267 
number corresponding to this freedom immediately after the index 5. 
The group macro-complexion is then determined as follows : 
in dv, dw, (dq: dr), “there are” mn, single molecules 
Nin molecules belong- 
ing to pairs of molecules with 
the freedom (dr dé, dé, dp), ete. 
(43) 
Determination of the micro-complexion : 
For this as in the treatment of smooth ellipsoids at the conclusion 
of $ 4 we subdivide the respective spaces into equal dw’s, equal dw’s, 
equal do’s, equal dy’s, equal dp,’s and equal (dq, dr,)’s. If these are 
determined for the position of each molecule, we have then a definite 
micro-complexion. We may refer to § 4 for the proof that the micro- 
complexions thus determined represent cases of equal probability. 
The number of individual macro-complexions in the group macro- 
complexion is 
nl! 
Nara! 241141 EE Er 
The number of micro-complexions in the individual macro-complexion: 
To determine this the macro-volume-elements are again to be 
considered as independent of each other. Let * represent the number 
of equal micro-volume-elements dw,,... in dv,, u the number of 
equal elements of surface of the unit radius sphere, points on whose 
surface give the directions of the axes of the doublets, v the number 
of equal elements dx (y= the angle representing the rotation of the 
molecule around the axis of the doublet), and »’ the number of equal 
elements dp, (pr = the speed of rotation around the axis of the doublet). 
We shall first ascribe to each molecule its dw, its do, its dy, and 
its dp, for each micro-complexion ; we shall then give it its dw and 
~its dq,di, as specified by (43). The latter is then without influence 
upon the number of micro-complexions. 
In dv, we have to place 7, specified molecules : 
Ben enen ee Mig ine ar dr (EN 
Of these 7), specified molecules are single 
Ni 3 iy belong to pairs with the freedom 
(dr dé, dé, dp), 
if Na = Nana Fr Nanga « ++ Mea +. 
45 
Mn = Ayub Men «Mam. EE 
The placing of the 7, molecules (for the approximation here 
18 
Proceedings Royal Acad. Amsterdam. Vol. XIV, 
