Instruction for Using a Slide Rule

Instruction for Using a Slide Rule

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[Transcriber's Notes]Conventional mathematical notation requires specialized fonts andtypesetting conventions. I have adopted modern computer programmingnotation using only ASCII characters. The square root of 9 is thusrendered 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 originaltext. There are two versions of the HTML files, one closely, and a second with images of the slide rulesettings for each example.By the time I finished engineering school in 1963, the slide rule was awell worn tool of my trade. I did not use an electronic calculator foranother ten years. Consider that my predecessors had little else touse--think Boulder Dam (with all its electrical, mechanical andconstruction calculations).Rather than dealing with elaborate rules for positioning the decimalpoint, I was taught to first "scale" the factors and deal with thedecimal 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 thus1.23 * 9.3 * 1E3 * 1E-5The exponents are simply added.1.23 *  9.3 * 1E-2 =11.4 * 1E-2 =.114When taking roots, divide the exponent by the root.The square root of 1E6 is 1E3The 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]INSTRUCTIONSfor using aSLIDERULESAVE TIME!DO THE FOLLOWING INSTANTLY WITHOUT PAPER AND PENCILMULTIPLICATIONDIVISIONRECIPROCAL VALUESSQUARES & CUBESEXTRACTION OF SQUARE ROOTEXTRACTION OF CUBE ROOTDIAMETER OR AREA OF CIRCLEINSTRUCTIONS FOR USING A SLIDE RULEThe slide rule is a device for easily and quickly multiplying, dividingand extracting square root and cube root. It will also perform anycombination of these processes. On this account, it is found extremelyuseful by students and teachers in schools and colleges, by engineers,architects, draftsmen, surveyors, chemists, and many others. Accountantsand clerks find it very helpful when approximate calculations must bemade rapidly. The operation of a slide rule is extremely easy, and it iswell worth while for anyone who is called upon to do much numericalcalculation to learn to use one. It is the purpose of this manual toexplain the operation in such a way that a person who has never beforeused a slide rule may teach himself to do so.DESCRIPTION OF SLIDE RULEThe slide rule consists of three parts (see figure 1). B is the body ofthe rule and carries three scales marked A, D and K. S is the sliderwhich 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 witha hair-line. The scales A and B are identical and are used in problemsinvolving square root. Scales C and D are also identical and are usedfor multiplication and division. Scale K is for finding cube root. ScaleCI, or C-inverse, is like scale C except that it is laid off from rightto left instead of from left to right. It is useful in problemsinvolving reciprocals.MULTIPLICATIONWe will start with a very simple example:Example 1:  2 * 3 = 6To prove this on the slide rule, move the slider so that the 1 at theleft-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 theC 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 = 6.70As before, set the 1 at the left-hand end of the C scale, which we willcall the left-hand index of the C scale, over 2.12 on the D scale (Seefigure 2). The hair-line of the runner is now placed over 3.16 on the Cscale and the answer, 6.70, read on the D scale.METHOD OF MAKING SETTINGS[This 6 inch rule uses fewer minor divisions.]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 majordivisions, each of which is, of course, equal to one-tenth (0.1) of theamount represented by the whole interval. The major divisions are inturn divided into 5 small or minor divisions, each of which is one-fifthor two-tenths (0.2) of the major division, that is 0.02 of thewhole 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 thissubject, notice that in the interval from 1 to 2 the major divisions aremarked with the small figures 1 to 9 and the minor divisions are 0.1 ofthe major divisions. In the intervals from 2 to 3 and 3 to 4 the minordivisions are 0.2 of the major divisions, and for the rest of the D (orC) scale, the minor divisions are 0.5 of the major divisions.Reading the setting from a slide rule is very much like readingmeasurements from a ruler. Imagine that the divisions between 2 and 3 onthe D scale (figure 2) are those of a ruler divided into tenths of afoot, 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 (notshown in figure 2) to one on the left-hand end of the C scale would he2.12 feet. Of course, a foot rule is divided into parts of uniformlength, while those on a slide rule get smaller toward the right-handend, but this example may help to give an idea of the method of makingand reading settings....