Purser — On Ether Stress, Gravitational and Electrostatical. 208 



element plane is perpendicular to r, i.e. to the line of force. The stress 

 is now formed by putting 



Ql Of "Z 



~ for cos A, cos B, cos C. 



2^l£,r^\ 



r r 

 Its magnitude is therefore 



O,.. I -R -^ T 



dr J 

 (2) where the element plane contains r, i.e. the line of force. Here 



X cos A + y cos B + z cos C = 0, 



k 

 and the normal stress is 'A/uB. Putting in now for B its value — , we see 



that the stress in case (1) is opposite in sign, and in magnitude double 

 that in case (2) ; in other words, under the conditions imposed above, the 

 electrical stress will consist of a tension along the line of force, accompanied 

 by a pressure of half the amount in all directions perpendicular to the line of 

 force. The gravitational stress similarly will consist of a pressure along the 

 line of force accompanied by an equal tension of half the amount in all 

 directions perpendicular thereto. In the cases discussed, the stress is 

 therefore different from the Maxwellian. 



We have now, therefore, determined a system of strains of a homogeneous 

 isotropic ether, and hence of stresses, which will give a zero action for 

 a dielectric cell containing no nucleus of free electricity, and where such 

 is contained, the known electric force acting upon it. This system will 

 also give the known electric stress at the surface of conductors. For we 

 have seen that in its action on a small element it is equivalent to the 

 Maxwellian system, which leads at once to this stress by the consideration 

 of the small block of the surface-layer dn dS on dS as base. 



It remains to consider briefly the possibility of satisfying the necessary 

 equations of displacement by an ether of different elastic quality, and more 

 especially by the rotational ether of M'Cullagh. 



In this the work-function is given by 



denoting the molecular relations given by 



div dv 

 dy dz ' 



dAc dw 

 dz dx 



dv du 

 dv dy ' 



