67 



envelope a spherical conic whose principal diametral arcs 



are 2a, and 2j3 ; they will pass through the fixed points, and 



the centre of the conic will be the pole of the great circle 



passing through the two fixed points. 



1^. The base of a spherical triangle being a quadrant, if 



• , , 7 1 II cot^a . cot'^iS , , 



Its base angles a, b, be such that- — ^H — - — ^— I, where 



a and /3 are given arcs, the locus of the vertex will be a 

 spherical conic, whose principal diametral arcs are 2a, and 

 2/3 ; they will pass through the extremities of the given qua- 

 drant, and the centre of the conic will be the pole of the 

 quadrant. 



Some of the preceding theorems lead to new and very 

 general properties of the conic sections : and one (No. 6) 

 gives rise to a new and remarkably simple organic de- 

 scription of them. It should be observed that the arcs here 

 spoken of are all arcs of great circles. 



His Grace the Archbishop of Dublin having taken the 

 Chair, the President continued the reading of Dr. Robin- 

 son's Paper " On the Determination of the Constant of 

 Refraction by Observations with the Mural Circle of the 

 Armagh Observatory." 



The author remarks, that the problem of astronomical 

 refraction is embarrassed by two causes of error. The dif- 

 ferential of the refraction is obtained by supposing the at- 

 mosphere to consist of spherical shells concentric with the 

 earth ; and the integral of this, by assuming some mathe- 

 matical relation between the height above the earth and the 

 corresponding density of the air. He shews that the first 

 of these cannot be rigorously true ; and that the relation 

 between density and height, besides being unknown in ge- 

 neral, may be expected to vary with the latitude. He 

 therefore considers all existing refraction tables as approxi- 



