444 
DE. ANDEEWS ON THE GASEOUS STATE OF MATTEE. 
one another ; in the second state, or state of change corresponding to the fall to the 
liquid, this ratio changes rapidly ; while in the third, or, as we may designate it, the 
liquid-volume state, new molecular conditions supervene, as shown by the increase in the 
value of p. 
As the result of the foregoing investigation, the relations between pressure and 
volume in the ordinary gaseous state at different temperatures may be stated in the 
following terms : — 
On any two isothermal curves which show the volume of carbonic acid gas under 
change of pressure at definite temperatures, the values of p at the homologous points 
being always equal, or 
pv=p'v' (A) 
(where, it must be carefully observed, v and v 1 are the volumes of the gas on different 
isothermals), it has been shown that for all such homologous points on any two 
isothermals 
(B) 
where ^ is a constant. 
The full import of homologous points will be further understood from the following 
considerations : — Let the line a b represent a volume of carbonic acid gas at the tempe- 
rature t and pressure p, and let the pressure be increased to p', the new volume a' b' of 
the gas will be less than a b~,. Let the gas be now heated at the pressure p' till its 
