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en 
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may be brought about. The chance, that the volume element dr 
contains no molecule is the chance, that all the » molecules of the 
unity of volume lie outside the element. For one molecule this change 
is 1—dr, so for the x molecules (l1—dzr). Now the moment Mr 
may be brought about by the fact that in g elements dz we have no 
molecule, in p—q—1 we have a molecule, every one of which 
has an arbitrary amplitude az: and in the last element with the 
amplitude „an == Ma — Saz,. The chance of being brought about 
in this way, is: 
(1-—.r)"9 (ndt)P—4 Py (1441) Fi (541) one F, (p = q—{r1) Fy, Mins A1) 
d (Gazi) d (gai) « « « d (p—qg—az1) d Man. 
We find the total change for an amplitude between AM, and 
M, + dM, by first integrating with respect to jaz1 , 241 « « «pg Gi 
between the limits — oo and +, and by adding the results 
for all values of g. 
As we have to do this for the case in which p=o, we execute 
this addition by multiplying with dg and by then integrating with 
respect to g between the limits 0 and co. These formulae hold 
always, independent of the size of AzAy Az, and as we have found 
for it for a region with many molecules 
2 
Mz 
EUV see ew hares dS YinA xz. Ay. Az. 
Oya 5 
this formula will also hold if Az Ay Az is so small that the chance 
that it contains a molecule, is slight. 
In this we have assumed, that the fact, that at a certain point 
P a definite moment [Mei] prevails, has no influence on the chance 
for the moment of the immediately surrounding points. This would 
be true only if the molecules themselves had no extension. If how- 
ever point P lies in a molecule, which has extension, the surrounding 
points will also have moments of the same direction and the same 
phasis as P. If this circumstance however, causes a deviation from 
the here derived law of probability, it will probably be very small 
for gases. 
Our resuit shows that in the unity of volume the total region 
in which /; is contained between the limits f, and A + df, is: 
