f 252 ) 



01- {R=2): 



(lx 



d.v /„ ,v 



T, 





So this a})pi'oaches to — , but as will appear prescuth-, lor the 

 determination of tlie term 



..(1-..) f 1- ^-J - (•^— ''•') (l-2-^-) 



we must also i-etaiu the terms of lower order, as those of higher 

 onler disappear. We have further : 

 d.v'^ 



.V 1- 



d.r 



X — ,?■') — ,/;' 



o'.f' UX , IL\ 



= {x-x) 



I ax — ax y\, 



1— '! ^ + 



The term mejitioned bceonies therefore : 



= (x-x')(l-L). 



(x-x) ( (1-,/) (l-L) - (1-2.) ) = (.,•-..') {x-L}. 

 Hence we get 



d'T\ fdT 



ax 1 

 2 l'dT\ x—L \ X 



X U\ — IL\ 



T\<lxJ^ X (x-xyi\ X w. 



01' introducing the value of L, and of 



JT 



Ix 



2T 



dl 



dx 



^f i_ _ 14_1 



47', 



'7i 



{x-xyj\ u\_ 



7, V .;• 



a X u\-ii\ 

 7\ X u\ 



-2-- — -T , ,, 



X J X u\ X X (x — X ) 7 J 





« 4:7',\ A-'l 47', u\ ax — ax 



1 ^ ^_ 1 .^ ^>— 2-^ ,--^ 



7'^ 7j y X { q^ u; {x — x)J, 



Now («-Jt, =: ^^2 + « — <f', ("'i),, = (/i, SO that we finally get : 



d'T\ _ 1 /dT 



■i'^'. + lT) JyH-i^'r-^C'y,^ «-«')- 



<t I — 



(9) 



' l-(- 



where f ] has the value üivcii iji (H,. 



