495 
as well as with silk, wool, cotton and cellulose the order of the 
three following dyestuffs was: erystal-violet, “neufuchsin’, patent blue. 
The same order, however, is noticed in the distribution of these 
dyestuffs between water and alcohol. Here again is shown the great 
analogy between the absorption of the dyestuff in tibres and the transition 
of the colouring matter into another solvent, which leads to the 
assumption that the absorbed dyestuff is present as a solid solution 
in the fibre. 
We, therefore, conclude that the dye absorption in fibres is mainly 
a phenomenon of solid solution and that the assumption of a surface 
adsorption is in many cases unnecessary and should, therefore, be 
discarded. 
Delft. Inova. Chem. Lab. Technical High School. 
Mathematics. — “On loci, congruences and focal systems deduced 
from a twisted cubic and a twisted biquadratic curve”. I. 
By Prof. Hrenprik pr Vries. 
(Communicated in the meeting of September 28, 1912). 
1. In the Proceedings of the Meeting of this Academy on Saturday 
Sept. 30, 1911, p. 259, Mr. Jan pe Vries has investigated the locus 
of the points sending to three pairs of straight lines crossing each other 
three complanar transversals, and in the Proceedings of the Meeting 
of Nov. 25, 1911, p. 495, Mr. P. H. Scuoure has made the same 
investigation for the points sending to (n + 2), pairs of straight 
lines crossing each other (n +2), transversals lying on a cone of 
-order n. In the following pages one of the three pairs of lines will 
be replaced by a twisted cubic, the two others by a quartic curve 
of the first kind. Through a point P one chord « of 4° passes and 
two chords 6 of 4" pass; we ask after the locus of the points ? for 
which the line a and the two lines 5 lie in one plane. 
We imagine a chord a of 4°. Through an arbitrary point P of 
this chord pass two chords 6,,6,* of 4* and in the plane ab, lies 
one chord 5, which does not meet 6, on /* itself, in ab,* one such- 
like chord 6,*; if for convenience sake we call the points of inter- 
section of 6, and 4,* with a both Q, then in this way to each point 
P two points Q correspond. However, it is clear that to each 
point Q also two points P correspond, so that on a a (2,2) 
correspondence arises with four coincidences, and for these it is evident 
that the triplet a + 20 is complanar. However, it is easy to see 
