587 
its velocity. This causes the motion to take place no longer in a 
closed curve, the path becoming a rosette and an uncertainty arising 
as to the limits between which the integrals in (23) have to be 
taken '). In order that we might make a conclusion from the view- 
point of the adiabatic hypothesis, it would first have to be investi- 
gated, which quantities are adiabatically invariant in this case. 
§ 8. Connexion of the adiabatic hypothesis with the statistic 
basis of the second law *). 
BoLTZMANN’s statistical mechanical deduction of the second law 
and especially of the equation 
EA Aa, + A,Aa,+... 
_@ 
has been based upon a definite agreement as to what regions in 
the (q,p) space for the molecules (‘“u-space’”’) will have to be consi- 
dered as “a priori equally probable’. As such regions were taken 
sak A log He Ea 3 (26) 
» 
/ » 
to which in the g-space equal liga | Ser f dq,....dpn viz. 
ev 
correspond. BotrzMANN ascribes the same weight to each part of 
the u-space 
G (g, p) = constant 
By the hypothesis of PLanck’s energy-steps and its generalizations 
this no longer holds, for here a weight 
G (q; Ps @) 
dependent on gq, p, and a we may say to be introduced. In 
other words to all regions of the g-space the weight zero is ascribed, 
except to the discontinuously spread ‘‘adinissible” regions, the situation 
of which is defined by the value of the parameters a. Here espe- 
cially this last circumstance is of importance. 
The problem may be formulated in the following way: How 
must we confine the choice of the weight function G(q,p,a)—how 
that of the “admissible” regions especially with regard to their depen- 
deney on the «’s—in order that Boirzmany’s equation (26) remains 
valid ? 
This question has been treated by the author, first in a special 
case *), afterwards generally *). 
1) A. Sommerretp |. c. p. 499 
2) Comp P. Enrenrest. Zum Bourzmany’schen Entrepie-Wahrsch. Theorem. Phys. 
Zschr. 15 1914 p. 657. 
3) Comm. A (1911) § 5. 
4) Comm. D (1914). 
