316 
Sats The considerations which follow apply to any gas or liquid 
in which compressibility is taken into account, but viscosity and heat con- 
duction are neglected. From the point of view of gas dynamics such a sub- 
stance is conveniently characterized by its caloric equation of state, which 
specifies the internal energy UJ as a function of two characteristic param= 
eters, preferably of the specific volume y and the specific entropy Ss 3 
(1) Om Ss) 
Then the density Q is 
| 
(2) Sa a eee 
Vv 
and the pressure p and temperature ae are given by the eauations 
(3) Pie eS |, Siege Soke 
ov os 
The equations of motion will be stated in the Lagrange-ian form, 
for the main part of this discussion one-dimensionally. Then each elemen- 
tary volume of the substance is characterized by a label q, its position 
being X at the time at , rhe purpose of the equations of motion.is to de- 
termine % as a function of @,UC. 
(4) me ane) 
It is convenient to choose the label a in such a manner that the substance 
contained in the interval “A, a+ da has the mass cL.@ . T.,e. that the 
“density in the label spacet' is identically {, This being understood, it 
is immaterial whether the label @ is also the position yx at some "initial 
instant" t A (which is frequently the case) or not. 
With the above convention concerning the label, the specific volume 
Vv is simply given by 
x 
(5) y 402 
(7 
e 
The conservation of momentum states that 
