(517) 
5th. The hitherto unexplained peculiarities of the electro-capillary- 
curve are in this way fully explained. 
6th, The capillary-electrometer of LIPPMANN is according to 4th 
not at all reliable for an accurate measuring of the differences of 
potential between metal and electrolyte. 
March 1902. 
Mathematics. „Right lines on surfaces with multiple right lines”. 
by Prof. JAN DE VRIES. 
§ 1. If a surface St of order n possesses a line J of multiplicity 
n— 2, it is cut in a conic by any plane passing through /. In order 
to find the locus of the centre of these conics we consider the sec- 
tion Cr of S by the plane at infinity. The point ZL, on! at infinity 
is a point of multiplicity »—2 on this curve; so C2 is of class 
(4n—6) and admits of 2(n—1) tangents passing through Z,, and tou- 
ching it elsewhere. Each of these tangents determines a plane 
through ! cutting St in a parabola; so the locus of the center is a 
curve of order 2(n—1), of deficiency zero, cutting / 2n—3-times. 
‘This curve meets S* a number of (2n—3)(n—2)-times on / and 
2(n—1)-times at infinity; the remaining points of intersection are 
double points of degenerated conics. From this ensues the known 
property that the line / of multiplicity (n—2) is met by (3n—4) 
pairs of single lines. '). 
§ 2. If / is chosen for the axis OZ of a right-angular system of 
coordinates the surface S# can be represented by an equation of the form 
An (#, 9) + Ani (% y) 2 + Bri (#9) + 
+ Ans (@; 4) ze + Br (4, y) 2 + Cn—2 (ze, y) = 0, 
the indices n, (n—1), (n—2) denoting the order of the corresponding 
functions A,B,C. 
From this is evident that an S" with given (n—2)-fold line / 
can be made to pass through (6n—3) more points chosen at random. 
As we have 6n—3 = 5 (n+1) + (n—8) it seems that for n >7 we 
1) See e. g. R. Srurm, Math, Annalen, vol. IV, p, 249, 
