Purser — On Ether Stress. Gravitational and Electrostatical. 201 



when clu) is elemental solid angle. The strain components are given by 



dS 



yfca = (1 + 2e) 



M = (1 + 2£) 



he = (1 + 2£) 



2kf = (1 + 2£) 



2kg = (1 + 2e) 



m" ^r cos X cos ^ - 3e 

 7/r -- cos jjL cos i? - Se 



fZ/S 



111'' — T- COS V COS C = 3£ 



,.2 



wi^ — ^ (cos fx COS C + COS V cos 5) - Ge 



7 c ' 



7/1- — - (cos V COS ^ + COS A cos 6') - 6£ 



dS 

 2kh = (1 + 2£) 1 1 w^ -^ (cos X cos ^ + cos ^ cos A) - 6£ 



7?t^ cos^AfZw + £ m-doj, 

 m^ COS'ixdh) + £ 7?lWa;, 

 m^ COS' vd(o + £ rirdw, 



m^ cos /x cos pr^'w, 

 7/i.^ cos V cos Ac/(o, 



«i- cos A cos ^c?(u. 



These give the elongation quadric the axes of which determine the 

 principal axes of stress, which will, in general, be different from the 

 Maxwellian. 



Two cases may be specially considered : 



(1) ^ indefinitely small compared with A, which is the case when the 



ether is incompressible, or when the resistance to compression is indefinitely 



larger than the rigidity. In this case, the first terms in the expression 



for a, h, c, f, g, h are evanescent in comparison with the others, and we 



may write the elongation quadric in the form (a, I, c,f, g, li^x, y, z) = C, 



where 



« = il\ m^ (1-3 cos^A) dfi), 



h = £ JJm^ (1-3 cos^^) dto, 



c = ejjiu-(l-Seos'^v)d(ij, 



/ = -£// m^ cos fi cos V d(i), 



g = - £ ij rii^ COS V cos A du), 



h = - a^j riv cos A cos jx doj. 



Under the same circumstances, it will be found that the stress-quadrie 

 becomes {A, B, C, F, G, E%o:, y, z) = C, where 



A = z II iiv cos'A d(D, 

 ^ = £ J"| m~ C0S-/X fZcu, 

 G = ^W nv cos-y d(i), 

 F = e jj 'in- cos /x cos v du), 

 G = a jj m^ cos V cos A du), 

 jS" = £ J/ m- cos A cos fx dw. 



R. I. A. PROC, VOL. XX\T;I., SECT. A. [29] 



