( 341 ) 
Mm, (2 1 m?,,m a 
Vapl = Uxk + |e vy. (a—-) mG ot pt a 3 RT, mi, aon 
30 
which formulae, after some reductions, can be put in the form in 
which Kersom has given them (Comm., n°. 75). Also the following 
well known equation *) results directly from equations (59) and (60) 
Pxpl— Pak = ky, (Fapt— T xk) Cele J eae baa” yee ce (62) 
which also according to equations (49), (50), (55) and (57) holds for 
the coordinates of the critical point of contact and for the apex of the 
border curve. 
From the coordinates of the plaitpoint of mixtures of carbon 
dioxide with a small proportion of hydrogen *) («= 0, 0,05 and 0,1) 
I derive the following formulae’ 
T pl T (1 — 0,30 a + a) 
Papl = pe(1 + 4,42-+ 112?) Ae spare wan ta nd tO) 
Vapl= vr (1 — 0,402 — 8 2?) 
In connection with the formulae (16) I obtain directly from these : 
Papl Prk 
1 “cpl — Tar, 
—1,66(1 + 2), 
in good harmony with equation (62) (£,, = 1,61) ®). Using the value 
k = — 513 ®), I moreover find that the formulae (59) and (60) 
applied to mixtures of carbon dioxide and hydrogen become: 
Prpi=T, (1+ 0,038 2) and pryi—pel +642); . (63) 
hence the agreement with the formulae (63) is decidedly bad, as has 
also been remarked by Krrsom (oc. cit., p. 13). We cannot, 
however, draw any conclusions from this; it is improbable 
that the inaccuracy of the data should cause this great deviation ; 
but from the fact that terms of higher order produce such a great 
influence in the mixture « — 0,05, we see that quadratic formulae 
are very unfit for this comparison °), the more so as it appears from 
1) Comp. v. p. Waars, Versl. Kon. Akad., Nov. 1897. It also follows directly 
from the equation of state (13) in connection with (15), by expressing that the 
elements of the plaitpoint satisfy this equation and by neglecting terms of a higher 
order than the first. 
2) VeRSCHAFFELT, Thesis for the doctorate, Leiden 1899. 
3) Comp. also Kersom, Joc. cit., p. 14. 
RN Er dr 
*) Derived from ——- —- == — 32,2 (Keesom, p. 12). 
Pv]: OWOT 
5) By introducing the values for 2 =0,2 (comp. Verscuarrett, Arch. Neerl., 
(2), 5, 649 ete, 1900, Comm. n°. 65, and Keesom, loc. cit. p. 12) they certainly 
will not become better. 
