167 



IV. "On the Tangential of a Cubic." By ARTHUR CAYLEY, 

 Esq., F.R.S. Received February 11, 1858. 



(Abstract.) 



In my "Memoir on Curves of tbe Tbird Order," Pbil. Trans, 

 vol. cxlvii. (1857), I had occasion to consider a derivative which may 

 be termed the " tangential" of a cubic, viz. the tangent at the point 

 (#, y, z) of the cubic curve (*J#, y, zf=Q meets the curve in a 

 point (, r), ), which is the tangential of the first-mentioned point ; 

 and I showed that when the cubic is represented in the canonical 

 form x 3 -\-y 3 +z 3 + 6lxyz=0, the coordinates of the tangential may be 

 taken to be x(y 3 z 3 ) : y(z 3 x 3 ) : z(x 3 y 3 ). The method given 

 for obtaining the tangential may be applied to the general form 

 (, by c,f, g, h, i,j, k, l$jx> y, zf : it seems desirable, in reference to 

 the theory of cubic forms, to give the expression of the tangential 

 for the general form ; and this is what I propose to do, merely indi- 

 cating the steps of the calculation, which was performed for me by 

 Mr. Greedy. 



V. " On the Constitution of the Essential Oil of Rue." By C. 

 GREVILLE WILLIAMS, Esq., Lecturer on Chemistry in the 

 Normal College, Swansea. Communicated by Professor 

 STOKES, Sec. R.S. Received February 15, 1858. 



(Abstract.) 



The essential oil of rue and its products of decomposition have 

 been examined by several chemists. Will analysed it many years ago, 

 and deduced the formula C 28 H 28 O 3 as the result of his analyses. The 

 principal investigation of it was made by Gerhardt, who regarded it 

 as the aldehyde of capric acid. The production of capric acid from 

 it by the action of nitric acid, as observed by Gerhardt and also by 

 Cab ours, has been considered as corroborative of the 20 carbon for- 

 mula. It is evident, however, that the formation of capric acid 

 merely indicates the aldehyde to contain not less than 20 equivalent^ 

 ..^ carbon. 



