24 Prof. Powell o« the Undulatoty TTieorij of Light. 



~dt^ ~ 1 L 



f {r) -\- cos^ uf {r 



4 



cosa cos j3,/(r) "\ 



cos a cosyf(r) 



An 



A? 





S{^ cos^cos«/(>) ^^1^ 

 cos /3 cos yf[r) 



+ s r cospcosy /jr) ^^1 



(12.) 



s^^ co^yc°^«./W ^jj 





fLi= J + S 



L 



+ S 



{ 

 { 



cosy COS ^f{r) 



f(r) + cos^y/(r) 





These are the differential equations, which will represent 

 the motion of a system of molecules which, being subject to 

 the action of mutual attractive or repulsive forces, are slightly 

 disturbed from the positions which they occupy in the state 

 of equilibrium of the system. 



These equations are those before alluded to as being, in 

 fact, the same which M. Cauchy has established in the me- 

 moir in his third volume. In the subsequent investigation in 

 the fourth and fifth volumes, he at length deduces the well- 

 known partial differential equation for vibrations (a being the 

 rectilinear displacement of a molecule and s a constant) 



d^8 



= 5^ 





and from the form of its integral he establishes the laws of 

 the propagation of the plane waves. 



The celebrity of the discussions relative to this formula 

 carried on by Euler and D'Alembert (Berlin Acts 1747), and 

 decided by La Grange (Turin Memoirs 1759), as well as 



