595 
as the added heat. Then equation (72) becomes: 
PALO DARL as EE ee 
or 
A 
NQ SCE LOGE ol) De EE A Ae 
7 
This equation is then compared with the entropy law. 
B. BorrzManN has further investigated, whether it is possible to 
alter the above considerations, referring to systems with periodic 
motions, in such a way that they may be applied to systems with 
quasi-periodie motions e.g. to the motion of a point in a rosette 
under the influence of a centre of force’). 
Now the terms p,Ag, in equation (n) give rise to difficulties. 
These terms do not vanish now, neither by an integration from one 
perihelium to another, -nor for one on a complete rotation (p = 0 
to p= 2a). Therefore BorrzmannN has still tried the following: On 
both paths he chooses such stretches that these terms vanish and 
speaks then of “orthogonal” variations of the end configurations A 
and 2. If however we pass from a motion | through different 
intermediate motions to a finitely different motion (N), going back | 
again to (/) through other intermediate motions, then the succeeding 
“orthogonal” variations finally give other end configurations A and 
B for the motion than those from which we started (BoLTZMANN 
has illustrated this with examples). 
From this BorrzMANN concluded that the second law would have 
to be derived not by means of pure mechanics, but only by statistic 
mechanics. Proceeding as in § 7 it is however possible to indicate 
adiabatic invariants also for such a case. 
AvP PBN.) PX SEL 
Motions in an isotropic elastic field of force according to the 
quantum hypothesis of Sommurrer.y. Comparison with Pianck’s formulae. 
Let us put: 
| 
p= eae 
oe “ee ! | (a) 
n= DP, mij 
Then according to SOMMERFELD : 
fa ap mn See tO) 8 fa ap =a Et oee mare 
Now we have however: 
1) L. Bourzmann. Bemerk. über einige Probleme der mechan. Wärmetheorie 
Cap. Ill. (Wien. Ak. 75 (1877) p. 62---100 —= Abh. Il. p. 122); Vorles. über 
Prine. d. Mech. Bd Il. p. 156. 
38* 
