306 



WILSON AND MOORE. 



Now by (36) the general form for a third derivative is 

 dXrs ^ 



Xrst — 



dxt 



d^Xr 



dXsdxt 





-2, 



X. 



l 



d [r s) . \r s) dXr, 



+ 



dxt ( in ) ( m ) dxt _ 



-S. 



A« 



+ Xr 



\r t 



( 711 



S t) 

 VI \ 



and 



Hence 



dXm _ .. I V V i "'' ^ 

 dxt ( V ' 





-2 X ^'' '^ S'" ^1-2 



( VI ) ( p ) 



f VI ) ( VI 



and 



Y — Y — — ^ Y 



dxt ( VI ) dXs { in ) \i P ) ' m 



r t) {p s 



)] 





{r s\ 

 1 \ 





= - 2,„.Y 



ivi-^-'-lvi] 



r 5 



7?2, 



-Ymt 



dxt ( ??? ) a.rs ( 7?i > \L P ) { fn ) 



