421 



44. The system of circles u, ft' 7, have corresponding to them the 

 system of conies & - L = 0, S* + M '= 0, N= 0 ; common chords, 

 L + M= 0, Jbf+2V=0, N-L = 0; and let the anharmonic ratios be 



A-2, A.' 2J «/ 2 , i/ 2 , I/' 2 , 



then the corresponding system of equations is 



J^^ + J^m + J^EE =0 ., (93) 

 j^z) + + jms^w) __ 0; m 



ip&^JM^, J5CT ) = 0; (96) 



45. The system of circles a, ft, 7', have corresponding to them the 

 system of conies - L = 0, S i - M = 0, /S* + iV= 0 ; common chords, 

 Z-M=0, Ji" + iV=0, 1V+L = 0. 



Let the anharmonic ratios be 



3> A 3> /*3> ^ 3> v 3) 



then the corresponding system of equations is 



j^S + ^S + ^S-oi (97) 



KOSHiV) 



(99) 



J^) + J^ + J^ ) = o _ (ioo) 



46. "We have in the last four articles given the equations of the 

 sixteen pairs of conies having double contact with a given tonic, and 

 touching three others also having double contact with the same given 

 conic ; and it is evident, from Articles 12, 14, 32, that Dr. Hart's 

 theorem holds for each of the four systems into which we have written 

 the equations. 



E. I. A. PROC. VOL. IX. 3 K 



