925 
a 
tangents conjugated to each other in this way are in correspondence 
(4,4). By projecting the pairs of this correspondence out of a line 
a, the pencil of planes (7) is arranged in a correspondence (12,12). 
As each coincidency furnishes a line p= R,S, resting on a the 
3 
developasle under discussion is of order 24; it has o*® and o* for 
fourfold curves. 
Any chord r* of 9* meeting 6* belongs to the complex, for in 
the common point of 7* and «* the points ? and S coincide. The - 
chords r of g? cutting a line / generate a seroll of order four with 
v* as nodal curve; so the locus of the chords 7 is a scroll of order 12. 
On the latter surtace ¢* is a sirfold curve, for through any of its 
points pass the common edges of the two cones projecting 9° and o°. 
So the complex (p) contains two scrolls of order twelve, the 
generatrices of which are chords of ane of the curves o*, o* and 
secants of the other. 
Let p* be a chord of g* not meeting o*; then the tangent 7, in 
one of the points A, common to o* and that chord must contain 
the point P. If P moves along that tangent, S describes a curve o,'; 
the cone projecting the latter curve out of Rl, has 6 edges in common 
with that of which y’ is director curve. So any point of 4? bears 
6 rays p*. As an arbitrary chord r can be cut by chords p* in its 
points common to g* only, so all in all by 12, the locus of the 
chords under discussion is of order 12. 
So the complex contains tivo scrolls of order twelve, built up out 
of chords of one of the curves 9°, 6°. 
Physics. — “Determinations of the refractive indices of gases under 
high pressures.’ Second communication. “On the dispersion 
of aw und of carbon diowde.”’ By Prof. L. H. SmerrtsrMa, 
(Communicated by Prof. H. KAMERLINGH ONNms). 
(Communicated in the meeting of November 30, 1912). 
4. The dispersion of air. | 
This has already been repeatedly determined both for the visible 
spectrum and for the ultra-red and ultra-violet rays. The results, 
however, diverge considerably, and, moreover, the dispersion has 
never been measured under high pressure. 
Through the kindness of Prof. KAMERLINGH ONNES compressed air 
was placed at my disposal with which dispersion determinations were 
made in exactly the same way as those for hydrogen described in 
a former paper. 
