454 
The development of the theory is most easily carried out in terms of the 
label (Lagrange) coordinate I, , the position in the undisturbed fluid of 
density 9, of a volume element which at time t has the position f. The 
transformation from the Eulerian coordinate }* to the Lagrangian coordinate 
Y, is effected by means of the definition, 
or 
icra = eal (8.3) 
" 
and the Lagrangian equation of continuity, which is 
mie 
or Mae 
) t = Are (8.4) 
"5 t FP 
for spherical symmetry. Eqs. &.2 are thus transformed to 
‘ J 
(EET DIR eae 2 - au , 
Ac Te iid 
Ou ré p) = O 
bose” Ke 5t ; (2.5) 
YVilw 
ct 
f 
-_— 
i 
et 
~——— 
Ne 
where W is the particle velocity, p the pressure in excess of the pressure 
bo of the undisturbed fluid, is the density, Pe the density of the undis- 
turbed fluid, t the time, and ji* the Euler coordinate at time t of an element 
of fluid with Lagrange coordinate " - Eqs. 8&5 are supplemented by the 
equatio.. of state of the fluid and the entropy transport equation d5/ ot =0 5 
the latter of which we shall not explicitly use. Eqs. 8.5 are of a hybrid 
form in that we use the Lagrange coordinates ie and t as independent 
65 
