253 
dip dÔ dy = A, B, sin O dp, dq; dr, 
if we stipulate that the sign of equality in this and similar expres- 
sions means that in the integral the expression on the left may be 
replaced by that on the right with the proper modification of the 
limits of integration. 
Let us further write do for an element of the surface of the sphere 
of unit radius, by points on which we can indicate the direction of 
the axis of revolution of the ellipsoid ; we then obtain 
do 
sin 0 
dp dô = 
Hence 
dp dO dy dp dO dy = A, B,? do dy dp, dg; dr. 
We shall therefore obtain micro-elements of equal probability (cf. 
p. 246 note 2) if we measure equal dw’s, equal dw’s, equal do’s, 
equal dy’s and equal dw,’s, and combine them. 
If each molecule is assigned to a particular micro-element, then 
the micro-complexion is completely determined. 
The number of individual macro-complexions in the group macro- 
complexion is 
n! 
. Merde ie i ee 
(compare what was said concerning the corresponding expression in $ 3). 
The number of micro-complexions in the individual macro-complexion 
is determined as follows : 
The various volume-elements dv are again independent of each 
other (cf. $3). Let us consider the 7, molecules in dv,. To each 
molecule we ascribe its proper speed of translation §&, 4, and speed 
of rotation pr, qr, rr determined by (15). We then “place” the first 
molecule in one of the v elements dy, then in one of the x ele- 
ments dw and lastly in one of the u elements do. This can be done 
in xuv different ways. 
We now dispose of the second 
molecule. For this we have still » 
elements dy at our disposal, but 
for the other coordinates there 
are fewer places available than 
was the case with the first mole- 
cule. Outwards along the normal 
to each point of the first ellipsoid 
mark off a distance a (equal to 
half the major axis) (Fig. 2),then 
each dw outside the surface thus 
Wie 
