172 Rev. H. Moseley on a Mackmejbr Calculating the 



The three arms of the wheel PQ are pierced by apertures, 

 through which pass, accurately fitting them, the three rods of 

 the rigid frame EF, which frame turns in fixed bearings at C 

 and D upon hollow axes, through which axes pass the cylin- 

 drical extremities or gudgeons of the screw CD. 



The wheel PQ traverses the frame EF longitudinally, and 

 at the same time carries it round with it in its revolutions : and 

 it admits of being ^xecl upon the frame at any distance from 

 either extremity. The frame carries an index S. 



AGH is a cone, whose side AG is parallel to the screw 

 CD, which turns by means of a spindle AB upon fixed bear- 

 ings, and which is continually pressed upon the edge of the 

 wheel PQ by a spring acting upon the extremity of its spin- 

 dle. The cone is of some soft metal, brass for instance. 

 The edge of the wheel PQ is very thin, of steel, and milled, 

 so that it imprints a minute tooth upon the soft face of the 

 cone at every point where it levolves in contact with it. 



The spindle AB carries an index R. The indices R, S, T 

 point to equidistant divisions upon fixed circles, not shown 

 in the Plate; and each of them is connected with a train of 

 wheels and pinions, whose numbers of teeth are in the pro- 

 portion of ten to one, and which serve to measure the com- 

 plete number of revolutions and parts of a revolution made by 

 each index. 



Now certain dimensions (hereafter to be determined) being 

 assigned to the different elements of this combination, it may 

 be shown, — 



1st. That if the frame EF be fixed, and the screw CD 

 turned until the index T points to anj' given number N3, and 

 then the frame be released, the wheel PQ Ji.ved upon the 

 frame, and the cone turned until the index R points to any 

 other given number N,, then will the index S point to the 

 product of the numbers N, and N3. 



2nd. That if, as before, the frame EF be fixed, and the 

 screw turned until the index T points to any number Ng, and 

 then the wheel PQ bejixed on the frame, the frame released, 

 and the cone turned until the index S points to any other 

 number Ng, then will the index R point to the quotient of Ng 

 byN3. 



3rd. That if the screiso CD be fixed, the wheel PQ and the 

 frame released, and certain other adjustments made, and if the 

 cone be turned until the index S points to any number N, 

 then will the index R point to the logarithm of that number. 



4th. That if the spindle of the cone be connected with the 

 axis of the screw CD by means of two bevelled wheels, so that 

 the rotation of the one shall always bear a given relation to 

 that of the other, then the frame EF and the wheel PQ being 



