M. Lorenz on the Theory of Light. 89 



determined accordingly by 



o)dt= cos adx or a>dt = sin adz. 



But while the time and the coordinates of space vary simulta- 

 neously, the phase (kt — B— nz) remains unaltered. We thus 

 have 



= kdt— -j-dx and 0=kdt—ndz, 



which equations, in conjunction with the foregoing, give 



kcosa = (o-r- and ksma = con. . . . (19) 



If the values of p and p given in (5) and (7) be now introduced 

 into the expressions for the components £ and £ and if we further 

 put 



©*{=? and©*£=£ (20) 



we get 



?= A i~ -m e(kt ~ nz) > ( 21 ) 



dx 





(22) 



in which A, represents a constant factor. 

 We have, further, by (8), 



u= +| log sin 2a = const. +^logf (o q -^-) } 



from which last expression the constant may be omitted. We 

 thus have, in one of the two cases resulting from the double sign, 



«=-ilog(»sg) (23) 



By putting this value of u into the expressions for 5 and s', and 

 regarding x as an independent variable, we obtain by the equa- 

 tions (21) and (22), 



d 



-j- | CO 



dx 



,1 

 d— £ 



[••-Tfa-J + (&) f=0, . . . (24) 



A r 1 d Z~\ 1 - 



dxlJd8\*dx] + tfS=°- • • ■ ( 25 > 

 \dx) 



