br> +21: 4.32 / 12 =.36<br> +22: 5.23 / 6.15 =.85<br> +23: 17.1 / 4.5 = 3.8<br> +24: 1895 / 6.06 = 313<br> +25: 45 /.017 = 2647<br> +<br> +<br> +THE CI SCALE<br> +<br> +If we divide one (1) by any number the answer is called the reciprocal<br> +of the number. Thus, one-half is the reciprocal of two, one-quarter is<br> +the reciprocal of four. If we take any number, say 14, and multiply it<br> +by the reciprocal of another number, say 2, we get:<br> +<br> +Example 26: 14 * (1/2) = 7<br> +<br> +which is the same as 14 divided by two. This process can be carried out<br> +directly on the slide rule by use of the CI scale. Numbers on the CI<br> +scale are reciprocals of those on the C scale. Thus we see that 2 on the<br> +CI scale comes directly over 0.5 or 1/2 on the C scale. Similarly 4 on<br> +the CI scale comes over 0.25 or 1/4 on the C scale, and so on. To do<br> +example 26 by use of the CI scale, proceed exactly as if you were going<br> +to multiply in the usual manner except that you use the CI scale instead<br> +of the C scale. First set the left-hand index of the C scale over 14 on<br> +the D scale. Then move the indicator to 2 on the CI scale. Read the<br> +result, 7, on the D scale under the hair-line. This is really another<br> +way of dividing. THE READER IS ADVISED TO WORK EXAMPLES <br> +16 TO 25 OVER AGAIN BY USE OF THE CI SCALE.<br> +<br> +<br> +SQUARING AND SQUARE ROOT<br> +<br> +If we take a number and multiply it by itself we call the result the<br> +square of the number. The process is called squaring the number. If we<br> +find the number which, when multiplied by itself is equal to a given<br> +number, the former number is called the square root of the given number.<br> +The process is called extracting the square root of the number. Both<br> +these processes may be carried out on the A and D scales of a slide<br> +rule. For example:<br> +<br> +Example 27: 4 * 4 = square( 4 ) = 16<br> +<br> +Set indicator over 4 on D scale. Read 16 on A scale under hair-line.<br> +<br> +Example 28: square( 25.4 ) = 646.0<br> +<br> +The decimal point must be placed by mental survey. We know that <br> +square( 25.4 ) must be a little larger than square( 25 ) = 625 so that <br> +it +must be 646.0.<br> +<br> +To extract a square root, we set the indicator over the number on the A<br> +scale and read the result under the hair-line on the D scale. When we<br> +examine the A scale we see that there are two places where any given<br> +number may be set, so we must have some way of deciding in a given case<br> +which half of the A scale to use. The rule is as follows:<br> +<br> +(a) If the number is greater than one. For an odd number of digits to<br> +the left of the decimal point, use the left-hand half of the A scale.<br> +For an even number of digits to the left of the decimal point, use the<br> +right-hand half of the A scale.<br> +<br> +(b) If the number is less than one. For an odd number of zeros to the<br> +right of the decimal point before the first digit not a zero, use the<br> +left-hand half of the A scale. For none or any even number of zeros to<br> +the right of the decimal point before the first digit not a zero, use<br> +the right-hand half of the A scale.<br> +<br> +Example 29: square_root( 157 ) = 12.5<br> +<br> +Since we have an odd number of digits set indicator over 157 on<br> +left-hand half of A scale. Read 12.5 on the D scale under hair-line. To<br> +check the decimal point think of the perfect square nearest to 157. It<br> +is<br> +<br> +12 * 12 = 144, so that square_root(157) must be a little more than 12 or<br> +12.5.<br> +<br> +Example 30: square_root( .0037 ) = .0608<br> +<br> +In this number we have an even number of zeros to the right of the<br> +decimal point, so we must set the indicator over 37 on the right-hand<br> +half of the A scale. Read 608 under the hair-line on D scale. To place<br> +the decimal point write:<br> +<br> +square_root( .0037 ) = square_root( 37/10000 )<br> + += 1/100 square_root( 37 )<br> +<br> +The nearest perfect square to 37 is 6 * 6 = 36, so the answer should be<br> +a little more than 0.06 or .0608. All of what has been said about use of<br> +the A and D scales for squaring and extracting square root applies<br> +equally well to the B and C scales since they are identical to the A and<br> +D scales respectively.<br> +<br> +A number of examples follow for squaring and the extraction of square<br> +root.<br> +<br> +Example<br> +31: square( 2 ) = 4<br> +32: square( 15 ) = 225<br> +33: square( 26 ) = 676<br> +34: square( 19.65 ) = 386<br> +35: square_root( 64 ) = 8<br> +36: square_root( 6.4 ) = 2.53<br> +37: square_root( 498 ) = 22.5<br> +38: square_root( 2500 ) = 50<br> +39: square_root( .16 ) = .04<br> +40: square_root( .03 ) = .173<br> +<br> +<br> +CUBING AND CUBE ROOT<br> +<br> +If we take a number and multiply it by itself, and then multiply the<br> +result by the original number we get what is called the cube of the<br> +original number. This process is called cubing the number. The reverse<br> +process of finding the number which, when multiplied by itself and then<br> +by itself again, is equal to the given number, is called extracting the<br> +cube root of the given number. Thus, since 5 * 5 * 5 = 125, 125 is the<br> +cube of 5 and 5 is the cube root of 125.<br> +<br> +To find the cube of any number on the slide rule set the indicator over<br> +the number on the D scale and read the answer on the K scale under the<br> +hair-line. To find the cube root of any number set the indicator over<br> +the number on the K scale and read the answer on the D scale under the<br> +hair-line. Just as on the A scale, where there were two places where you<br> +could set a given number, on the K scale there are three places where a<br> +number may be set. To tell which of the three to use, we must make use<br> +of the following rule.<br> +<br> +(a) If the number is greater than one. For 1, 4, 7, 10, etc., digits to<br> +the left of the decimal point, use the left-hand third of the K scale.<br> +For 2, 5, 8, 11, etc., digits to the left of the decimal point, use the<br> +middle third of the K scale. For 3, 6, 9, 12, etc., digits to the left<br> +of the decimal point use the right-hand third of the K scale.<br> +<br> +(b) If the number is less than one. We now tell which scale to use by<br> +counting the number of zeros to the right of the decimal point before<br> +the first digit not zero. If there are 2, 5, 8, 11, etc., zeros, use the<br> +left-hand third of the K scale. If there are 1, 4, 7, 10, etc., zeros,<br> +then use the middle third of the K scale. If there are no zeros or 3, 6,<br> +9, 12, etc., zeros, then use the right-hand third of the K scale. For<br> +example:<br> +<br> +Example 41: cube_root( 185 ) = 5.70<br> +<br> +Since there are 3 digits in the given number, we set the indicator on<br> +185 in the right-hand third of the K scale, and read the result 570 on<br> +the D scale. We can place the decimal point by thinking of the nearest<br> +perfect cube, which is 125. Therefore, the decimal point must be placed<br> +so as to give 5.70, which is nearest to 5, the cube root of 125.<br> +<br> +Example 42: cube_root( .034 ) = .324<br> +<br> +Since there is one zero between the decimal point and the first digit<br> +not zero, we must set the indicator over 34 on the middle third of the K<br> +scale. We read the result 324 on the D scale. The decimal point may be<br> +placed as follows:<br> +<br> +cube_root( .034 ) = cube_root( 34/1000 )<br> + += 1/10 cube_root( 34 )<br> +<br> +The nearest perfect cube to 34 is 27, so our answer must be close to<br> +one-tenth of the cube root of 27 or nearly 0.3. Therefore, we must place<br> +the decimal point to give 0.324. A group of examples for practice in<br> +extraction of cube root follows:<br> +<br> +Example<br> +43: cube_root( 64 ) = 4<br> +44: cube_root( 8 ) = 2<br> +45: cube_root( 343 ) = 7<br> +46: cube_root( .000715 ) = .0894<br> +47: cube_root( .00715 ) = .193<br> +48: cube_root( .0715 ) = .415<br> +49: cube_root( .516 ) = .803<br> +50: cube_root( 27.8 ) = 3.03<br> +51: cube_root( 5.49 ) = 1.76<br> +52: cube_root( 87.1 ) = 4.43<br> +<br> +<br> +THE 1.5 AND 2/3 POWER<br> +<br> +If the indicator is set over a given number on the A scale, the number<br> +under the hair-line on the K scale is the 1.5 power of the given<br> +number. If the indicator is set over a given number on the K scale, the<br> +number under the hair-line on the A scale is the 2/3 power of the given<br> +number.<br> +<br> +<br> +COMBINATIONS OF PROCESSES<br> +<br> +A slide rule is especially useful where some combination of processes is<br> +necessary, like multiplying 3 numbers together and dividing by a third.<br> +Operations of this sort may be performed in such a way that the final<br> +answer is obtained immediately without finding intermediate results.<br> +<br> +1. Multiplying several numbers together. For example, suppose it is<br> +desired to multiply 4 * 8 * 6. Place the right-hand index of the C scale<br> +over 4 on the D scale and set the indicator over 8 on the C scale. Now,<br> +leaving the indicator where it is, move the slider till the right-hand<br> +index is under the hairline. Now, leaving the slider where it is, move<br> +the indicator until it is over 6 on the C scale, and read the result,<br> +192, on the D scale. This may be continued indefinitely, and so as many<br> +numbers as desired may be multiplied together.<br> +<br> +Example 53: 2.32 * 154 * .0375 * .56 = 7.54<br> +<br> +2. Multiplication and division.<br> +Suppose we wish to do the following example:<br> +<br> +Example 54: (4 * 15) / 2.5 = 24<br> +<br> +First divide 4 by 2.5. Set indicator over 4 on the D scale and move the<br> +slider until 2.5 is under the hair-line. The result of this division,<br> +1.6, appears under the left-hand index of the C scale. We do not need to<br> +write it down, however, but we can immediately move the indicator to 15<br> +on the C scale and read the final result 24 on the D scale under the<br> +hair-line. Let us consider a more complicated problem of the same type:<br> +<br> +Example 55: (30/7.5) * (2/4) * (4.5/5) * (1.5/3) = .9<br> +<br> +First set indicator over 30 on the D scale and move slider until 7.5 on<br> +the C scale comes under the hairline. The intermediate result, 4,<br> +appears under the right-hand index of the C scale. We do not need to<br> +write it down but merely note it by moving the indicator until the<br> +hair-line is over the right-hand index of the C scale. Now we want to<br> +multiply this result by 2, the next factor in the numerator. Since two<br> +is out beyond the body of the rule, transfer the slider till the other<br> +(left-hand) index of the C scale is under the hair-line, and then move<br> +the indicator to 2 on the C scale. Thus, successive division and<br> +multiplication is continued until all the factors have been used. The<br> +order in which the factors are taken does not affect the result. With a<br> +little practice you will learn to take them in the order which will<br> +require the fewest settings. The following examples are for practice:<br> +<br> +Example 56: (6/3.5) * (4/5) * (3.5/2.4) * (2.8/7) = .8<br> +<br> +Example 57: 352 * (273/254) * (760/768) = 374<br> +<br> +An alternative method of doing these examples is to proceed exactly as<br> +though you were multiplying all the factors together, except that<br> +whenever you come to a number in the denominator you use the CI scale<br> +instead of the C scale. The reader is advised to practice both methods<br> +and use whichever one he likes best.<br> +<br> +3. The area of a circle. The area of a circle is found by multiplying<br> +3.1416=PI by the square of the radius or by one-quarter the square of<br> +the diameter<br> +<br> +Formula: A = PI * square( R )<br> + A = PI * +(square( D ) / 4 )<br> +<br> +Example 58: The radius of a circle is 0.25 inches; find its area.<br> +<br> +Area = PI * square(0.25) = 0.196 square inches.<br> +<br> +Set left-hand index of C scale over 0.25 on D scale. square(0.25) now<br> +appears above the left-hand index of the B scale. This can be multiplied<br> +by PI by moving the indicator to PI on the B scale and reading the<br> +answer .196 on the A scale. This is an example where it is convenient to<br> +multiply with the A and B scales.<br> +<br> +Example 59: The diameter of a circle is 8.1 feet. What is its area?<br> +<br> +Area = (PI / 4) * square(8.1)<br> + = .7854 * square(8.1)<br> + = 51.7 sq. inches.<br> +<br> +Set right-hand index of the C scale over 8.1 on the D scale. Move the<br> +indicator till hair-line is over .7854 (the special long mark near 8) at<br> +the right hand of the B scale. Read the answer under the hair-line on<br> +the A scale. Another way of finding the area of a circle is to set 7854<br> +on the B scale to one of the indices of the A scale, and read the area<br> +from the B scale directly above the given diameter on the D scale.<br> +<br> +4. The circumference of a circle. Set the index of the B scale to the<br> +diameter and read the answer on the A scale opposite PI on the B scale<br> +<br> +Formula: C = PI * D<br> + C = 2 * PI * R<br> +<br> +Example 60: The diameter of a circle is 1.54 inches, what is its<br> +circumference?<br> +<br> +Set the left-hand index of the B scale to 1.54 on the A scale. Read the<br> +circumference 4.85 inches above PI on the B scale.<br> +<br> +EXAMPLES FOR PRACTICE<br> +<br> +61: What is the area of a circle 32-1/2 inches in diameter?<br> +Answer 830 sq. inches<br> +<br> +62: What is the area of a circle 24 inches in diameter?<br> +Answer 452 sq. inches<br> +<br> +63: What is the circumference of a circle whose diameter is 95 feet?<br> +Answer 298 ft.<br> +<br> +64: What is the circumference of a circle whose diameter is 3.65 inches?<br> +Answer 11.5 inches<br> +<br> +5. Ratio and Proportion.<br> +<br> +Example 65: 3 : 7 : : 4 : X<br> +or<br> +(3/7) = (4/x)<br> +Find X<br> +<br> +Set 3 on C scale over 7 on D scale. Read X on D scale under 4 on C<br> +scale. In fact, any number on the C scale is to the number directly<br> +under it on the D scale as 3 is to 7.<br> +<br> +<br> +PRACTICAL PROBLEMS SOLVED BY SLIDE RULE<br> +<br> +<br> +1. Discount.<br> +A firm buys a typewriter with a list price of $150, subject to a<br> +discount of 20% and 10%. How much does it pay?<br> +<br> +A discount of 20% means 0.8 of the list price, and 10% more means<br> +0.8 * 0.9 * 150 = 108.<br> +<br> +To do this on the slide rule, put the index of the C scale opposite 8 on<br> +the D scale and move the indicator to 9 on the C scale. Then move the<br> +slider till the right-hand index of the C scale is under the hairline.<br> +Now, move the indicator to 150 on the C scale and read the answer $108<br> +on the D scale. Notice that in this, as in many practical problems,<br> +there is no question about where the decimal point should go.<br> +<br> +<br> +2. Sales Tax.<br> +<br> +A man buys an article worth $12 and he must pay a sales tax of 1.5%. How<br> +much does he pay? A tax of 1.5% means he must pay 1.015 * 12.00.<br> +<br> +Set index of C scale at 1.015 on D scale. Move indicator to 12 on C<br> +scale and read the answer $12.18 on the D scale.<br> +<br> +A longer but more accurate way is to multiply 12 * .015 and add the<br> +result to $12.<br> +<br> +<br> +3. Unit Price.<br> +<br> +A motorist buys 17 gallons of gas at 19.5 cents per gallon. How much<br> +does he pay?<br> +<br> +Set index of C scale at 17 on D scale and move indicator to 19.5 on C<br> +scale and read the answer $3.32 on the D scale.<br> +<br> +<br> +4. Gasoline Mileage.<br> +<br> +An automobile goes 175 miles on 12 gallons of gas. What is the average<br> +gasoline consumption?<br> +<br> +Set indicator over 175 on D scale and move slider till 12 is under<br> +hair-line. Read the answer 14.6 miles per gallon on the D scale under<br> +the left-hand index of the C scale.<br> +<br> +<br> +5. Average Speed.<br> +<br> +A motorist makes a trip of 256 miles in 7.5 hours. What is his average<br> +speed?<br> +<br> +Set indicator over 256 on D scale. Move slider till 7.5 on the C scale<br> +is under the hair-line. Read the answer 34.2 miles per hour under the<br> +right-hand index of the C scale.<br> +<br> +<br> +6. Decimal Parts of an Inch.<br> +<br> +What is 5/16 of an inch expressed as decimal fraction?<br> +<br> +Set 16 on C scale over 5 on D scale and read the result .3125 inches on<br> +the D scale under the left-hand index of the C scale.<br> +<br> +<br> +7. Physics.<br> +<br> +A certain quantity of gas occupies 1200 cubic centimeters at a<br> +temperature of 15 degrees C and 740 millimeters pressure. What volume<br> +does it occupy at 0 degrees C and 760 millimeters pressure?<br> +<br> +Volume = 1200 * (740/760) * (273/288) = 1100 cubic cm.<br> +<br> +Set 760 on C scale over 12 on D scale. Move indicator to 740 on C scale.<br> +Move slider till 288 on C scale is under hair-line. Move indicator to<br> +273 on C scale. Read answer, 1110, under hair-line on D scale.<br> +<br> +<br> +8. Chemistry.<br> +<br> +How many grams of hydrogen are formed when 80 grams of zinc react with<br> +sufficient hydrochloric acid to dissolve the metal?<br> +<br> +(80 / X ) = ( 65.4 / 2.01)<br> +<br> +Set 65.4 on C scale over 2.01 on D scale.<br> +Read X = 2.46 grams under 80 on C scale.<br> +<br> +<br> +In conclusion, we want to impress upon those to whom the slide rule is a<br> +new method of doing their mathematical calculations, and also the<br> +experienced operator of a slide rule, that if they will form a habit of,<br> +and apply themselves to, using a slide rule at work, study, or during<br> +recreations, they will be well rewarded in the saving of time and<br> +energy. ALWAYS HAVE YOUR SLIDE RULE AND INSTRUCTION BOOK WITH YOU, the<br> +same as you would a fountain pen or pencil.<br> +<br> +The present day wonders of the twentieth century prove that there is no<br> +end to what an individual can accomplish--the same applies to the slide<br> +rule.<br> +<br> +You will find after practice that you will be able to do many<br> +specialized problems that are not outlined in this instruction book. It<br> +depends entirely upon your ability to do what we advocate and to be<br> +slide-rule conscious in all your mathematical problems.<br> +<br> +<br> +CONVERSION FACTORS<br> +<br> +1. Length<br> +<br> +1 mile = 5280 feet = 1760 yards<br> +<br> +1 inch = 2.54 centimeters<br> +<br> +1 meter = 39.37 inches<br> +<br> +<br> +2. Weight (or Mass)<br> +<br> +1 pound = 16 ounces = 0.4536 kilograms<br> +<br> +1 kilogram = 2.2 pounds<br> +<br> +1 long ton = 2240 pounds<br> +<br> +1 short ton = 2000 pounds<br> +<br> +<br> +3. Volume<br> +<br> +1 liquid quart = 0.945 litres<br> +<br> +1 litre = 1.06 liquid quarts<br> +<br> +1 U. S. gallon = 4 quarts = 231 cubic inches<br> +<br> +<br> +4. Angular Measure<br> +<br> +3.14 radians = PI radians = 180 degrees<br> +<br> +1 radian = 57.30 degrees<br> +<br> +<br> +5. Pressure<br> +<br> +760 millimeters of mercury = 14.7 pounds per square inch<br> +<br> +<br> +6. Power<br> +<br> +1 horse power = 550 foot pounds per second = 746 watts<br> +<br> +<br> +7. Miscellaneous<br> +<br> +60 miles per hour = 88 feet per second<br> +<br> +980 centimeters per second per second <br> += 32.2 feet per second per second<br> += acceleration of gravity.<br> +<br> +1 cubic foot of water weighs 62.4 pounds<br> +<br> +1 gallon of water weighs 8.34 pounds<br> +<br> +<br> +<br> +Printed in U. S. A.<br> +INSTRUCTIONS FOR USING A SLIDE RULE<br> +COPYRIGHTED BY W. STANLEY & CO.<br> +Commercial Trust Building, Philadelphia, Pa.<br> +<br> +</big> +</body> +</html> |