255 
We shall make an estimate of the value of 4 by means of the 
following values, which have all been chosen very favourably. 
Density of magnetisation 1.000 
2 J 2m 
Teas i50.g)s—' 100,4 — 10, 14 hikt, 
We then find 
ty @ = — 0,00013, 
from which we may conclude, that the deviation will be hardly 
perceptible. 
Mathematics. — “The circles that cut a plane curve perpendicularly’. 
I]. By Prof. Henprik De VRIES. 
(Communicated in the meeting of February 26, 1916). 
§ 7. We found in the preceding $ that through the point Z, pass 
three different kinds of branches of the rest nodal curve, and in 
particular the branches of the first kind arose in groups of 4 at a 
time. If S,., Ss. are two simple points of intersection of 4% with 
/, then the lines of connection of these points with Z, are double 
torsal lines of 2 (§ 2), and the 4 sheets passing through these torsal 
lines eut each other in + branches of the rest nodal curve, which of 
course all pass through Z,, and have only one tangent here, viz. 
the line of intersection of the two tangent planes along the torsal 
lines, ie. the line of connection of 7, with the intersection of the 
asymptotes of 4” in Sy and Sox. 
The branches of this first kind behave again differently according 
to their going towards the foci and the vertices, or to other points 
of k; the branches going to the foci and the vertices are their own 
images with regard to 3, those to other points, as the nodes, the 
cusps, the intersections of the isotropical tangents, are each other’s 
images. This difference has an influence on the nature of the tangents 
in Z,; for a branch that is its own image Z, must be a point of 
inflexion, as on a straight line passing through this point and cutting 
the curve twice, the two points of intersection approach to Z, from 
different sides; two branches on the contrary that are each other's 
images and pass through Z,, simply have the same tangent in this 
point. But whichever of the two cases may arise the projection of 
4 branches belonging together produces a node in the intersection 
of the associated asymptotes of 4”. If namely a twisted curve is 
projected out of one ef its points of inflection, the projection possesses 
