72 
Proceedings of Royal Society of Edinburgh. [sess. 
agreement with the experimental data for carbonic acid. The critical 
temperature is too high, the pressure and volume both too large. 
The isothermals which it gives, for temperatures at various inter- 
vals above and below the critical point, are very similar in their 
general form to those originally given by Andrews, with the modi- 
fication suggested by J. Thomson. In one respect, however, they 
show a considerable divergence of character:— viz., in the position 
of the point of inflexion in the vapour region ; which appears to be 
somewhat too far outside the region of saturated vapour in presence 
of liquid. 
If we write next 
97g j_ T 
?'(Y - •‘ > >) •= 1000" ^ 
15,984 9250 
V-l + Y^2 
we find, at the critical point, 6*87, 74 atm., 30° C. This presents 
a pretty fair agreement with Andrews’ data, and is not liable to 
the objection raised against the former tentative formula, probably 
because j3 has been taken greater than either a or y. As the same 
may be said for very different sets of constants, such as 
P (V-1)=1000^ 
62,390 55,829 
Y + 06 + V + 0-4 
it is clear that nothing definite can be asserted as to the true values 
of the constants until the labour of deducing them directly from 
the experimental data has been successfully undertaken. The result 
might give us some real information as to the range and intensity 
of the molecular force. 
If we assume the critical values V 0 , E 0 , p 0 , from experiment, the 
general equation of the Isothermals takes the form 
MV-/5) = E-^{ 
(V°-y ) 3 
V-y 
( V 0 -*) 3 l 
V-a j 
in which the disposable constants are reduced to two. For there is 
a single relation among a, /?, ana y, viz., 
3Vo = a + / 8 + y+- 0 . 
po 
This, like the values of A and C, is given by the condition that 
the three values of V are equal at the critical point. 
