1055 
Chemistry. — Note on our paper: “The Allotropy of Lead 1” 
by Prof. Ernst Corner and W. D. HerDERMAN. 
In our first communication on the Allotropy of Lead *) we stated 
that we resumed our investigations on this subject after having 
received a letter from Mr. Hans Herrer in Leipsie which showed us 
the way in which fresh experiments had to be directed. In this 
letter Mr. Herrer kindly invited us to continue these investigations. 
As Mr. Herrer writes in a letter dated Jan. 21st 1915: “Gewünscht 
hätte ich freilich, dass der Ort, an dem ich meine Versuche machte, 
das hiesige Chemische Laboratorium, in der Veröffentliehung genannt 
worden ware’, we comply with pleasure with his request by publishing 
the above statement. 
Utrecht, January 1915. VAN ’T Horr- Laboratory. 
Mathematics. — “Characteristic numbers for a triply infinite system 
of algebraic plane curves” By Prof. Jan pe Veris. 
(Communicated in the meeting of Dec. 30, 1914). 
1. The curves of order n, c”‚ of a triply infinite system I (complex) 
cut a straight line / in the groups of an involution /,° of the third 
rank. The latter possesses 4 (n — 3) groups with a quadruple element ; 
/ is consequently four-point tangent, ¢,, for 4 (n—3) curves c”. Any 
point P is base-point of a net N belonging to I, hence point of 
undulation, #,, for si curves c”".*) If ¢ rotates round P, the points 
Rk, describe a curve (R,)p of order (4n—6), with sixfold point P. 
The tangent ¢, cuts er moreover in (n—4) points 5; the locus 
GS)p has apart from P, 4 (n—3)(n—-4) points in common with /. 
The tangents ¢, of a net envelop a curve of class 6n (n—3) *);-as 
P is sixfold point on the curve (#,) belonging to the net determined 
by P, P will lie on 6n (n—38) — 24 or 6 (n—4) (n-+1) tangents t, 
of which the point of contact FR, lies outside P. So P is a 6 (n—4)(n-++1)- 
fold point on (S)p, and the order of this curve is 4 (n —3) (n—4) 
+ 6 (n-+1)(n—4) or 2 (n—4) (5n-—3). 
Let us now consider the correspondence which is determined in 
1) Proceedings 17, 822 (1914). 
2) Cf. p. 937 of my paper: “Characteristic numbers for nets of algebraic 
curves”. (Proceedings Vol. XVII, p. 935). For the sake of brevity this paper will 
be quoted by N. 
3) N. p. 936. 
