(834 7 
in the last term I shall express the co-efficient of (,—yr%)° for cori- 
venience by A. 
Substituting this in equation (30) we obtain to the first approxi- 
mation an equation of the second degree, which now no longer 
represents a parabola but an ellipse or a hyperbola. The coordinates 
of the centre are: 
i Mor 1 2 Me M40 
= pTe and ve = vx, — ———{| =m -———— ET 
den d RT ms, BAE on k 
while the straight lines 
p=prT and v=or + DP 
are conjugate axes. With respect to these axes the coordinates of 
the border curve are p and p,—pz, so that the equation of the 
border curve with respect to those axes is: 
m, 
PK (pp) == t= — — (TT). 
Mao i 
In the same case the equation of the ee line is: 
Pp, — Km’,, (weer) = — = *(T—T;,), 
3 30 
with respect to the conjugate axes : 
e=eT, and v=v7y,.4+ DB; 
Fees : : : 5 > Pi PTE : 
where #' is obtained through substituting «—«7,; for — in @, 
Moy 
We must now distinguish two cases. 
a. K<0O; the equations of the border curve and the connodal 
line represent ellipses. Provided 4,, << Oand #,, <0 these ellipses are 
real when 7’< 7}; they lie only partially — to the first approxi- 
mation half — in the real part (wv > 0) of the y-surface. We find 
two plaitpoints of which only one is in the real y-surface and two 
critical points of contact co-inciding with the plaitpoints (at least to 
the degree of approximation considered here, i. e. to the order 
V(T—T;); the coordinates of these points are: 
1 PRE 
en ee a Kh, (1 — Tx) 
30 
Drie =P meld (LT 
Pl Te — PT Kk, k) 
Moy sale! ta kay ye Bi 
UTyl = UTr — Ve : Hm, —_ (T—T}). 
shee a Ae Moy Ms (RL; sE Kk t) 
If 7—T7;, the border curve and the connodal line shrink to 
one point, the critical point of the pure substance; and if 7'> Tj, 
there is no longer a border curve nor a connodal line. 
