and Electromagnetic Theory. 333 



The use of X'... «' '... as multipliers in forming the energy- 

 equation suggests that in a dynamical scheme they have the 

 character of velocities, confirmed to some extent by their 

 appearance in external conditions; while KX... Ma... have 

 the character of momenta which accords with the use of 



K~ ... in the fundamental equations. Thus in (38), (a) is 



a mixed, and (b) a momental expression for S; and if we 

 start from (&), X' may be defined as 



X -cltffx) = X + «M(r7-tcy8)/V, 



and a' as </S 



=5(K0 =« + 'K(«>Y-t.Z)/V, 



which are the relations II. To express S in terms of X'... 

 a?..., the equations II. must be inverted, giving 



X(l-«V2w 8 /V 2 ) = X^eVV-^Sw^-eMV-HV-^O *^| 



and 

 S'(l-eV2«7V*) = ^2X'*+ ^S^ + e^V-'SufTV-ZW 



K> 9 //. 2 Me 2 /; 2 



_^-( 2 uX') 8 -^-(W)« 



using S' for the expression in terms of letters with dash. 

 The result of differentiating with regard to X'... a! ... is 



rfS' ™ dW ,, 



as we should expect. It will also be found that 



1%' eKM, rfS .... 



_ = __(X^-Y«) = -^. . . . (40) 



The vector of wmich the ^--component is -=r- (X/3 — Ya) 

 will be denoted by (PQR), and we have for 6=1, 



S = E-2Pw, or E = S + 2Pw = S + T; . . (41) 

 but for the aberrational case, e=l//* 3 , 



B-B-Sj, or e'»8+s|?-S*S^S^*> . (42) 



Attending fir>t to the normal case (41 ) } E appears as the 



