294 



M. L. Lorenz on the Identity of the 



therefore some reason for taking a— —r=. ; and if this value fl\/2 



v2 

 be substituted for c in equations (A), the accuracy of this as- 

 sumption is confirmed by the circumstance that the equations 

 assume now a very simple form, and lead to exactly the same 

 differential equations as those which I formerly deduced for the 

 vibrations of light, with the addition of only a single member. 

 For, in accordance with equations (2), we have 



*H) >'H) "HD *»'H)1 



dt 



= -2 



W 



+ 



dy 1 



where the differentiation in reference to x f , y 1 , and z 1 must be 

 carried out in such a manner that r will be considered constant, 

 and 



de' 



dt 



= —2 [«'/*— -JcosX + z/u — -jCOSJJL + w'U — jcosv 



If these values be substituted in 



dn = CC Cdcc'dy'dz ' ^y-'i) + n 



dt 



by partial integration and introduction of the designations a, ft, y 

 we obtain 



dn = 



dt 

 Moreover from (5), 



-K: 



da 

 dx 



dy dz. 



«> 



1 d** a 



^rfF =A * a + 4,re ' 



and in like manner for ft, y. If now these values be substituted 

 in the equations (A), after they have been differentiated in re- 

 ference to tj and if c=a\/2, we get 



— — -la _ d (dy du\ d /dot dft\ 

 4 k dt "~ dz\dx dz) dy\dy dx J 



— it -u 4. — ^ (^ u — d@\ d (dft dy\ 



4k dt ~~ dx\dy dx) dz\dz dy)' 



jL^j_4 ,— d idft_dy\_ d (dy dct\ 



4k dt ~ dy\dz dy) dx\dx dz)' 



(8) 



