1 78 Rev. H. Moseley on a Machine for Calculating Numbers. 

 then N4=N,3, (6.) 



and N,= ^F4; (7.) 



so that (under this combination) the number N4 shown by 

 the index of the second frame is, in every position, the cube 

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

 shown by the index R is tiie cube root of that shown, at the 

 same time, by the index of the second frame. 



In like manner, by placing any number of like systems ofn 

 frame, screw and wheel, upon the side of the cone, the third 

 screw receiving its motion from the second frame, the fourth 

 from the third, &c., any other powers of the number Nj, or 

 roots of the numbers Ng, N^, &c. may be conceived to be deter- 

 mined, the power shown by the last index, or the root by the 

 first, being one greater than the number of frames so applied. 



The four equations of condition (a.), (/3.), (y.), (S.) between 

 the nine quantities n^, 71^, 7/g, n_^, n, n', \, », p leave five of them 

 undetermined. These are to be assumed of such values as 

 ma}' be found most convenient in the construction of the 

 machine, the general principle of which it is the object of this 

 paper to explain. 



The Plate in particular, as has already been stated, is by 

 no means intended to show the details of the construction 

 of the machine, or even the general proportions of its parts, 

 but simply to illustrate its principle. There are, indeed, some 

 elements of its construction, which, for the sake of simplicity, 

 have been altogether omitted from it. These are the trains 

 of wheels which must be connected with each of the axes car- 

 rying the indices R, S, T to register the complete numbers of 

 revolutions made by those indices, and the divided circles to 

 which the indices point, showing such portions of the num- 

 bers Nj, N4, &c. as correspond to less than one complete re- 

 volution. 



It will be obvious that, since the number No represents (in 

 the first adjustment of the instrument) the product of the 

 numbers Nj and Ng, the divisions on the circles pointed to 

 by the indices R and T must be greater than those of the 

 circle pointed to by the index S, or the numbers 7?j and n,^ less 

 than the number n^j- 



It will, moreover, be observed, that the instrument, whilst 

 it differs from other calculating machines, and claims to be 

 superior to them in the simplicity of its combinations, differs 

 also, and is inferior to them in this respect, that the truth of 

 its registrations is dependent on the mechanical accuracy of 

 its construction. 



Those elements of the machine, on the mechanical truth 



