176 Rev. H. Moseley on a Machine for Calculating the 



dices be all made to point lo zero when the wheel PQ is at 



the apex of the cone, then, representing as before by Nj, Nj, 



N 

 Ng the numbers shown at any time by the indices, ?i ' will 



represent the number of revolutions made by the screw whilst 



the number N, is registered by R, and therefore — ^ A the 



distance AP by which the wheel PQ will have been moved 



from the vertex of the cone ; so that — ^ X sin « will be the 



radius PM ot the circle which the point P of the cone is in 



the act of describing, and k sin «.27r ' the small arc 



which it actually describes whilst the increment ANj is regis- 

 tered by the index R. But AN2 being at the same time 

 registered by the index S, the circumference of the wheel will 



AN 

 describe a space represented by -. 27rp ; 



«2 



AN. ^ «Ni ^ AN, 



«o "^ n, n. 



... AN,= (^-!:^).N,AN,. 



And passing to the limit and integrating between the limits 

 zero and Nj, 



N.= (^)-N.'- 



If, therefore, the quantities A, n, Hj, «2> P> » ^^ so assumed that 



:1, ...... . (y.) 



2« 2p / 



then N2=NiS (4.) 



and Ni='v/n;; (5.) 



so that the number Ng shown by the index S (under this 

 adjustment of the instrument) is, in every position, the square 

 of the, number shown by the index R ; and conversely, the 

 number shown by the index R is, in every position, the square 

 root of the number shown by S. 



If a second frame and screw and wheel, similar to EF and 

 CD and PQ, be conceived to be placed parallel to the side 

 AH of the cone, and if the cone be so pressed upon the edges 

 of both these wheels as to carry them round with it in its revolu- 

 tion ; if, moreover, the axis of the second screw be so connected 



