PROCEEDINGS 



OF 



THE ROYAL IRISH ACADEMY. 



1846-7. No. 61. 



February 8th, 1847. 



REV. HUMPHREY LLOYD, D. D., President, in the 

 Chair. 



The Rev. Henry Tibbs and John O'Donovan, Esq., were 

 elected members of the Academy. 



A paper by the Rev. M. Roberts, on the lines of curva- 

 ture on the surface of the Ellipsoid, was read by Mr. Ingram. 



The analogy between the lines of curvature on an ellip- 

 soid, and a system of homofocal plane or spherical conies, 

 was first remarked by Mr. M. Roberts, in a note communi- 

 cated by M. Liouville to the French Academy of Sciences, 

 where he has shewn, among other things, that the sum (or 

 difference) of the geodetic distances from the umbilics to any 

 point of the same line of curvature is constant. The follow- 

 ing properties, which he has recently obtained by assigning 

 a significant geometrical meaning to the constant introduced 

 by M. Jacobi in the integral of the differential equation of 

 the geodetic line, appear worthy of the attention of geometers: 



1. Assuming the distance between the umbilics (interior) 

 as the base of a system of triangles, whose sides are geodetic 



VOL. III. 2 K 



