Faraday-Maxwell Mechanical Stress. 647 



are immediately deducible from the analogy of a medium 

 whose state of mechanical stress causes foreign bodies 

 embedded in it to be urged this way or that. 



o 



The magnetic vector in free aether is not constituted 

 by translational cetherial velocity. 



10. In a previous communication to the Philosophical 

 Magazine* an attempt was made to prove that (in free 

 aether) neither the magnetic nor the electric vector is to be 

 identified with translational velocity of the aether. As the 

 cogency of the arguments then put forward has been called 

 in question t, and as my own conviction remains unshaken, 

 a more precise proof will now be offered, which I trust will 

 be found satisfactory. 



11. Consider a train of plane-polarized plane electro- 

 magnetic waves, which is being propagated in free aether in 

 the direction of --increasing, the electric vector being parallel 

 to the axis of %, and the magnetic vector parallel to the axis 

 of //. In this case the vector-potential reduces to a com- 

 ponent which is parallel to the axis of #, and is a function of 

 z—Yt, where V is the velocity of radiation. Writing — with 

 Maxwell's notation — (F, G, H) for the vector-potential, 

 (a, b, c) for the magnetic induction, and (P, Q, E) for the 

 electromotive intensity at any point, let the suffix unity be 

 used to distinguish the wave-train now considered, and let 

 us put 



(F 1 ,G 1 ,H 1 ) = {^~V0,0,0}. . . . (1) 



Then (« l9 &„ <•!) = {(>, tf/U-VO, 0}, ... (5) 



and (P 1 ,Q l ,B,) = {V^-Vi),d,0}; • • (6) 



so that Pi-V&! (7) 



For a second train of plane waves polarized parallel to the 

 first, and propagated in the direction of --decreasing, we 

 shall similarly have 



P 2 =-V6 2 (8) 



* June 1907, pp. 694-696. 



t Letters dealing with this subject have appeared in ' Nature ' (1907) : 

 " The Structure of the Ether," 0. JRichardson (May 23), Lodge (June 16), 

 0. V. Burton (June 13), E. Cunningham (July 4), C. V. Burton (July 

 18). " The .Ether and Absolute Motion," Larmor (July 18). 



