344 Mr. R. Hargreaves on Radiation 



in this connexion that (I) is always to be regarded as the 

 fundamental form of the equations. 



since ft8 '=« 3 M ^ j + ^tua z , 



= ( mia /-^/)/(l~U 1 /Y)+(m 2a /--Z 2 A / )/(l--U 2 /y), 



since m 1 _ m 2 __ fim 3 



1-Uj/V" 1-U 2 /Y~ 1-U^V 

 = m^j — 1$! + w 2 « 2 — 1 2 /3 2 = Zi + Z 2 . 



(ii.) KZ, M7 being continuous as well as aZ/3'X'Y', we 

 expect KZiX' + Myaf, and KZY' + JM^/S' to be continuous. 

 Further, if we write 



E%X I / «(Zi + %) (X 1 ' + X 2 ') = Z 1 X 1 ' + Z 2 X 2 ' + (Z^' + Z.X/) 



a question of the independence of the original and reflected 

 waves in the first medium arises, i. e. the question whether 



Z X X 2 ' + Z 2 X/ + 7l «/ + 72 V = 0. 



This proves to be the case when the method o£§ 11 is applied, 

 and all the quantities are expressed in terms of (a, /3, 7). 

 Now 



KZX' + M7a'=KZX + M7«+ i{Z(t^y-tt'^) + y(ti;Y-i'Z) } 



= KZX+M 7 *+^(Y7-Z/3), 

 when the aberrational forms 



X' = X+^(u7-™/3), J=a+\{wY-vZ) 



are used. Similarly, 



KZY' + M r /3'=KZY + M7/3+ ^(Z«-X 7 ). 



When this is combined with the statement as to continuity 

 there results 



|(ZX+ 7 «) + ^(Y 7 -Z / 8)} i + -[ ]y={KZX+MY«+|- (Yy-Z/S)}^ 



