THEORY OF ELECTROMAGNETISM. 
727 
and by taking the pure part of both sides of eq. (17) we get 
m'co = sv(i-vvr - o-'c oyv) + w ss ( T 'yr - <r'yv) + x v n~^q + <Fx<*n • <i~\ 
whence, putting 
y]= -2 x (ll"x =~ 2 X (JI 'X • • • ■ 
we have from eq. ( 12 ) 
2f = 2[f] - [2V + SS (r'.VT + o-’yT)} + SV {t ( ),VT - <x'( 
+ (x V W _1 ( )2 + '2 v x'( )v-7~ 1 } 
Note that the terms here depending on rj may be put in the form 
x Y w -1 ( )^ + 2 v x'( W-? -1 
wliere — is the self-conjugate linear vector function given by 
zr = \pVr)( )+V0( )y . . . . 
( 20 ), 
(21). 
( 22 ), 
(23). 
For purposes of physical interpretation it is often legitimate to assume the present 
and standard positions to coincide. In this case ^ = 1, x = x" = 1 , so that 
2 f = 2 [f ] - {21+ tS (r T VZ + ayl)} + 2V {t ( ) T Vl - a ( )yl} (24), 
and if, further, l is a homogeneous quadratic function of the o-’s and r’s, 
2 f = 2 [f] + 2V{r( )yl-cr{ )yl} .(25). 
55. For future use we will make two deductions from these results. First suppose 
that 
l = / 0 + m( 2 ^K 0 - 1 d ' 3 — ...... (26), 
where K 0 , p , 0 are absolute constant scalars—the specific inductive capacity and magnetic 
permeability of a vacuum, and where l 0 is expressed in terms of the undashed letters. 
Thus it is only in the part of l independent of l 0 that the change of variables is made. 
In this part there is one r, viz., d', and one a', viz., H' ; and 77 = 0 . Hence 
(f>' a) = — 2vi~ 1 x^-Iox'oj — 2ttK 0 ~ 1 dw d — p, 0 H<uH. , /87r . . . (27). 
Next let l 0 ' be what l 0 becomes when expressed in terms of the dashed letters. 
