( 556 ) 



From these we derive, by differentiation with respect to $, and ri 

 respectively 



and 



ö't' fdv du\ 1 dw^ 



dèdri ^ \Pn di]J ^ 2 ^ ^ dri 



du\ 1 dw, 



— — — (v—vy.--^. 



= — (v—u) . w, . 



dèdri ' ' ' V ö§ 



By means of the two non-differentiated equations and by equation 

 (VII), we deduce from our last equation : 



and - «,, .-=«., ^^^ - ^-, j + -(.-„). _ . 

 or : 



tü. — - = — (y — m) . -^ and xl\ — = — —{v—u) . — — , 



from which ensues : 



— xi\ xo. {v — u) ■=: -—— and — xo.xo. (v—u) = — — . 

 ^ ^ dl] dS 



ö|Ö7j ö|d7j 



