MOTION OF ELECTEIFIED SYSTEMS OF FINITE EXTENT, ETC. 177 



First for axes fixed to the aether we may assume the system 



,/3y a/3 a a y dp a\ ra 2 M (K-i) 3 



~ ~ ^~ > ^~ ~~ a > 5 5/ ~ 1 57 "^ rr 2" 



o?/ 82 3z da; ex dy/ [St K dx 



8Y_8Z az_ax ax_aY\_ a, R , 

 aT a?/' ax " az ' ay 8x/~8^ a ' p ' 7 ' 



for a body moving parallel to x with velocity u. 



These give for the velocity of propagation of radiation the value 





K 2 J K 



which agrees with FRESNEL'S assumption as far as the first power of u. 



Further, interpreting a, ft, y as magnetic and X, Y, Z as electric force, the equations 

 contain FARADAY'S law. The convection current due to material polarisation, viz., 



is, however, difficult to explain on account of the factor 2. 

 Second, and again for fixed axes, we may assume the system 



8/3 8 8y 8/8 9a\ _ f_3_ it (K 1) 8 



"a2' a"8^' aT"8l// :: l^ K ~a^ 

 r , / /8Y_8_z az_a_x ax_a_Y\ /8 , M(K-I) a \^ fl , 



y U 3y' Sx " 3z ' Sy a.r/"l8 K 3x\ ( "' P ' 7 >' 



These give for the velocity of radiation 



C' + ) 



again in agreement with FRESNEL'S assumption. 



In this system, which possesses the great advantage of symmetry, we may interpret 

 a, ft, y as magnetic force. In order to reconcile the equations with FARADAY'S law 

 we require to distinguish (X, Y, Z) as the sethereal electric force and 



v, t(K-l) 7 M (K-l) 



' Y+ - Z --- 



as the total electric force. The convection current due to material polarisation is now 



M(K-l) 8 , Y Y 7 , 

 ~~ (X) Y> Z) 



and presents no diificulty of interpretation. 

 VOL. ccx. A. 2 A 



