Purser — On Ether Stress, Gravitational and Electrostatical. 195 



Let us now in the first place proceed to form tlie equations of stress. 

 These will be (I use Dr. Williamson's notation) : — 



clA ^ ^ ^_ X ^ 

 dx dy ' dz dx' 



dH dB dF _ d4 

 dx dy dz dy'' 



da dF^ clG _ d^ 



dx dy dz ^ dz ' 



h being a certain constant, p the density, whether of gravitational or 

 electrical matter. 



Now, in the gravitational problem, p = — j-^ , in the electrical = -—^ . 



47r 47r 



Now it is readily seen that 



fv',, |vv, ^v^, 



admit of being written in the forms 



dA' dH' dG' 



dx dy dz 



dH' dB^ cir 

 dx dy dz ' 



where 



dG^ dF dC^^ 

 dx dy dz ' 



- = *i(IJ-(fJ-(tJ 



4iY- f'-^Y- f^Yj, 



B' = ^ 



G' = i 



dy J \ d, 



^, ^d4_ d<p_ ^, ^ d(p_ d(p_ ^, ^ d<}) dtj, 

 dy dz ' dz dx ' dx dy 



Our problem will then be solved, quoad stress at least, if we take 



A, B, G, F,G,H = \- 



— 47r 



in the gravitation, or -— in the electrical cell x {A\ B', C, F', G\ H), i.e. the 



47r 



state of stress equivalent to that represented by A', B', C, F\ G, H' . This 

 latter now is easily seen to represent in the electrical problem a stress 



[28*] 



