A SPHERE IN A VISCOUS LIQUID. 49 



we obtain 



irpa a + 2 



K$ +*)+* 



where M' is the mass of the liquid displaced. Now, if V were constant, we should 

 obtain from (13) 



and 

 whence 



We must now change t into r, V into F (t -T)d T , and integrate the result with 

 respect to T from t to 0, and we obtain 



and the equation of motion of the sphere is 



(M + JM> + ^ ^ F(l - r) (i^r + a ^ )r/ T = (M - M'V/. (15) 



Integrating the definite integral by parts, and remembering that F(0) = 0, the 

 result is 



and, differentiating with respect to t, (15) becomes 



Let <r be the density of the sphere, and let 



MDCCCLXXXVIII. A. H 



