594 
Adding (l) to (4) we obtain 
t 
A | alee OS ie hap [AEH AAa] + 2 pin Aq EpraÂqna - (m) 
e A 
Supposition C. Let both motions be periodic (periods Pand ?. 
+ AP). Let us now take for both motions the time integral over 
their period. Now 
PhB—= pha, further gaB= qhA 
and 
gnB + ÄqnPp = gna + Aqua 
so that the two last terms of the right hand side of (m) neutralize 
each other. We thus find: 
t 
A | SURT — PIAE + ADAT soe REN 
A 
Supposition D. The motions t and II can be adiabatically changed 
into each other. The adiabatic change {I, IB lasts a time rather 
long compared with P and P+ AP. Only during this time the 
parameter « changes (from a to a+ Aa). At the same time the 
system does the work 
A Aa 
on the outer force. This is just the difference between the energies 
of the motions II and I, the latter being the larger of the two. 
a ge SF) ah ee ee, (p) 
Therefore 
P 
ef “.2T =? + te Me (ge orn 
0 
The symbol 4’ will remind us, that we have not to do with an 
arbitrary variation, but that just two adiabatically related motions 
are compared. This is the proof of equation (3) in § 5. 
Remarks: A: Equation (7) has been deduced already by BorTzMANN 
and Cuiausivs, when thev tried to deduce the entropy law purely 
mechanically without using statistical methods’). 
They do not confine themselves to adiabatic influences and consider 
therefore the quantity : 
AH 22 ANG KO Peo tt (r) 
1) L. Borrzmann. Wien. Ak. 58 (1866) p. 195 [= Abh. Bd. I N°. 2]: Pogg. 
Ann. 143 (1871) p. 211 [== Abh. I NO. 17]; Vorles. Princ. d.Mech. Bd. II. p: 181. 
R. Crausius Pogg. Ann. 142 (1870) p. 4385. 
