of Maxwell's Electrical Theory. 185 



V(E 0l H 02 + E 02 H 01 ) = Y{u x h 2 a 2 + «A«J 



=A 1 A 2 V{(i cos 6 1 +j 1 sin ^) ( - i sin 2 +/ 2 cos 2 ) + (t cos 2 



+j 2 sin 2 ) ( - i sin #i +ji cos X ) } 

 = A t A 2 { {k x + & 2 ) cos (^ - 6 2 ) + V; lt ? 2 sin (0 X - 6 2 ) } 

 =A l A 2 {2^cos C cos (^i—^ 2 ) + * sin 2C sin (^i-^)}, 



where 2C, as indicated in fig. 5, is the angle between,;, and j 2 

 and between k x and & 3 . Hence when neither cos nor sin C 

 is zero, i. e. when the waves are not parallel, we must have 

 both cos (#i — 2 ) ana " sin^i — 2 J constant throughout space 

 and time, i. e. 6 1 — 3 must be constant. But since 6 1 involves 

 Z\ and 2 involves z 2 , this is impossible. Hence two such 

 waves cannot coexist. 



14. This shows that if a wave incident on a reflecting 

 surface be of the present type, it is if in free aether altered in 

 type by the reflected wave. 



Even this, however, is not completely condemnatory of the 

 present hypothesis ; for 



(1) Although such waves will be altered in type we have 

 not shown in what manner, and I am at present unable to do 

 so. They may be only so altered that the alteration does 

 not affect our senses. This, however, I consider extremely 

 improbable. 



(2) We have no experimental evidence that in free aether 

 such alteration does not occur. In our most perfect vacua the 

 density is such that if they could be assumed continuous 

 material plenums, Maxwell's ignoration of the equilibrium 

 equation would be justifiable. Though we have every reason 

 to believe that they are not such plenums, yet owing to our 

 ignorance of the effect on the aether of the proximity of 

 material atoms, I think we are justified in so regarding them 

 for present purposes. If this assumption be made, Maxwell's 

 theory of light is applicable to all terrestrial experiments. It 

 would still remain on the present hypothesis to be proved that 

 the apparent positions and spectra of the heavenly bodies are 

 not appreciably altered by the interferences just considered. 

 This would seem by no means so difficult as the task just now 

 proposed. 



But there is another grave difficulty. We have no guarantee 

 that the velocity of light in space will be practically a con- 

 stant. If, for instance, there were in the solar system a 

 circulation of the aether whose velocity was comparable with 

 that of light, the apparent positions of the sun and planets 

 would be largely affected. 



Phil. Mag. S. 5. Vol. 36. No. 219. Aug. 1893. 



