102 



investigation and for the case of any quadric function of n variables, 

 was first obtained by M. Hermite in the memoir " Remarques sur 

 une Memoire de M. Cayley relatif aux determinants gauches," Cam- 

 bridge and Dublin Mathematical Journal, t. ix. pp. 63-67 (1854). 

 This solution is in my Memoir " Sur la transformation d'une func- 

 tion quadratique en elle-meme par des substitutions lineaires," Crelle, 

 1. 1. pp. 288-299 (1855), presented under a somewhat different form 

 involving the notation of matrices. I have since found that there is 

 a like transformation of a bipartite quadric function, that is a lineo- 

 linear function of two distinct sets, each of the same number of 

 variables, and the development of the transformation is the subject 

 of the present memoir. 



V. "On some of the Products of the Destructive Distillation 

 of Boghead Coal." Part II. By C. GREVILLE WILLIAMS, 

 Esq., Lecturer on Chemistry in the Normal College, 

 Swansea. Communicated by Professor STOKES, Sec. R.S. 

 Received December 17, 1857. 



[Abstract.] 



In this paper the author describes the method adopted by him for 

 the separation of the three classes of hydrocarbons forming the more 

 volatile portion of the distillate. On treatment with bromine in 

 presence of water, the naphtha is entirely converted into a heavy oil, 

 containing the C n H n series chemically, and propyle and benzole me- 

 chanically combined. The two latter may be removed by mere 

 distillation on the water-bath. They are easily separable by fuming 

 nitric acid, the benzole being dissolved while the propyle is un- 

 touched. The nitro -benzole obtained in this manner, on treatment 

 by Bechamp's process, yields aniline mixed with a little tolui dine, but 

 no bases belonging to any other class. 



The bromine compound (in consequence of its preparation in pre- 

 sence of water) could not be obtained free from oxygen. When kept 

 for some time it separates into three layers, the upper being water 

 faintly acidulated with hydrobromic acid, the middle bromine " com- 

 pound, and the lower, hydrobromic acid of 37 per cent., and the 



