291 



theorem it will be necessary to consider one term in the for- 

 mula, which will be the diflFerential of an arc of a line of cur- 

 vature; just as, by considering two conjointly, we were led to 

 the expression for the length of a geodesic arc. 



♦' The formula of M. Liouville, which I have employed, ad- 

 mits of being interpreted in several ways. For instance, ana- 

 lytically speaking, it gives us Abel's theorem respecting the 

 comparison of ultra-elliptic functions of the first class and 

 second species; and, regarded under this point of view, it fur- 

 nishes us with the solution of the following problem : 



" ' Being given three arcs of a line of curvature on a sur- 

 face of the second degree, to determine two others dependent 

 upon them algebraically, so that the sum of the five arcs, taken 

 with their proper signs, may be equal to a right line.' 



" In conclusion, I beg to disclaim any originality in the 

 foregoing communication. Everything which I have advanced 

 on the subject is implicitly contained in the very elaborate 

 memoir of my friend M. Liouville." 



February 26th, 1849. 



REV. HUMPHREY LLOYD, D. D., President, 

 in the Chair. 



On the recommendation of the Council, 



It was resolved, — That £100 be placed at the disposal 

 of the Secretary of the Academy, for the purchase of Irish 

 MSS. at the Stowe sale. 



The President communicated some facts respecting the re- 

 markable atmospheric wave which passed over Dublin in the 

 course of the present month, together with a notice of the more 



