526 



Ar Bs Cl _ 



AA' ■'■ BB' "^ CC ~ ■ 



Let now two other chords be drawn from A making with A« very 

 small angles, so as to form with it the edges of a very small pyramid, 

 and let other chords parallel to them be drawn from B and C, forming 

 also with B/3 and Cy the edges of two other small pyramids. Ima- 

 gine a sphere fixed in space, from whose centre are drawn three lines 

 parallel to the three chords drawn from A, or from B, or from C, and 

 conceive the surface of the pyramid, of which they are the edges, to 

 penetrate that of the sphere ; then will the attractions of the three py- 

 ramids, reduced each to the direction of the axis passing through its 

 vertex, be to Ar, B«, Ci as the intercepted surface of the sphere to 

 the square of its radius ; and therefore the sum of each of those at- 

 tractions, divided respectively by AA', BB', CC, will be to unity in 

 the same ratio. Conceive pyramids thus related to be multiplied in- 

 definitely, and the spheroid will be exhausted at once from each of the 

 three points A, B, C, while half the surface of the sphere is exhausted 

 by the parallels drawn from its centre. Hence it appears that the 

 sum of the whole attractions at A, B, C, divided respectively by 

 AA', BB', CC, is to unity as the surface of a hemisphere to the 

 square of its radius, or as 2?r to 1 ; and therefore 



is 4.42+^^ = 4^. 



a c 



January 22. 



REV. James H. TODD, D. D., Vice-President, in the Chair. 



Mr. W. H. Hudson exhibited specimens of Irish books, 

 now in the course of publication in Cork, which are Utho- 

 graphed. He described the advantages which that process 

 presents over types, for composition in the Irish character. 



Dr. Kane read a paper on the Chemical Composition of 

 the different kinds of fuel found in Ireland. 



