180 Mr. A. M e Aulay on a Modification 



moving, and in case of a forced irregular disturbance would 

 move with velocities comparable with that of light. This 

 will explain how we can on the present hypothesis account 

 for the encroachment with sufficient rapidity of light waves 

 on a previously dark region. 



But there is a difficulty I have not been able to surmount. 

 Eq. (14) is not linear in the electromagnetic vectors, and 

 hence in general the superposition of two solutions of our 

 equations does not give a third solution. I will show directly 

 how a single plane wave which is sufficiently arbitrary to 

 leave room for the explanation of polarized light &c. can be 

 borne by our aether, but I have failed in the endeavour to see 

 what the effect on each other of two plane waves inclined to 

 one another would be. It looks as if they must be altered in 

 kind by their encounter, and this is contrary to several optical 

 facts. 



9. Without further preface I proceed to the consideration 

 of case I. It may be remarked that a great part of the work 

 below relating to this case is applicable to ordinary dielectrics, 

 so that though I am inclined to reject the case, the work is 

 not thrown away. 



Our equations are now (5), (11), and (11). Equations (11) 

 are for present purposes more conveniently written by eq. 

 (23) § 63 of ' Electromag.' 



(47r)-^'H<=:-dD>/-dt + Yv , VV'c7'\ n ~ 



-V'E'=dB'/d* + V V 'VB'cr'/> ' ' W 



the V being unnecessary before y'H' and y'E' when K 7 and 

 fi' are constant scalars, as we suppose to be the case for the 

 sether. Putting now 



HV=H , EVK' = E , iVK'=l, . . (16) 

 VH =dE /^ + Vv'VE o-' ^ 



With this notation eq. (14) becomes 



V(E oV 'E + H v'H ) = (18) 



Notice that if c l is zero equations (17) reduce to Maxwell's. 

 Hence any solution of Maxwell's which also satisfies eq. (18), 

 or, what amounts to the same, when o 1 is zero any solution of 

 Maxwell's which renders VE H constant at every point is a 

 solution also of our problem. We shall be led to such a 

 solution below. 



10. The only case I have been able to discuss is a plane 

 wave with E and H in the front. Suppose, then, E and Hq 



