therefore 



dW { dV ( 

 dy " d 



an Ijicompressible Viscous Fluid. 



\ dx ° dy dz ) dc 



353 



d&i 



7 dx ' 



But S,- is a solid spherical harmonic of degree i ; and therefore 

 satisfies the equations 



and consequently 



Again 



dWi dYj 



dy dz 



=(;+i) 



d$i 

 dx 





1 cffij J / 



7* dv I V " /M /-7o/ y-7/v 



)*"*§} 



r dr I l dx j 

 Equation (40) now becomes 



= ldRif , 

 r dr 



H- 2 t }-*•§• • («) 



The second and third of equations (39) give two others similar 

 to (41). Since 



dhi _ dh. x dhi __ dh t y dhi _ din z 

 dx dr r' dy dr r 9 dz dr r 



these may all be written as 



These equations are to be satisfied only when r = a, andmani- 



