XVI. On certain Conditions under which a Perpetual 



Mutton is possible. 



By GEORGE BIDDELL AIRY, MA. 



MEMBER OP THE ASTRONOMICAL SOCIETY, FELLOW OF TRINITY COLLEGE, AND OF TUK 



CAMBRIDGE PHILOSOPHICAL SOCIETY, AND PLUMIAN PROFESSOR OF ASTKONOMV 



AND EXPERIMENTAL PHILOSOPHY, IN THE UNIVERSITY 



OF CAMBRIDGE. 



[Read Bee. 14, 1829.] 



It is well known that perpetual motion is not possible with 

 any laws of force with which we are acquainted. The impo.s- 

 sibility depends on the integrability per se of the expression 

 Xdx + Ydy + Zdz : and as in all the forces of which we have 

 an accurate knowledge this expression is a complete diiferential, 

 it follows that perpetual motion is incom])atible with those forces. 



But it is here supposed that, the law of the force beinj? 

 given, the magnitude of the force acting at any instant depends 

 on the position, at that instant, of the body on wliich it acts. 

 If however the magnitude of the force should depend not on 

 the position of the body at the instant of the force's action, but 

 on its position at some time preceding that action, the theorem 

 that we have stated would no longer be true. It might happen 

 that, every time that the body returned to the same po.sition, its 

 velocity would be less than at the preceding time : in this ca,se 

 the body's motion woidd ultimately be destroyed. On the con- 

 trary it might happen that the body's velocity in any position 



