CHEMISTRY: GOMBERG AND SCHOEPFLE 
457 
be chosen so that the coordinates of the focal points of a harmonic con- 
gruence are of the respective forms 
In this case equation (18) assumes the form (1), so that the choice of 
coordinates referred to its equivalent to finding a particular solution 
of (18). 
Since the congruence F1F2 is harmonic to both N and iVi, it follows 
that the equations of any transformation T in homogenous coordinates is 
reducible to the form (2). If the coordinates of N satisfy (18), the 
equations are of the form 
where now ^ is a solution of (18). 
When the equations of the transformation are of the form (2), each 
solution of the point equation of N gives a new transform by means of 
(5). The equations of the preceding results continue to be true, and 
parallel nets are replaced by any transforms. 
Although these results have been stated in terms of 3-space, they hold 
for two dimensional spreads in /^-space, provided that a congruence is 
defined as a two parameter family of lines possessing two famiHes of 
developables. 
^Eisenhart, Trans. Amer. Math. Soc, New York, 18, 1917, (97-124). 
2Bianchi, Ann. Mat., Milano, (Ser. 3), 11, 1905, (93-158). 
THE MOLECULAR WEIGHTS OF THE TRIARYLMETHYLS 
It is now generally accepted that the free radicals of the triphenylmeth- 
ane series owe their unique unsaturated character to the presence of a 
trivalent carbon atom in the molecule. In many cases the molecular 
weight has been found to be double that calculated for the free radical. 
Nevertheless, even in these cases the presence of a compound with a single 
unsaturated carbon atom is still recognized, and the assumption is made 
that there exists, in virtue of partial dissociation, a mobile equilibrium: 
(19) 
(20) 
By M. Gomberg and C. S. Schoepfle 
CHEMICAL LABORATORY. UNIVERSITY OF MICHIGAN 
Communicated May 31, 1917 
RgC-CRs^RsC+RsC. 
