1)74 



1 

 If ^ — <^ 1 we obtain those cases which we are accustomed to call 

 n 



"adsorption". Analogous to (8) we ought to attribute here the devia- 

 tion from Henry's law to "dissociation". But nothing of the kind 

 has been found experimentally. 



JO. Hence, in the above-mentioned matter, I believe I have 

 demonstrated that Henry's law (law of division) and tlie law of 

 Proust are si)ecial instances of the adsorption-isotherm. This is in 

 complete iiarmony with the results of the investigations recently 

 published by Reinders M and Gkorgievics ^). 



Zwolle, February 1914. 



Mathematics. — ''Cubic involutions in the plane". By Prof. Jan 

 DE Vries. 



(Communicated in the mcoling of February 28, 1914.) 



1. The points of a phxne form a cubic involution (triple involution) 

 if they are to be arranged in groups of three in such a way, that, 

 with tlie exception of a finite number of points, each })oint belongs 

 to one group oidy. Suchlike involutions are for instance determined 

 by linear congruences of twisted cubics. The best known is produced 

 by the intersection of the congruence of the twisted cubics, which 

 may be hdd through five fixed points ; it consists of oo^ polar 

 triangles of a definite conic (-Reye, Die Geometrie der Lacje, 3^ Au/lage, 

 2*^ Aldheilung, p. 225). According to Caporali ') it may also be 

 determined by the common polar triangles of a conic and a cubic. 

 A quite independent treatment of this involution was given by 



Dr W. VAN DER WOUDE "). 



In what follows only cubic involutions will be considered posses- 

 sing the propert}' that an arbitrary line contains one pair only, and 

 is consequently the side of a single triangle of the involution. The 



1) KoUoïd. Zbitschr. 13 9G (1913). 



2) Zeltschr. f physik. Ghem. 84 353 (1913). 



3) Teoremi sulle curve del terzo ordine (Transunti R. A. dei Lincei, ser. 3a, 

 vol. 1 (1877) or Memorie di gei»metria, Napoli 18S.S, p. 49). If a\. = and^>2^. = 

 are those curves, then the involution is determined by ay^aya^ = 0,h^.h =0, 



*) The cubic involution of the first rank in the plane. (These Proceedings 

 volume XII, p. 751—759). 



