317 
a ?.) 
(6 Dex 2 -y (28) 
+ 
i.e. by (3) and (5) 
(7) te Spe eee 
oC Mea ie \ /S 
The conservation of energy, on the other hand, gives a relation which is 
easily transformed with the help of (3) and (7) into 
(3) oh See 
Wie 
In all these equations q@ i 6 are the independent variables. 
§2. Equation (8) implies that if S is constant at some initial 
instant € = ee , then it stays constant at all times, and so (8) can be 
replaced by 
(9) < = Se = Constant. 
This principle of isentropy then makes (7) the sole equation governing the 
motions, and renders the problem amenable to analytical or numerical treat- 
ment. 
It is essential to realize that the decisive equation (8) expresses 
the conservation of energy, and nothing else. MThus, although it involves 
the specific entropy alone, it expresses nevertheless the first, and not the 
second law of thermodynamics. Furthermore, since (8) secures the constancy 
of specific entropy along the world line of each elementary volume, the sec-- 
ond law, which requires that specific entropy should never decrease along 
that line, does not now impose any additional restriction. 
§3. It is well known that a motion satisfying (7), (8), develops 
sooner or later a discontinuity of the first derivatives ox ; ax . More 
On Pes 
precisely: apart from exceptional and degenerate cases, no solution can be 
