1885.] equations of vibrations of ether in a light wave. 289 



which is easily seen to be zero, and w 3 ' is also evidently zero. 



Thus the parts of the stress due to co 3 and co 3 ' do not themselves 

 vanish under the conditions 



^1 + lk + d S= o 



dx dy dz 



and P xy = P yx , etc., but no work is required to produce the cor- 

 responding strains. 



We may however find a valid reason for omitting these terms 

 of a third order, from the consideration that if we suppose the ex- 

 pressions for £, 7), £ such that our equations if written in full are 

 applicable in the immediate neighbourhood of the source itself, the 

 terms contained in co 3 would be the ruling terms and would as they 

 are of an odd order be liable to a change of sign, and hence would 

 be incompatible with stability of the medium. I shall therefore 

 consider that these terms may be omitted from our equations. 



4. I shall now proceed to analyze these stresses, and as a 

 preliminary I shall shew that the vectors, 



di; drj d£ 

 dt' di' dt ' 



d£ _ dt] di; d£ drj di; 



dy dz ' dz dx' dx dy ' 

 are at right angles, for 



dl(d^_dn\ dy(dg_d£\ d£(dsn_al[ 

 dt \dy dz) dt \dz dx) dt \dx dy, 



evidently vanishes by (6). 



Take first the part of the P's due to g> 2 , and for simplicity 

 take a point in the axis of x distant r from the origin as the 

 point considered, and the axis of y parallel to the momentary 



and 



.(16) 



resultant of 



dl 

 dt 



drj 



di 



dt 



-tj , that of z parallel to the resultant of 



d% _d^ d% d£ dv di; 

 dy dz ' dz dx ' dx dy 



