BY MARTIN GARDINER, C.E. 105 



elegant and simple method of solution to the general problem in 

 the " Annales des Mathematiques" 



In 1847, Mr. Townsend (of Trinity College, Dublin) pointed 

 out an easy method of demonstrating the correctness of Poncelet's 

 process by means of anharmonic properties of conies. 



In 1847, Mr. Gaskin (of Jesus College, Cambridge) furnished 

 a solution which was edited by Professor Davies (of the Royal 

 Military Academy) and published in the " Mechanics' Magazine." 

 This method of solving the general question is evidently nothing 

 more than an extension of the methods of Castillon and Ottajano. 



Mr. Gaskin has also paid much attention to this problem in an 

 appendix to his work entitled " Solutions to Geometrical Problems; " 

 and he is unquestionably the first geometer who succeeded in 

 arriving at a true conception of the contingent porismatic relations 

 of the data. 



The inquisitive reader may consult the third volume of 

 " The Mathematician " for a more detailed history, including the 

 labours of Euler, Lexell, Fuss, Gergonne, Servois, Econtre, Rochat, 

 Noble, Wallace, Lowry, Swale, Hearn, &c. 



PAPEB No. 4. 



Researches concerning n'gons inscribed in surfaces of the second 



degree 



by MARTIN GARDINER, C.E. 



[Read 17th June, 1863.] 



1 . Let S represent a surface of the second degree ; and let 

 o , o 2 , .... o n be a series of n fixed points, designated as first, 

 second, &c., according to the subscript numbers. Let a a^ .... 



?*'gons, the sides of each of which pass in order through the n 

 points. 



