131 



Charles Watkins Merrifield, Esq. 

 Gavin Milroy, M.D. 

 Rev. Walter Mitchell. 

 Ferdinand Mueller, M.D. 

 William Newmarch, Esq. 

 Laurence Oliphant, Esq. 

 Edmund Alexander Parkes, M.D. 

 Frederick William Pavy, M.D. 

 George Peacock, Esq. 

 John George Perry, Esq. 

 Bedford Clapperton T. Pirn. 

 William Pole, Esq. 

 Henry E. Roscoe, Esq. 



Philip Lutley Sclater, Esq. 

 Charles Frederick Alexander 



Shadwell, Capt. R.N, 

 Maxwell Simpson, Esq. 

 Henry John Stephen Smith, Esq. 

 William Stokes, M.D. 

 George Johnstone Stoney, Esq. 

 Alexander Strange, Major 7th 



Madras Cavalry. 

 Thomas Tate, Esq. 

 Henry Ward, Capt. R.E. 

 C. Greville Williams, Esq. 

 James Young, Esq. 



The following communications were read : 



I. " On the Porism of the in-and-circumscribed Polygon." 

 By ARTHUR CAYLEY, Esq., F.R.S. Received February 

 20, 1861. 



(Abstract.) 



The Porism referred to is as follows, viz. two conies may be 

 so related to each other, that a polygon may be inscribed in the one, 

 and circumscribed about the other conic, in such manner that any 

 point whatever of the circumscribing conic may be taken for a vertex 

 of the polygon. I gave in the year 1853, in the Philosophical Ma- 

 gazine *, a general formula for the relation between the two conies, 

 viz. if U=0 is the equation of the inscribed conic, V=0 that of the 

 circumscribed conic, and if disc (U + V), where is an ar- 

 bitrary multiplier, denotes the discriminant of U + V in regard to 



* See the papers" On the Geometrical Representation of the Integral 



dx^r V(*+aXH-*)(-H-<Of" Phil. Mag. April 1853. 



" Note on the Porism of the in-and-circumscribed Polygon," Phil. Mag. Au- 

 gust 1853. 



"'Correction of two Theorems relating to the Porism of the in-and-circum- 

 scribed Polygon," Phil. Mag. November 1853. 



" Developments of the Porism of the in-and-circumscribed Polygon," Phil. 

 Mag. May 1854. 



