SLIDE (or SLIDING) RULE. The sliding-nde is an instrument for the mechanical performance of addition and subtraction, which is converted into an unent for the mechanical performance of plication and division by the use of logarithmic) scales, instead of scales of equal para.
This instrument has been greatly undervalued in our country, in which it was Invented, and is very little known on the Continent ; for though a French work on the subject. published in 1S25, which is fol lowed by the writer of a more recent mathematical dictionary in the same language, assures us that in England the eliding rule is taught at schools at the same time with the letters of the alphabet, we believe it would be more correct to say that nine Englishmen out of ten would not know what the instrument was for if they saw it, and that of those who even know what it is for, not one in a hundred would be able to work a simple question by means of it. For a few shillings most persons might put into their pockets some hundred times as much power of calculation as they have in their heads : and the use of the instrument is attainable without any knowledge of the properties of logarithms, on which its principle depends.
We have before us a logarithmic scale, of which A n, called the radius, may stand for the logarithm of 10, 100, 1000, &c. : but if A n should be, say the logarithm of 100, then A c is that of 20, A d of 30, and so on. if this scale be repeated several times, beginning again at B, and if it be also large enough to be subdivided to a greater extent than can be shown in the diagram, any multiplication can be approxi mately performed by addition, and any division by subtraction ; which may be done with a pair of compasses. That is to say, the figures of the product may be found, exactly or approximately, and the meaning of the figures must be settled from the known character of the result. For example, to find 4 times 15 z-First, let A n mean the logarithm of 100, then A a is that of 15; next let A n mean the logarithm of 10, then A e is that of 4. Take A a on the compasses, and set it on to the
right of e ; it will be found that the point g is attained, directly under 6. But 4 times 15 must be tens ; therefore 60 is meant, or 4 x 15=60. Next to divide 90 by 45 : froln A k take A 8, or set off A S from k towards the left. The point c will be attained, under 2, which is the quotient. Next to find 7 times 5 : set off Af from It towards the right, and the point 7 of the scale following n will be attained, and 35 is the answer. But had it been to multiply 7 by .5 or 5-tenths, this 35 would have meant or 3i. Attempts are made in works professing to ex plain the sliding-rule to give rules for the determination of the cha racter of the figures in the answer, but without any success. It is all very well for a few chosen examples, but an attempt to do without the book soon shows the insufficiency of rules. If, on a large scale, 653 should be the figures of an answer, common sense, applied to the pro blem, must say whether it is '0653, .653, 6'53, 65.3, 653,6530, 65300, &c. which is meant. A knowledge of decimal fractions is therefore indispensable.
Now these additions and subtractions might be performed by a pair of rulers made to slide each along the other ; but whether they are kept together by the hand, or whether tho one ruler slides in a groove along the edge) of the other, matters; nothing to the explana tion. The following diagram represents the two rulers in one relative position. Hero 1 on the slide is made to match 2 on the fixed ruler, and the instrument is now in a position to multiply by 2, to perform every division in which the quotient is 2, and to work every question in the rule of three in which the ratio of the first term to either the second or third is that of 2 to 1, or of 1 to 2. And here let us observe, that much the beat way of beginning to use the sliding-rule is not by working given questions, but by setting the slide at hazard, and learn ing to read the questions which are thus fortuitously worked.