98 Proceedings of the Royal Irish Academy. 



It is of interest to examine the surface-traction exerted by the ether on 

 the surface of the sphere. In general the components of stress are given by 



^ = A A + 2m — , 



dx 



i? = AA.24^ 



dy 



,, . ^ dio 



C = \A + 2fi --, 



i^= /i(- + 



fdv div 

 Vfe "" dy)' 



-, fdw du\ 



j^ fdiL dv 



\dy dx 



At the surface A vanishes, and the terms in fx alone remain. We have 

 also 



du 

 dx 



= B -It - x^ -J-, 

 r dr 



dv 

 dy 



= B + — -r— , 



r dr 



dw 



„ z- dB 



'dz 



r dr 



dv div 2yz dB 

 dz dy r dr' 



div du 2zx dB 

 dx dz r dr' 



du dv 2xy dB 

 dy dx r dr' 



The components of unital stress on any element plane whose direction 

 cosines are cos A, cos B, cos C are then 



tX/ U/H 



2nR cos A + 2ix - -^ {x cos A + y cos B + z cos C), 



2uB cos -5 + 2fx--T- (^' cos A ■\- y Qo^B + z cos C), 

 ^ r dr 



2uB COS C -i- 2u - -r- (X cos ^ + 7/ cos ^ + 5! COS C). 



r dr 



