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portion of a “surface” of 12 dimensions and the quantities q,. .p, 
play the part of curvilinear parameters on this surface. 
We define!) the following expression as the ‘“u-weight” {u} of 
this region: 
oy = h3 E+4+5)—6 a À fan re dg, dp, >. . UP a 
where the integration is to be extended over the region in question. 
In future applications ($ 4) the molecule will have to pass through 
the total volume V of a vessel and similarly through all possible 
orientations. Accordingly, integrating with respect to the co-ordinates 
q, we have 
fu} = Get —8 dar Barf. (dp, … dp, Scr EN 
The corresponding expressions for di- and mon-atomic molecules 
are as follows 
e= tds VA. | fap, dp .. a 
at weet 80. fa fdpy dps ann 
In (8) EH n=? and in (4) =1, but we have left the power 
of h in its above form in order to obtain the formulae in our 
calculations later on as symmetrical as possible ($ 4). 
§ 3. The constitution of the gas-mixture. 
In a vessel of volume V X, Y, Z atoms of say 3 different chemical 
elements (atomic masses mz, m,, mz) may be introduced. These 
molecules can associate to molecules in a number of different ways. 
At a special moment let there be present j different kinds of mole- 
cules; a molecule of the kind 2 may consist of &;,1;,5; atoms and 
may possess the following mass, moments of inertia and potential 
energy respectively : 
Mi; B Oo Ris Gs, a Se 
The arbitrary constant contained in 4;, we shall fix by the follow- 
ing rule: we shall ascribe to the atoms a potential energy 0, when 
they are completely separated from each other; y; is therefore a 
negative quantity, viz. equal to the negative work which the atoms 
give off, in uniting to form the molecule. 
It may happen that, owing to the special distribution of similar 
atoms in a molecule, the latter possesses more than one completely 
) Comp. the illustration of this definition by means of a special simple case 
n addit. notes I. 
RM MN 
