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XLVI. Improvement on the Sriding-Rule. By Silvanus 

 Bevan, Esq. 



iVlosT of the following description of a little invention of mine, 

 which seems likely to extend the uses of the sliding-rule, was 

 prepared about nine months ago with a view to insertion in the 

 Philosojjhical Magazine ; but more important matters having 

 then occasioned it to be neglected, I now offer it for that pur- 

 pose. 1 call it my invention, because it is new to nie, and to 

 all my scientific friends to whom I have shown it ; and because 

 the advantages which it promises over the old construction 

 would probably have prevented it from lying dormant if it had 

 previously occurred to others. And I thinli I am warranted, in 

 this conclusion by the circumstance, that but a very short time 

 had elapsed after its first promulgation, when so much of it as 

 appeared to be adapted to the purposes of the Board of Excise 

 was introduced into general practice under its authority. 



The annexed drawing (PI. I II. fig..5) shows that, instead of having, 

 like the common sliding-rule, a fixed and a moveable line of num- 

 bers, each reaching from 1 to 10, and repeated to a second 10; 

 mine has one line reaching from 1 to 10, and another reaching 

 from about 3 to 10, and thence onward to J3'3 ; or more exactly, 

 from the square root of 10, 3-16-'>, to the repetition of the same 

 number ; one of these lines being inverted, or counting from 

 right to left, whilst the other is placed in the usual m.anner. By 

 this construction, without any diminution of its uses (as I shall 

 presently show), the sliding-rule is reduced to one half its usual 

 bulk, to the great increase of its portability and convenience; or, 

 if its original length be retained, the size and accuracy of its di- 

 visions are doubled. But these are the least of its advantages: 

 for while it performs the usual ojjerations of multiplication, di- 

 vision, and proportion, with as nuich facility as the common 

 sliding-rule, it also shows, on inspection, the square root and all 

 the factors of a number given. For, by the construction of the 

 line of numbers, the distance between the first and second terms 

 of a given proportion equals the distance between the third and 

 fourth ; and by the inversion of one of the scales it happens, 

 that if the stH.-ond and third terms are made to coincide, the first 

 and fourth will coincide also. Hence it follows, that in any 

 given position of the slide, the products of coincident nimibers 

 are equal throughout ; ami if one of these numbers be unity, the 

 correspondent mnnber is the product of every contiguous pair, 

 which are consequently its factors, and its root is shown bv 

 their equality. For exam|)le: Let it be required to uudtiply lii 

 by 4: — place thase two factors together, as in the figure; and 

 opposite to I will be found tlie product 64. Divide 64 by 2 re- 

 place 



