— 103 — 



the degree a m {6 x, ^y • • •) with Coefficiants which are functions 

 of the degree a in the variables (x, y • •). Among varions spe- 

 cial results he has been led to some on the expansion of the 

 factorial xx-f-1 x-f-2 • • -x-f-r — l connected with 

 those in your paper Grelle t. 43. The second Edition has ap- 

 peared of Dr. Salmons lessons on the Modern higher Algebra 

 expanded to a thickish volume of 300 pages — there are two 

 great peaces of calculation in it, that of the discriminant of the 

 general sextic function (a, b, c, d, e, f, g) (x, y) ^^ and of the skew 

 invariant of the IS**^ degree of the same sextic function: and in 

 connexion with this an interesting speculation as to the form of 

 the invariantivc criteria for the reality of the roots of a sextic 

 equation. Have you seen in the Comptes Rendu the veiy 

 interesting papers by DeJongaieres^^) on the number of curves 

 C' which satisfy given conditions of contact with a given curve 

 U*" ? — A more complete paper with the demonstrations is already 

 printed and will 1 suppose shortly appear in Crelle.^''') I have to 

 thank you for the remittance which I received some weeks ago 

 thro' Mess'^'' Williams & Norgate. I remain, dear Sir, yours 

 very sincerely 



A. Cayley, 

 Cambridge 4^»^ Dec. 1866. 



^*) Jonguieres, Fauque de, Jeau Philippe, Ernest, geb. 3. Juli 1820 in 

 Carpentras, Vice-Admiral. 



«Nombre de courbes d'un meme Systeme qui coupent des courbes 

 donnees sous des angles donnes.> 



Pariser Compte-Rendus, 2 p., 58. 

 Paris, Memoires savants etrangers: 



«Generalisation des courbes geometriques et en particulier Celles 

 du 4« ordre.» 65 p. 1862. 



^*j A. Caylay: «Surface du 4'= ordre avec 16 points singuliers.» 7 p. 

 Crelle (65 und 73. 1866 und 71). 



