514 Mr. A. Cayley on the Skew Surface 



the copper a somewhat smaller proportion of aluminium than 10 

 per cent. 



" The present price of the English-made 10 per cent, alumi- 

 nium bronze is 6s. 6d. per lb. ; but there is reason to believe 

 that, as the process of extracting the aluminium becomes more 

 largely practised, and the demand for the metal increases, the 

 price will fall. The above price is four or five times that of gun- 

 metal. A much smaller quantity, however, of the new alloy than 

 of gun-metal will give the same strength ; and when it is con- 

 sidered how small a ratio the cost of the material bears to the 

 cost of workmanship in refined apparatus, it will be found that 

 even at the present price of the new alloy its cost is not prohi- 

 bitory, whilst the advantages attending its use promise to out- 

 weigh the increased expenditure. 



" In the foregoing paper, which I am aware is very imperfect 

 and incomplete, I have sought no more than to contribute such 

 an instalment of practical information regarding this remarkable 

 material as may be of service to those who, like myself, contem- 

 plate making use of it, of whom I trust there will be many ; for 

 by its use we shall, I venture to think, confer on such structures 

 at once greater strength and less weight, and so diminish tension, 

 flexure, and distortion, to an extent calculated sensibly to improve 

 the higher order of instruments of physical research." 



LXX. On the Skew Surface of the Third Order. 

 By A. Cayley, Esq.* 



THE skew surface of the third order, or "cubic scrole" 

 (disregarding a certain special form), may be considered 

 as generated by a line which always passes through three direc- 

 trices ; viz. a plane cubic having a node, and two lines, one of 

 them meeting the cubic in the node, the other of them meeting 

 the cubic in an ordinary point. The analytical investigation 

 possesses some interest as an illustration of the analytical theory 

 of skew surfaces in general. 



Take for the equation of the cubic 



(a 3 + P)xy~ (* 3 + y S )«P=0, 



which belongs to a cubic having a node at the origin, and passing 

 through the point (a, /3) ; and for the equations of the two lines 



(x— mz=0j y—nz=0), 



(*-« =0, 2/-/3=0). 



Then, (X, Y, Z) being current coordinates, the equations of the 



* Communicated by the Author. 



