320 ON THE RECENT PROGRESS OF ANALYSIS. 



JACOBI. Note von der Geodatischen Lime auf einem Ellipsoid, u. s. w. 

 0. xix. 309. M. Jacobi has here announced the important dis- 

 covery that the equation to the shortest line on an ellipsoid is 

 expressible by means of Abelian integrals of the first class. As 

 this is perhaps the first application made of Abelian integrals 

 since their recognition as elements of analysis, I have thought it 

 well to mention it in this place. A translation of the note is 

 found in Liouville's Journal, vi. 267. 



Demonstratio nova Theorematis Abeliani. C. xxiv. 28. Y. R. 



p. 308. 



. Zur Theorie der elliptischen Functionen. C. xxvi. 93. This 



paper contains series for the calculation of elliptic functions, and 

 a table of the function q. 



Ueber die Additions-theoreme der Abelschen Integral e zweiter 



unddritter Gattung. C. xxx. 121. We find here some remark- 

 able formulae. V. R. p. 310. 



Note sur les Fonctions Abeliennes. C. xxx. 183. This note 



relates principally to the fact announced in M. Jacobi's letter to 

 M. Hermite. Y. L. vm. 505. 



Ueber einige die elliptischen Functionen betrefienden For- 



meln. C. xxx. 269. 



Extrait d'une Lettre 3, M. Hermite. L. vm. 505. Y. R. 

 p. 312. 



Extraits de deux Lettres de M. Jacobi, &c. Schumacher's 



Nachrichten, vi. 33 [Sept. 1827]. They contain the first an- 

 nouncement of his theorem. 



Demonstratio Theorematis ad Theoriam Functionum Ellipti- 



carum Spectantis. Schumacher, vi. 133. The first published 

 demonstration of his theorem. See also Legendre at p. 201 of 

 the same volume. Y. R. pp. 259 and 260. 



JURGENSEN. Sur la Sommation des Transcendantes a DifFerentielles 

 Algebriques. C. xix. 113. 



Remarques Generates sur les Transcendantes a Differentielles 



Algebriques. C. XXIIL 126. Y. R. p. 248. 



IVORY. On the Theory of the Elliptic Transcendents. Phil. Trans., 



1831, p. 349. Y. R. p. 288. 

 LIBRI. Sur la Theorie des Nombres. Memoires des Savans Etran- 



gers, v. 1. 



Sur la Resolution des Equations Algebriques, &c. C. x. 1 67. 



These memoirs are referred to in the controversy between MM. 

 Liouville and Libri. 



LIOUVILLE. Sur lea Integrates de Yaleur Algebrique. Journal 



