271 
5 ! 
becomes — B, in agreement with the circumstance that both q, and 
“ 
r,;, but not p,, participate in the heat equilibrium in consequence of 
the torques exerted by the doublets upon each other. 
For the thermal equation of state we again get (39), with 5 now 
equal to 
Ek gn P 55 
af ois BRA it Oe onbe se Dont lane (55) 
in which 
Tr nm 27 
—hu 
PS ffe ie —-1) r° sin O, sin O,drd0 ,dO,dp . . (56) 
cs 000 
P’ is convergent for t=, so that as far as (55) is concerned 
the assumption is no longer necessary that the field of the doublet 
is annihilated at distances greater than +t (the same is true for 
(53) if P’ is introduced in the expression for s). 
In order to evaluate the integral P’ we shall write 2 cos 6, = 
geosp and sind, =gsinw (g20,0<w<a), so that 
2 cos O, cos 0, + sin O, sin A, cos p = g (cos W cos A, + sin w sin A, cos p). 
In the plane containing the line 
BA and the axis of the doublet at 
A draw an angle CBE == w, and 
introduce the angles HBD = & and 
CED =p' as the new independent 
variables instead of 0, and p *). The 
integration with respect to p' gives 27. 
Fig. 5. Integration with respect to ® can 
also be done with ease. Let us then substitute g as independent 
variable instead of 6, and we get 
in which 
2 dg 
— (e7—e 9 — 209), 
cv3 Vg —1 
1 
1) This comes to the same thing as introducing the angle between the axis of 
the doublet B and the field at that point caused by the action of the doublet A. 
Cf. Van per WaAts Jr. These Proceedings June 1908. 
