448 [March 5, 



The present memoir (in the composition of which I have been 

 assisted by a correspondence with Dr. Salmon) contains a further 

 development of the theory of the skew surfaces generated by a line 

 which meets a given curve or curves : viz. I consider, 1st, the sur- 

 face generated by a line which meets each of three given curves of 

 the orders m, n, p respectively; 2nd, the surface generated by a 

 line which meets a given curve of the order m twice, and a given 

 curve of the order n once ; 3rd, the surface which meets a given 

 curve of the order m three times ; or, as it is very convenient to 

 express it, I consider the skew surfaces, or say the " scrolls," 

 S(m, n,p), S(m 2 , w), S(m 3 ). The chief results are embodied in the 

 Table given after this introduction, at the commencement of the 

 memoir. It is to be noticed that I attend throughout to the general 

 theory, not considering otherwise than incidentally the effect of any 

 singularity in the system of the given curves, or in the given curves 

 separately : the memoir contains, however, some remarks as to what 

 are the singularities material to a complete theory ; and in particular 

 as regards the surface S(z 3 ). I am thus led to mention an entirely 

 new kind of singularity of a curve in space viz., such a curve has 

 in general a determinate number of "lines through four points" 

 (lines which meet the curve in four points) ; it may happen that of 

 the lines through three points, which can be drawn through any 

 point whatever of the curve, a certain number will unite together 

 and form a line through four (or more) points, the number of the 

 lines through four points (or through a greater number of points) 

 so becoming infinite. 



II. "Researches on the Refraction, Dispersion, and Sensi- 

 tiveness of Liquids." By J. H. GLADSTONE, Ph.D., 

 F.R.S., and the Rev. T. P. DALE, M.A., F.R.A.S. Re- 

 ceived February 5, 1863. 



(Abstract.) 



This communication contains the results of some inquiries which 

 were started by the authors in a previous paper " On the Influence 

 of Temperature on the Refraction of Light " *. The same apparatus 



* Phil. Trans. 1858, p. 887. 



