L044 
aperiodic region: indeed, as soon as ZL becomes negative, it is 
impossible to satisfy (55) with a positive set of values of A and M. 
As before, in the aperiodic region the lines, along which i is 
constant, are straight lines, determined by equation (55) ; the boundary 
between the periodic and the aperiodic regions (7’—= o, 0 =o) is 
the envelope of these straight lines. The case is represented in the 
adjoining qualitative diagram (fig. 2) which gives the condition when 
J 
k’—R is finite. Owing to the values of 7 being limited in the 
aperiodic region the bounding curve does not touch the J/-axis 
asymptotically as it did in the case when R’—R was infinitely 
small. In the periodic region the curves 0 — const. and 7’ = const. 
are similar to fig. 1, except in so far as they now intersect the M-axis 
as in the diagram of Comm. 148c; indeed fig. -2 obviously forms a 
transition between fig. 1 and the diagram mentioned, in the latter 
of which the boundary coincides with the A-axis. 
8. The above equations also hold in the case, when R’ < R. 
It appears, however, that by putting 2’ = 0 — in order to pass to 
the case of a sphere filled with liquid —- w becomes infinite for 
