423 



P(L + M) _Q{M+N) _R(N-L) 



(110) 

 (111) 

 (112) 



4°. For the system of conies (97)-(100) corresponding to the sys- 

 tem of concurrent common chords L-M=0, M+N'=0 ) iVfZ = 0, 

 the lines through the points of contact are 



\ 2 





»2 



} 



P(L + M) 







■ L') 



/Y 2 









P(L + M) 



Q(M+JST) 



R (N- 



L) 



A/ 2 



fl 2 



»'* 





P(L + M), 





R(jsr- 





V 2 





"2 





P(Z-M) Q{M+N) P(JST+L) 









P(L-M) 





P(JV+L) 



\ 3 







P(L-M) 



Q{M+N) _ 



P(jsr+L) 





^3 





P(L-M) 





P(JY+L) 



V 8 



fa 



v z 



(113) 

 (114) 

 (115) 

 (116) 



Hence we have a method of describing the sixteen pairs of conies. 



In a subsequent paper I shall show that the greater number of the 

 equations employed in this paper are capable of double interpretations, 

 and also that the methods of demonstration employed can be used with 

 advantage in other parts of geometry. 



G. V. Du Noyer, Senior Geologist, G. S. I., M. H. I. A., presented the 

 following collection of Drawings from original sketches of various anti- 

 quities, to form Yol. VII. of a similar donation to the Library of the Aca- 

 demy. 



Early Irish and Pre-Norman Antiquities. 



No. 1. Cromleac in the townland of Ballynageeragh, county of"Wa- 

 terford. 



No. 2. Unfinished cromleac near Ballyphillip Bridge, Dunhill Glen, 

 county of "Waterford.^ 



* For detailed description of these cromleacs and remarks on the classification of an- 

 cient Irish earthen and megalithic structures, see a paper, by the same writer, in the 

 " Kilkenny Archaeological Journal" for April, 1866. 



