350 PROFESSOR CHALLIS, ON THE MOTION OF A SMALL SPHERE 



making some applications of it. I shall here only remark, in confirmation 



of the result, that if U J =1, that is, if the fluid move with the 



.- , .. dx 2mh m 2 ^ , ^, . 



uniform velocity m, -j- — z — * H 7^ — -rt ; and supposing the density 



of the sphere to be the same as that of the fluid in motion, and con- 



-- dx 



sequently 8 = e " , it will be found that —r- = m, neglecting m s , &c. 



This manifestly should be the case. If 



2tt 



* [ a) = Sin ¥ * " )' 



dx 

 the last term of the expression for «*- will be partly constant and partly 



variable, and it is plain from equation (12) that the accelerative force 



is the same as if the constant part did not exist. If <p' (t ] =0, 



whenever <p (t J =0, the sphere and the fluid will be stationary at 



the same instants. 



J. CHALLIS. 



Cambridge Observatory, 

 March 3, 1841. 



