342 
30 
which is of a very similar nature. Our approximative, numerical procedure 
applies to (55) in essentially the same way as to (15) in the one-dimensional 
case. 
Numerical investigations of (55) are very desirable, since such 
problems as the decay of a spherical shock belong in this class. This sub~ 
ject will also be considered in subsequent reports. 
§22. Truly two- or three-dimensional problems without the sym- 
metries used in §21 are more difficult to handle. Our general approximative 
procedure still applies, but there seem to be reasons to fear that here the 
necessary number of "molecules" becomes inconveniently large. As pointed 
out in §20, |4 or slightly more "molecules" may suffice in one dimension, 
but this suggests that /[+“% > 200. ana (434— 3 000 may be 
needed in truly two- or three-dimensional problems. These numbers seem too 
high for the existing machines, although 200 "molecules" are perhaps not al- 
together beyond capacity. The subject will be investigated further, particu- 
larly in view of the great importance of the hydrodynamical problems which a 
success in this direction would make accessible, 
In the truly many-dimensional cases the possibility of using other 
types of machines will also have to be investigated. In this respect the 
relay-selector type machines seem very promising among the "digital" ones. 
The exploration of the "non-digital", "physical analogy" type machines is al- 
so being undertaken; some of these seem to be quite promising, although of 
lower precision than the "digital" machines. 
