in certain Problems of' Viscous Fluid Motion. 627 

 where the summation extends over the positive roots of 



-JiQ>)=o. 



(29) 



The equation for the exponents of the solving function is 



-TV -r4— + -A—^ + ... -U 1=0. (30) 

 Writing #= — v\ 2 /a 2 , equation (30) reduces to 



M 2 (X)+XJ 1 (X,) = 0, (31) 



where k = 27rpa i /I. The equation can be deduced from (29), 

 by logarithmic differentiation, as indicated in (12) and (13). 

 The equations for the coefficients of the solving function 

 become 



+ 



+ 



V-/V ' V-Pi f V-/Y 2 



+ . 



;-o 



i 



Ao A. ft 



-A 1- 



V— P2 J V~ iV V— Pa 



: = 0K (32) 



where j0j, j» 2 » ••• are the roots of (29), and A, , X 2 , ... the roots 

 of (31). 



To solve these equations, we may adopt the same plan as 

 before. Assuming that a function f(r) can be expanded, in 

 the range < r < 1, in the series 



/(r) = 2BJ 2 (Xr), 



the summation extending over the positive roots of (31) 

 we have 



Now take f(r) = J 2 ( P r )i where p is a positive root of (29) : 

 alter obtaining the expansion and putting r = l, Ave arrive at 

 the result 



9 L-\ 2 



p being any one root of (29) and the summation being with 

 respect to the roots of (31). 



