TUE 

 LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[FOURTH SERIES.] 



NOVEMBER 1859. 



XLIX. A Mathematical Theory of Attractive Forces. 

 By Professoi- Challis*. 



^r^HE theory of physical forces which I have proposed in 

 A several preceding communications rests entirely on the 

 solution of a hydrodynamical problem, which may be thus enun- 

 ciated : — To find the result of the dynamical action of a series of 

 waves of an elastic medium which presses proportionally to its 

 densit}', on a small and perfectly smooth sphere, free to obey any 

 impulses communicated to it. In the course of the explanation 

 of a mathematical theory of the force of heat, given in the Num- 

 ber of the Philosophical Magazine for last JMarch, I have adduced 

 reasons for concluding that the small sphere might receive a 

 permanent motion of translation, by the effect of the part of the 

 pressure which depends on the square of the velocity of the 

 vibrating particles of the medium. The case more particularly 

 considered was that in which the action of the waves is mainly 

 on that half of the surface of the sphere on which they are im- 

 mediately incident, in which case, as was shown, the motion of 

 translation would take place in the direction of the propagation 

 of the waves. It is clear that such a distribution of the pressure 

 may exist when the breadth of the waves and the maximum 

 velocity of vibration are so small that the whole extent of the 

 vibration of a given particle is very small compared to the dia- 

 meter of the sphere ; for in that case the lateral spreading of 

 the waves, on being propagatedbeyond the first half of the sphe- 

 rical surface, may be so feeble as to disturb only to a small extent 

 the fluid in contact with the other half. In the theory of heat 



* Communicated by the Author. 

 Vhil. May. S. 4. Vol. 18. No. \2\.Nov. 1859. Y 



