426 Sir J. F. W. Herschel on a Machine 



the result. This idea (the principle of which, it will be observed, 

 is entirely independent of all numerical calculations, or of any 

 application of wheelwork to perform such calculations, and turns 

 entirely on the modifications which an uniform motion communi- 

 cated to the primum mobile can be made to receive in passing 

 through a train of wheels, levers, &c. and on the accuracy with 

 which circles and straight lines can be graduated and read off") I 

 mentioned as it occurred, and presently illustrated it by applica- 

 tion to the well known equation between the excentric and mean 

 anomalies in the elliptic motion of a planet. 



(2.) The combination of movements which then suggested itself 

 for this purpose, though theoretically correct, was practically liable 

 to many objections. It happened however that I was at that time 

 engaged in investigating the elliptic orbits of some of the most 

 remarkable double stars ; and in the course of that enquiry had 

 continual occasion for the numerical resolution of cases of this 

 equation in every state of the data. Finding the preliminary 

 trials requisite for establishing a rapid conveyance of the succes- 

 sive approximations consume a great deal of time, even more than 

 the approximations themselves when once effectually entered upon, 

 I set myself to consider whether some simple contrivance free from 

 such objections might not be found which would give me by in- 

 spection at least a first approximation to the solution, and thus 

 prove of immediate practical utility. After one or two failures 

 from attempting to unwind a thread from the circumference of a 

 wheel revolving on a fixed center, and after rejecting as impracti- 

 cable Newton's mechanical solution of the problem by the rolling 

 of a wheel upon a plane, it occurred to me that a wheel will revolve 

 uniformly and unwind a thread from it with a uniform motion 

 just as well whether it revolve on its own center as an axis, or be 



