264 
By introducing for g(r) a definite function which vanishes for 
r >t, or, at least approximates to zero with sufficient rapidity as r 
increases, we should obtain from (40) the value of the virial-coef- 
ficient B for that particular law of force. The case mentioned in 
the beginning of this section of molecules which can be regarded 
as rigid spheres of central symmetry exerting upon each other 
central attractive forces') which are a function of the distances 
between their centres, can be obtained from this result by allowing 
p(r) to approximate to — o for r less than o (6 = diameter of a 
molecule). We then get 
4 : 4 
B=—n | ey — 10° + foro .— ar dri, » . (41) 
2 3 3 
in which v==gp(o), so that —v represents the potential energy of 
a pair of molecules which are in contact. 
In this expression for B the first term represents the collision 
virial which, as first shown by Rerncanum, becomes, on account of 
the attractive forces, ef” times greater than the value found in $ 8; 
the second term represents the attraction virial, and is negative since 
p'(r) is negative for attraction. 
For g(r) = — *), in which g is greater than 3, and for which 
he 
c , 
v =—, this becomes 
01 
J 1b 
hv - — ——= (Av)? - — 
hv)... «(42 
pie gaan prans TEEN 
f 1 ; 
which gives, on replacing h by Game 2 betes of ascending powers 
oS 
or =. 
§ 6. The virial-coefficient B for rigid smooth molecules of central 
symmetry, having at their centres an electric doublet of constant 
moment. 
In this section we shall regard the molecules as rigid smooth 
1) These formulae also hold for repulsive forces and for forces which are for 
certain distances attractive, for others repulsive. 
2) The force which two molecules exert upon each other as a whole is then 
proportional to 7r— (g+). On the supposition of forces operating according to the 
above law between the volume-elements of splerical molecules supposed homo- 
geneous the resultant could not be regarded as a function r—9 (with q constant) 
of the distance between the centres. 
