341 
29 
this represents already a result which cannot be obtained by classical 
methods in the rigorous, hydrodynamical theory: the "collision" of a shock 
and a rarefaction. 
It is proposed to extend this method to more problems of this lat- 
ter type, involving more complicated one-dimensional interactions of shocks 
and rarefactions. The experience with Problems 1, 2, 3 shows that a "sub= 
stance" with 14 or 29 "molecules" is fully adequate to describe the finer 
nuances of hydrodynamic motion. We believe therefore that the possibilities 
which are opened up by this method are considerable. 
The equation of state (41) 
p2i-vttiv 
must of course be replaced by more realistic ones. Actually non-polynomial 
equations, e.g. the "adiabatic" 
(54) pe vo? 
can be handled by the punch-card equipment through appropriate arrangements 
quite simply and efficiently. 
Ali these problems, as well as the extension from the special equa- 
tion of state (18), (19) to the general one (1), (3), will be dealt with in 
subsequent reports. 
§21. Among more-than-one-dimensional problems, those of spheri- 
cal symmetry suggest themselves first. Here x and & may be viewed as the 
distances from the center of symmetry of the physical space or the labcl 
space, This replaces the hydrodynamical partial differential equation (15) 
by 
