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



N 

 PQ, and therefoi-e 27rp — ^ the space described by its circum- 



ference, we shall have 



Let now the quantities ?ij, n^, 7j.^, p, A, » be so assumed that 

 C-^^^ = l; («.) 



then N2=Ni.N3 (1.) 



that is to say, the number Ng shown by the index S is the 

 product of the numbers Ni and N3 shown by the indices R 

 andT. 



Dividing equation (1.) by Ng, 



N.= |^ P-) 



whence it follows that if, proceeding in other respects precisely 

 as before, we cause the cone to revolve, not until its own index 

 R points to a given number, but until the index S points to 

 the given number Ng, then will the index R of the cone show 

 a number N,, which is the quotient of Ng and Ng. 



To adjust the instrument to show the logarithms of num- 

 bers, let the wheel PQ be brought to the apex of the cone, 

 and let the screw CD be fixed, and the index S then made 

 to point to zero. Let the cone then be turned until the index 

 S points to unity, and in this position of the cone let the index 

 R be made to point to zero. The frame EF being then 

 allowed to turn freely, and the wheel PQ to traverse freely 

 on the frame, the number N, shown by the index R will 

 always be the logarithm of the number Ngshown by the index S. 

 For while the number N, is increased by the exceedingly small 

 number AN,, let the number N, be increased by AN^; the 

 parts of a revolution made hy the cone and wheel respectively 

 whilst Nj and Ng receive these small increments, will then be 



ANi , ANg , , ^ -. . ^ AN, , 



and ^, and the arcs to radius unity, l-n and 



"1 «2 "1 



AN. . N 



Stt ?. Moreover, the wheel PQ havini; made »-^ revolu- 



tions upon the fixed screw CD, will have been carried from 

 the ape.x of the cone to a distance from it represented by 



