1498 
possible mathematical solution for this case is the trivial one 
of zero pressure throughout the system.) We are therefore con- 
cerned only with cases (1) and (2). 
4.3 Mathematical solution of case (1): Since both equations 
(27) and (28) are hyperbolic, a general progressive wave solution 
may be written down at once. 
f(y, 4) = fy (uspg)t A, (>, g) oe 
MOG Os a7? whale 
where 
it 
er fas’ totys (31) 
2 = 2 9 
wai Wo 6a 7 ee (32) 
and where fi, fo, g, and Bo are arbitrary functions. 
al 
Making use of the boundary conditions given by 
equations (4) and (5): 
Lapp hl) = Glo O.te (33) 
LE aku) _ at, oro? Age) _ Gey 
Ou (34) 
( An ape 
Integrating equation (34): 
ALLE Lape # po)f aa gatp] 28 
= 22 = 
