332 Mr. R. Hargreaves on Radiation 



departure of S at the surface, in interpreting which we must 

 remember that n 2 is measured in the same sense as n„ so 

 that for the statical case n 2 — — %. The moving standpoint, 

 that o£ the dielectric, is essential for interpretation on the 

 right hand, i. e. S 3 is to bo taken as a substantive quantity. 

 The waves in free aether should be interpreted with reference 

 to the fixed standpoint for which E : and E 2 are the substantive 

 expressions. Hence, the proper form is 



(V« 1 -t ( ,)(l-U ] /V)E 1 +(Vn 2 - l ,)(l-U 2 /V)E 2 =(— 3 -^\s 3 (36) 



and E x experiences a transformation at the surface. The 

 interpretation in detail is got by applying 



Yn 1 E l =(Yn 1 -io)^> l i-n ] JJ l E 1 ^w^ 1 



to the two waves in aether, aud is: — The rate of progression of 

 energy in the original wave across a fixed plane provides the rate 



of transit of energy ( — 5 \ S 3 in the dielectric, the rate of 



transit of energy — V>* 2 E 2 for the reflected wave, the work 

 shown by n 1 U 1 E 1 +^2U 2 E 2 , and the energy-content Si + S 2 

 for the space opened out by the motion. To express the 

 same facts without use of wave-parameters (n, U), (II.) must 

 be applied to the forms for free aether, giving 



V(X£-Y«)=V(X'/3'-YV)+wS + (iGE-Z2uX--y2i 



= V (X'£' - Y V) + w$ + (uX 2 + vY z + wZ z ) . 



where 



X,= -(XZ + a 7 ), Z, = i(X 2 + Y 2 -Z 2 + « 2 + /3 2 - 7 2 ), 



are the components of a stress. 



In (36) the fraction of incident energy which experiences 

 the transformation for reflexion is 



.,_ (V B ,-to) (1 - U,/V)E, _ x 2 % ;v 3 B 2 

 - - (V« 1 -«,)(1-U 1 /V)E 1 VEi P r%' 



This quantity was required in the previous section, and will 

 be evaluated in solving the problem of refraction. [Or the 

 ratio of the terms in E x E 2 of (36) may be compared directly 

 with the last of (19).] 



§ 12. We may now consider more fully the expression S, 



KM * ' 



S^SXX' + ^W (a) 



_K , M v 2 eKM v __ ._; ( * (38) 



■ = ~2 ^X J + — 2a 2 -<- -— ■ Zu(Yy -— Z/3) (b) 



iUcc t 



}(37) 



