444 



Prof. Cayley on Skew Surfaces. 



[Jane 18, 



Metal. 



Chemical 

 equivalent. 



Eefraction- 

 equivalent. 



fepecinc 

 refractive 

 energy. 





39 



8-0 



0-205 





23 



4-6 



0-200 





7 



3-9 



0-557 





12 



3-7 



0-308 



Barium 



68-5 



7-8 



0-114 



Strontium 



43-8 



6'5 



0-148 





20 



6-2 



0260 





32-6 



4-8 



0-147 



Mckel 



29-5 



51 



0173 



Cobalt 



29-4 



5-2 



0177 





103-5 



12-1 



0-117 





100 



9-8 



0-098 





18 



11-4 



0-633 



These numbers are suggestive in many ways ; but I will only remark 

 the very high refractive energy of lithium, the practical identity of nickel 

 and cobalt, and the remarkable fact that the specific refractive energy of 

 the metals are (with one or two exceptions) in the inverse order of their 

 atomic weights. 



IV. " A Third Memoir on Skew Surfaces, otherwise Scrolls.'''' By 

 Prof. Cayley. Received May 30, 1868. 



(x'^bstract.) 



The present Memoir is supplementary to my "Second Memoir on Skew 

 Surfaces, otherwise Scrolls," Phil. Trans, vol. cliv. (1864) pp. 559-577, 

 and relates also to the theory of skew surfaces of the fourth order, or quartic 

 scrolls. It was pointed out to me by Herr Schwarz, in a letter dated Halle, 

 June 1, 1867, that in the enumeration contained in my Second Memoir 

 I have given only a particular case of the quartic scrolls, which have a 

 directrix skew cubic; viz. my eighth species, S (1, 3^), where there is also 

 a directrix line. And this led me to observe that I had in like manner 

 mentioned only a particular case of the quartic scrolls with a triple direc- 

 trix line ; viz. my third species, S (I3, 1, 4), where there is also a simple 

 directrix line. The omitted species, say, ninih species, 8(13), with a triple 

 directrix line, and tenth species, S (3"), with a directrix skew cubic, are 

 considered in the present Memoir ; and in reference to them I develope a 

 theory of the reciprocal relations of these scrolls, which has some very 

 interesting analytical features. 



The paragraphs of the present Memoir are numbered consecutively with 

 those of my Second Memoir above referred to. 



