834 
Ov; 
where v;,—— and V;, represents the corresponding sub-deter- 
dc, 
minant. We have identically 
Dv. ov. dv — 
__t—_ Sot Lo. 
Da da de » dc) 
hence 
ò Dv, dv, ie dv, dc’) 
a vn S= 0 
dc, Da dadc, 8 ) derden a » Oe, Ven 
and on the other hand 
D dv. dv. 070 
Da de, 5 Òa de, 
From (a) and (6) it follows that 
Sg 3) 
bn Deen 
(a) 
(b) 
(17) 
(17) 
(16) 
(16°) 
16”) 
(18) 
D Oer Do, a Ov. de” 
Dad. 1 Das x Oc) Oey 
or 
EE kad) 
—— =— 2 v, —. 
Da esi es Oe 
Substituting in (16) we obtain 
De 
Da th in do, 
Since Ev; V;,=0 for 2u and equal to T for 2= u, (16’) 
becomes 
DT _ dc’; 
pr cle, pn maa 
Da 00) 
Hence 
> dc’; 1 DE 
a d de; T Da 
Comparing this result with (13°) it follows that 
1 Deen 1 Dw 
YT Da w Da 
or 
DD sl 
og 
Da To 
In other words: Y/w is an adiabatic invariant or 
Y=of(e,...,v), w= TF (v,,.- +0) 
Substituting this value of w in the integral (10') we find 
I de. de, YF B 
eN: e, (rm) ff deden 
(18) 
(18°) 
(19) 
