ACTED UPON BY THE VIBRATIONS OF AN ELASTIC MEDIUM. 353 



direction contrary to that of the sphere's motion, the sphere will be reduced 

 to rest, and the velocity of the fluid along the surface of the sphere, from 

 what is proved above, will be V t sin 0. Hence by a known Theorem of 

 Hydro-dynamics, 



p'Bde*\ dt j _u ' 



and as jo = a*f>, and -jj- - V t sin 0, if we put m <p (t) for V t , it follows 



that, 



^^+mB<p'(t) sin 9 + \<f> (t)}* cos 6 sin = 0; 



(2 



whence, by integration, 



tf Nap. log. P - R<p' (t) cos 9 ~ 1JL cos 2 = a function of t. 



This equation agrees in its ultimate application with (10) of Art. 5, 

 and consequently leads to the same result. 



Cambridge Observatory, 

 Dec. 13, 1841. 



