328 Mr. R. Hargreaves on Radiation 



The argument is then lx' -V my ! + nz' — (X2 + U)£, and 



12 + U=-+U(l-e). 



(i.) Thus if e = 1, the wave travels with constant velocity 

 V/'fj, in relation to (%'y'z'), and appears to have the variable 



V 



velocity U in relation to (xyz). 



(ii.) But if e= -5, 



I2 + U = -+u(l-i\ o = I-2; 

 fi \ fj, 2 J p P 2 ' 



both are variable unless fi = 1, when there is no distinction 

 between (i.) and (ii.). 



For a dielectric (i.) is held to apply when the disturbance 

 originates in the dielectric, and the translation in question is a 

 motion relative to the dielectric. Case (ii.) is applicable to 

 waves produced in a dielectric by waves in free aether ; the 

 moving standpoint is that of the dielectric itself, and the fixed 

 standpoint is that in respect to which the originating wave 

 travels with constant velocity. 



The use of the moving standpoint simplifies the transition 

 from (i.) to (ii.). 



§ 10. We proceed to certain relations between the two types 

 of variables for a plane wave, and they will be written for 

 case (ii.) for which they are less obvious, because neither 

 standpoint shows a contant velocity of propagation. Applying 

 (24) to (23), we have 



KX=/i(niS-JBy), Ma=/i(mZ-nY) ") 



[; ■ (25) 



/*X = M(n/3-m 7 ), jua = K(mZ-nY) ) 



i. £., the relations between the inductions or inducing forces 

 are the same as for the statical case, though in (ii.) the velocity 

 is variable. An immediate consequence of (25) is 



K2X 2 =M2(^-w 7 ) 2 = M^ 2 =|sX 2 +y^ 2 =E, (26) 



the last giving a definition of E. We now express a! in 

 terms of a. ; thus 



a' = u + K(wY-vZ)/ia, 2 Y= <z+{w(ly-n*)-v(m*-l t 8)}lfjLY 

 and similarly . r(27) 



