830 
or putting a = const. approximately and representing the derivatives 
with respect to a by dashes: 
fr (a EEEN | 
inter OEeDn emule ee 5) §=1,2,...50 F: 
( ae ). ie 
zo Tapirepitivio v haine hd 
tan 
Since the equations have the canonical. form, we have as the 
fundamental A 
3 (ee dr tn 
Here we may not as before take 20. A further difficulty 
a 
presents itself: starting from a special line parallel to the ¢,-axis in 
the (c;, ti) space -— a special ‘‘stream-line’ — if we now vary a 
as equation (3) or (3’) show, the stream-line becomes broken up. 
If we then keep a constant again and take together the points, that 
lie on a straight line, @ will vary along this stream-line, since it 
contains points of different origin. Thus on the new line @ is not 
stationary, but explicitly dependent on ¢,. 
We now form *) the time-mean of 9, which we shall call @ and 
the difference e—o. Since fa (o—o) = 0, the quantity e—e in its 
dependence on ¢, shows elevations and depressions round about Q, 
the sum of the surfaces of the former being equal to that of the 
latter. Each point carries its g—g value along with it and hence 
the curve shifts regularly with the time ¢,. A stationary curve 
represents the tendency towards condensation (in an elevation) or 
rarefaction (in a depression) for the points of the stream-line, on the 
supposition of the change of a being sufficiently small. If we make 
our moving curve slide along the stationary one, in the course of 
time elevations will cover depressions ‘and vice versa. A further 
small change of a may therefore produce a diminution of the diffe- 
rence g—o. By this reasoning it becomes clear that starting from 
a stationary density a sufficiently slow change of a will to a corre- 
sponding degree of approximation produce a stationary density *). 
1) For the method now following comp. J. W. Grsss. Statistical Mechanics. 
Chapter XIII. 
8) Comp. J. M. Burcers. Proc. Amst. XX (1916) 149, Ann. d. Phys. 1917 
(2) and my paper in the Proc. Amst. |. c. 
