Wu and Whttney 
2 2 2 
i ie. LI ag at lei oe, (a8 d= + 6c Sc_ 
(2 
dF 
[ Jc vc a (38) 
n m 
+ cross product term between bc. and, 6T_or. .668., 
in which the subindices denote partial differentiation. The variations 
GE; sof depend on 6. as wellas on I’. For I to be mini- 
mum, we must have 
tied eck all Saar (19) 
yh 6 Pee SS we (20) 
in which 8B and 6 8B are understood to be related to [ and 6F by 
(9) and (14). Relation (19) assures I to be extremal, and with the 
inequality (20), I is therefore a minimum. 
Now, substituting (14) in (17) reduces it to 
1 
i ee | fe +H, [F, ]for( as + 6c. [ord ecaat (1 7)" 
=] I 
after inter-changing the order of integration, which is permissible 
under certain integrability conditions (see Tricomi 1957, § 4.3) 
which will be tacitly assumed to hold. Since the variations 6T (£&) 
1118 
