( 299 ) 
Analytically we bring this into the following form. As for each 
point of the pvT-surface 
de = dp - 
dp = 5). do + (55), dT 
Ee af OAN +. 
and as at the critical point (2) is equal to zero, we obtain for each 
JT 
curve passing through that point 
Gn 
en 
We are uncertain of the equality only when the curve has an 
element in common with the isotherm. In this case the value of 
dp\ dv : hte: ey: 
Gu) ap must be more closely investigated. This strict investigation 
V/T 
would therefore be also required for the border curve were this not 
rendered superfluous by the proofs 1 and 2. That the relation 
d d 
(F) =(¢ ) holds for the border curve must be ascribed to the 
AT’) cote or v 
circumstance that the latter lies in a cylinder surface, as mentioned 
above, which touches the pvZ-surface at the critical point. 
From a graphical representation of p as function of v in the 
neighbourhood of the critical point according to AMAGAT’s data 
for the isothermals of carbon dioxide 1 found: 
(=) — 7.3 and C4 ee ) = — 32.2 
T dw dr 
putting the critical volume 0.00426 and C,= 3.45 while 
would follow from an extrapolation of AMAGAT’s observations for 
the vapour pressures. 
With this uncertainty in (=) it may be well to investigate what 
OT 
would be yielded by different equations of state. _ 
