"204 Proeeedings of the Royal Irish Academy. 



The components of the resultant force on an element dc[ of the surface- 

 tractions on its bounding surfaces are 



- c- 



dy 



+ 



- 10 



- a' 



dz 



+ 





-P 



di) 



dx 



+ 



"'dy} 



In the case of homogeneous gravitating matter, we have then to satisfy 

 the equations 



^ dr] n dZ, _ ., d<p 

 dz dy dx' 



2 ^ _ 2 ^ _ 7 ^ 



dx dz dy' 



^dl dr) d(l> 



rt- — - &- — = hp -f. 

 dy dx dz 



Now, these give = hpV-cp. Hence they are possible for a point where 

 there is no matter, but not where there is, since then V-0 = - 47rp. It 

 follows that M'CuUagh's rotational ether is incapable of satisfying the 

 necessary displacement equations. 



It would appear, however, that these equations can be satisfied by a mixed 

 form, consisting of a work-function in a, h, c, f, g, h, corresponding to homo- 

 geneous isotropy, together with a work-function of the M'Cullagh type. 



In fact, we have only to add to the displacement forms, u, v, w; found 

 above, the supplemental v/, v\ w\ given by 



, dy , d\ , d\ , _, ^ 

 u = -^, V = — ^, to = "7^, where V-v = U, 

 dx dy dz 



the function ^ being suitably determined within and without the range of 

 gravitating matter. 



The same remarks will, of course, apply to the electrical problem. 



