462 



Prof. Cayley on the Curves 



[May 2, 



distinguished from all other Saurians. Thus Hatteria presents a strange 

 combination of elements of high and low organization, and must be re- 

 garded as the type of a distinct group. Its affinities and systematic 

 position may be indicated in the following synopsis of RECENT REP- 

 TILTA:— 



I. SaUAMATA. 



First order. Ophidia. 

 Second order. Lacertilia. 



Suborder A. Amphishcenoidea. 



Suborder B. Cionocrania. 



Suborder C. Chamceleonoidea. 



Suborder D. Nyctisaura. 

 Third order. Rhynchocephalia. 



II. LORICATA. 



Fourth order. Crocodilia. 

 III. Cataphracta. 



Fifth order. Chelonia. 



IV. "On the Curves which satisfy given conditions." By Prof. Cayley, 

 F.R.S. Received April 18, 1867. 



(Abstract.) 



The present memoir relates to portions only of the subject of the curves 

 which satisfy given conditions ; but any other title would be too narrow : 

 the question chiefly considered is that of finding the number of the 

 curves which satisfy given conditions ; the curves are either curves of a 

 determinate order r (and in this case the conditions chiefly considered are 

 conditions of contact with a given curve), or else the curves are conies ; and 

 here (although the conditions chiefly considered are conditions of contact 

 with a given curve or curves) it is necessary to consider more than in the 

 former case the theory of conditions of any kind whatever. As regards 

 the theory of conies, the memoir is based upon the researches of Chasles 

 and Zeuthen, as regards that of the curves of the order r, upon the re- 

 searches of De Jonquieres: the notion of the quasi-geometrical represen- 

 tation of conditions by means of loci in hyper-space is employed by Salmon 

 in his researches relating to the quadric surfaces which satisfy given con- 

 ditions. The papers containing the researches referred to are included in 

 a list subjoined. I reserve for a separate second memoir the application 

 to the present question, of the Principle of Correspondence. 



