( 348 ) 
tact curve with respect to the plaitpoint curve corresponds to the 
position of the critical point of contact with respect to the plaitpoint 
on the border curves, represented in an exaggerated way in fig. 16. 
To the second approximation those border curves are parabolae 
which touch the plaitpoint curve and have a vertical tangent at the 
critical point of contact, but to the first approximation they co-incide 
with the axis which is conjugate to the vertical chords and the 
equation of which according to (47), is: 
P == Pak a5 Koy eS T xk) = Pzpl Se kos (T—T pI). 
Hence these straight lines are parallel with the vapour pressure 
curve of the pure substance and terminate, on the plaitpoint curve, 
in the plaitpoint of the mixture to which they belong. 
14. Continuation of § 9: the critical point of contact. 
Mr. Kresom kindly informs me that the method given by him in 
Comm. N°. 75 and which leads very easily to the constants of the 
plaitpoint presents difficulties when applied to determine the constants 
of the critical point of contact. 
He however succeeded, by means of the method used by me in $ 9, 
in deriving the constants of the critical point of contact from the 
formulae '), given by Kortewee in his paper “Ueber Faltenpunkte”, 
Wien. Sitz. Ber. Bd. 98, p. 1154, 1889, and proceeded thus. 
It has been shown in Comm. N°. 59%, p. 367) that instead of 
deducing the coexistence-conditions by rolling the tangent-plane over 
the y-surface, we can also obtain them by rolling the tangent-plane 
over a w-surface, the latter being deduced from the y-surface by 
making the distance, measured in the direction of the y-axis, between 
this surface and a fixed tangent-plane the third coordinate perpendicular 
to z and v. We can go a step further in this direction by deducing 
a y’-surface by means of KorTEWEG’s projective transformation *) 
. on, _, (ou 
var)" (Ge), 
OH 
vi 
Here wy = WW — wry! 
a! = £ — ET 
v == v0 — VTpl 
') The simplest way of proving that the case c; = «in Kortewee’s formula (4) 
does not influence the present deduction, is by notin, that the area over which 
the development is applied is infinitely small in comparison with xT',. 
2) Proceedings Sept. 1900, p. 296. 
5) See Kortewee |. c. equation 38. 
