A SPHERE IN A VISCOUS LIQUID. 53 



by (24). Changing the order of integration, the last integral 



whence 



(33) 



Substituting this value of x(0 in (30), we obtain 



*-- M#W, + f o A/if 



Now 



f' <f>(r}dr _ f ' j f T e~*" rfu 



J v/(*-T)-J T J OV /{(<-T)(T-)} 



f' , f' e- A dr 



~' U 



E = X (I ~ e )' (34) 



also 



rfT _ ft p - * 



T) ~ J Jo 



, 

 = * 



o y - T)(T 

 ' -* 



. . . . . (35) 

 and 



( 36 ) 



whence 



^e- M ........... (37) 



Again, 



f e-^(f - )</ = we-" [' (< - u) du 



J o Jo 



= i^ 8 ~ A ', ........ (38) 



whence (31) and (32) finally become 



