885 
point of y* the cone | o:;esses an edge along which two sheets oscu- 
late each other (the <«ction has two branches with a common point 
of inflexion touching each other). 
A cuspidal edge connects any point A, of «a? with the correspond- 
ing point 8, of 3’. The locus of the line A,B, is a biguadratic 
scroll, of which « and 8 contain two generatrices. Any point of 
this scroll admits a complex cone with a cuspidal edge. 
Evidently the biquadratic scroll is ratonal, so it has a twisted 
cubic as nodal curve: For any point P of this curve the complex 
cone has two cuspical edges. 
By replacing the two conics «’, 3° (as bearers of flattened reguli) 
by two quadratic cones we obtain a complex evidently dually rela- 
ted to that treated above. 
If «° and g* touch the line c—« ? whilst ¢ corresponds to itself 
in the relationship between a and /, the complex degenerates into 
the special linear complex with axis c and a cubic complex. Evi- 
dently the same holds for the general biquadratic complex (§ 2) if 
the reguli admit a common generatrix corresponding to itself. 
Chemistry. — “On the system phosphorus’. By Prof. A. Smits, J. 
W. TerweN, and Dr. H. L. pe Leruw. (Communicated by Prof. 
A. F. HorLEMAN). 
(Communicated in the meeting of November 30, 1912). 
In a previous communication on the application of the theory of 
allotropy to the system phosphorus’) it was pointed out that the 
possibility existed that the line for the internal equilibrium of 
molten white phosphorus is not the prolongation of the line for the 
internal equilibrium of molten red phosphorus, in consequence of 
the appearance of critical phenomena below the melting-point of 
the red modification. The latter could namely be the case if the 
system aP—sP belonged to the type ether-anthraquinone, which 
did not seem improbable to us. 
This supposition was founded on the following consideration. In 
the first place it follows from the determinations of the surface- 
tension carried out by Aston and Ramsay’), that the white phosphorus 
would possess a critical point at 422°. Hence the critical point of 
1) Zeitsch f. phys. Chem. 77, 367 (1911). 
1) J. Chem. Soc. 65, 173 (1894). 
Cf. also Scuenck, Handb. ABeaa@ Ul, 374. 
Proceedings Royal Acad. Amsterdam. Vol. XV. 
