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systems with only two coordinates « and y, which are subjected 
to the condition that and y must be equal and continue to be so. All 
systems will then be found on the line OA and will move in the direction 
of this line, so all systems leaving the element of space drawn in 
the figure, or entering into it, will pass the two limits dv and dy at the 
same moment. If the condition is not that r and / must be rigorously 
equal, but only that thei difference must be very small, then all 
systems will be huddled up very near the line OA and a great part 
of those that pass the limit dv will also pass the limit dy. It is evident, 
that this circumstance is caused by the fact, that within the element 
dx dy the density is not homogeneous. If we choose therefore the 
the dimensions dr and dy so small, that the whole element lies with- 
in a region, where the density may be considered as constant, then we 
may again assume that the number of systems, passing both limits 
may be neglected, compared with the number of systems passing only 
one of the two limits. — 
If we choose therefore [(df‚)| and [(de‚)| small compared with the 
ROE A i DE Og ae 
mean vaiue O ae : ale (Gia) 
ratio to de®, and Jt again small compared with the quantities |(//,)| 
and |(da,)|, so e.g. having a finite ratio to dr”, it appears that in 
fact the number of systems passing more than one of the limits may 
be neglected. So the proof of the law of conservation of density-in- 
‚so e.g. having a finite 
phase is complete. 
The quasi-canonical distribution. 
If we wish to distribute the systems of an ensemble over the 
different phases in such a way, that the distribution does not vary 
with the time, so that the state of the ensemble is stationary, it is 
evident that we have to choose for P a function of the coordinates, 
which is constant in time. GaBBs chooses for this purpose the function 
/ 
e where & represents the energy of a system, and wp and @ are 
constant quantities for a given ensemble. He calls this distribution 
the canonical distribution. This simple law cannot be applied to 
systems consisting of ether. If we assumed it, the quantities |‚f] and 
[el would vary abruptly from element to element instead of varying 
fluently, and moreover the distribution would depend on the dimensions 
of the elements of space, which we have arbitrarily chosen. We 
must therefore assume another distribution which secures a fluent 
variation of the electric and magnetic displacements. 
