90 M. Lorenz on the Theory of Light 



By putting 



1 %- 4 



CO 



(<mydx 



y 



\dXy 



In the last equation, it is transformed into 



£ + ^S=°> ........ (26) 



dt»*^ 

 dx 



dx 



+ » 2 (9V o - • • • • • <w 



j- J =— 2 — n 2 ; and calling to 



mind that t and s enter into the magnitudes f , \ <j> only by the 

 factor e(*'-»*) V^T, it is evident that we may put 



rff 8 * V ~ l dz' d^ 



in place of the respective factors # 2 , n, n\ 

 "We thus get from equation (27) 



do* 



d<j> 



dx - 9 d 2 <l> d 2 <f> /OQN 



+ ®SiF=-^ ( 28 ) 



dx ' <fe 2 <# 2 



Equation (24) may also be deduced from the same equation 

 (27) if we put 



The constant a cannot, however, assume whatever value we 

 please ; for if this value of cf> be introduced into (26), we obtain 



an equation which must also hold good if co is independent of x. 

 But in this case, by our second hypothesis (2), -j- + -^'=0, or 



^& ^/_1 



here -j£ — w ^ — ■ 1 ? =0, whence follows a= - . The equa- 



dx m> 



tion thus becomes 



+ -£-M>. . . . . . (29) 



dx dz 



