Art. IX, — Fullers Calculating Slide-Rule. 

 By James J. Fenton. 



[Read 10th September, 1885.] 



Slide-rules, for use in approximate calculations, are not 

 nearly so well known as they deserve to be ; for, whilst 

 possessing all the advantages to be derived from logarithms, 

 they are entirely divested of their attendant technicalities. 

 If a book of logarithms be placed in the hands of any 

 intelligent person, unskilled in mathematics — no matter 

 how well the method of using them, and their great 

 advantages over the ordinary methods have been 

 explained — it is most unlikely he will take the trouble to 

 master them ; but with the slide-rule it is very different, 

 for, as the logarithms themselves are entirely ignored, and 

 ordinary numbers alone are dealt with, he might, by the 

 aid of a few simple rules, in a very short time become quite 

 proficient in manipulating it. With the rule it is not 

 necessary, as in the case of tabular logarithms, to look first 

 for the numbers, then for the corresponding logarithms, 

 adding thereto the differences for the last figure, trans- 

 cribing them to paper, finding their sum or difference (as 

 the case may be), and then reversing the process, so as to 

 translate the result into ordinary notation. These opera- 

 tions, simple in themselves, often take so long that many 

 expert calculators can (except in calculations involving the 

 powers or roots of numbers) in most cases obtain the result 

 in less time. In the case of the slide-rule, however, all 

 these obstacles are avoided, and an ordinary result in multi- 

 plication, division, squares, or square- roots may be obtained 

 at once by inspection with one or two simple movements of 

 the scale, the mental operations of addition or subtraction 

 being mechanically performed by the rule itself. 



The logarithmic scale, in its simplest form, consists of a 

 rule or line divided into parts proportional to the logarithms 

 of the natural numbers from 10 to 100. Take a line of any 

 length and assume it to be made up of 1000 equal parts ; 

 then mark off the number of such divisions corresponding 

 to the logarithms (indices being omitted) of 20, SO, 40, &c, 

 to 100, viz., 301, 477, 602, &c. ; to 1000 ; and place opposite 

 to these the corresponding numbers, after which the scale 



