XV. Description of a Machine for resolving by In- 

 spection certain important Forms of Transcendental 

 Equations. 



By Sir J. F. W. HERSCHEL, 



MEMBER OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY. 



[Read May 7, 1S32.] 



(1.) In the course of a conversation with Mr. Babbage on the 

 subject of applying machinery to the performance of numerical 

 computations it occurred to me that, seeing the perfection with 

 which every description of wheelwork and rectilinear or parallel 

 motion can now be executed, almost any combination of circular 

 functions involving as well the arc itself and its multiples and 

 sub-multiples, as their sines, cosines, chords, &c. might be repre- 

 sented by the motion of a point, or by the difference of motions 

 of two points, regulated by mechanism, with almost perfect preci- 

 sion, and that it would therefore need nothing more than to mark 

 the arrival of such a point at some definite line or circle, or to cause 

 the machine in some way or other to come to rest when such dif- 

 ference should attain a given magnitude, or when any other assign- 

 ed condition should be fulfilled, to obtain a solution of the equation 

 expressive of that condition ; which solution should be limited only, 

 in point of exactness, by the precision of the workmanship and 

 the accuracy attainable in hitting the coincidence and reading ofi' 



