845 



?^=|/ f"^-; (13) 



A, B, P and Q are complex constants which are determined by 

 the conditions at the boundaries. 



In the first place we have u = a for r = R, so that 



P{hR + \) + Q{bR —l) = aR'' (14) 



If the liquid is unlimited or at any rate may practically be con- 

 sidered as unlimited, u = for r = oo ; this leads to the condition 

 Q = (unless b were a pure imaginary quantity, i. e. /■ were real, 

 in which case the motion would be aperiodic, a case which we do 

 not consider here), and therefore 



R' br+1 ^ „ 



!/=0 i>-/Ar—R) (15) 



r' l>R+l ^ ' 



On the other hand, if the liquid is bounded by a stationary 



spherical surface of radius li' , the condition is that u = for 



r =^ R' at all times (again in the supposition that the lie |uid adheres 



to the surface of the sphere"» so that 



Pe-b./i'-Ii^bR' + 1) + Qe''<R'~'i{bR' —l) — 0; . . (16) 

 in that case 



P=_i_^' , Q = '—J , (.*) 



where 



1) — (bR + 1) (bR — 1) ,Kn-R _- {f,u _ 1) (Aff 4. 1) e~Kli'-li), (17') 



so that 



aR^ 

 u - - [(/» + 1) {l,K - 1) /"/?'-') — {br — 1) {bR + 1) e-'>.R'' ')] (17") 



6. If we put 



yh = ± (y' + f I) 

 it follows that 



y'» y"» ^ Ji Jijid o y'y" __ ^,"^ 



and therefore, seeing that 7' and 7" from their nature represent 

 real quantities: 



__ • (18) 



As a rule the circumstances under which the experiments are 



