835 
Tm fon fd do, Florent) cr ater eet celta LN) 
Now we can always arrange, that F becomes equal to 1. We 
have only to introduce, instead of one of the v;, the adiabatic 
invariant 
or 
trae net (a. v‚) 
and submit it to the condition 
òr, ; 
Ae” PMs PD AND ar TR Ee) 
We then find 
de. 7 Ov Oc 2 Ov * 
) see cn 
OE ates ton. 185) ar Br ò 
Tm VE tg 1 
DCE gn 3 de, v‚ x v, 
or substituting for Y its value w/F: 
or, F 
T* = wow ——- = Py tins Mrt Ae Be wey bi! 
a Ov, 1 ri en) 
Calling the thus normalized set of essential adiabatic invariants 
Colton et we find 
dee es in are eR 4) 
The v-space which is static with respect to adiabatic action is 
“weightless”: its density @ is simply equal to y(v,,...,v,). The 
quantities v,,...,v~% may be quanticized. Its property which is 
expressed by eq. (22) is nothing but the fundamental law which 
according to PLanck’s hypothesis the quanta-quantities have to obey ‘). 
By our theorem (18") this hypothesis is connected with the adiabatic 
invariants and thus finds a new confirmation. The property of the 
v-space being “weightless” displays the character of this fundamental 
law as a natural generalisation of the -old quanta-hy pothesis. 
§ 4. On the coherence of degrees of freedom. 
From the point of view now attained this very important con- 
ception appears as a natural consequence of our suppositions. If the 
number & — that of the essential integrals and adiabatic invariants 
— is smaller than the number of degrees of freedom », as appears 
from (22), some of the quantities v; must necessarily be of the dimen- 
1) M. PLaANck. Lc. 
