216 M. Lorenz on the Theory of Light. 



logous equations, derived from these by changing J , t) , f into 



¥o> ?o> ?o> and f' , %, ? into -f , -^ -? . The six 

 components are determined by these six equations, and the velo- 

 city s results from the determinant 



\ = 0. (18) 







f 



— e 



C l,l 



Cl,2 



C l,3 



-/ 







d 



C 2 ,l 



£2,2 



C 2, 3 



e 



~d 







^3, 1 



C 3) 2 



C 3,3 



- c i,i 



— C l,2 



— C], 3 







/ 



— e 



— ^2,1 



— C 2 ,2 



— £2,3 



-/ 







d 



— c 3)l 



— £3,2 



— C 3,3 



e 



-rf 







J 



This is a left symmetric determinant, and may therefore be 

 put equal to H 2 . If H be now determined according to the 

 known method, we get from the equation H = 0, 



c l, 1 ^2,2 £3,3 + *>C 2} 3 C 3> 1 Ci ) 2" mm Ci t i C 2>3 c 2 , 2 c 3, l C3, 3 C 1,2 



= c hl d 2 + c 2}2 e 2 + c 3)3 f 2 + 2c 2)3 ef+2c 3>l fd+2c h2 de. (19; 



When d, e, and /are =0, we get from this equation the same 

 expression for s (10) as that previously found. In general, how- 

 ever, these are small quantities of the same order as ct p ; the 

 right-hand member of (19), which we will denote by <? 2 , is accord- 

 ingly not a small quantity of the second degree; and the pre- 

 viously found value of s will in general admit of development 

 according to powers of q 2 , and will therefore undergo only an 

 imperceptible increase. This, however, becomes no longer pos- 

 sible if the left-hand member of (19) becomes quadratic, or differs 

 only very little from a square ; for in this case we should be able 

 to take the roots on both sides and to develope s by powers of 

 + q. This case occurs when we put v = 0, and take a>b>c t 

 or «<i<c. The left side of equation (19) then becomes 



\b* sVUv * 9 \fl* + cVJ' 

 and this expression, if 



P — 



wr= 



becomes equal to the square of — ( ^ — -g). 



By putting the approximate value of s, namely s=b, on the 

 right of equation (19), we get 



