THE REGENT PROGRESS OF ANALYSIS. 315 



In the following Index Crelles Journal is denoted by C., Liou- 

 villes by L., and the present Report by R. 



ABEL. Ueber die Integration der differential Formel ~=. wenn R 



und p ganze Functionen sind. C. i. 185. This paper contains 

 formulae of reduction. It is mentioned by M. Liouville, ' Jour- 

 nal de FEcole Poly technique,' 23d cah. p. 38. It appears in 

 French in Abel's collected works, Tom. I. 33. 



Recherches sur les Fonctions Elliptiques. C. n. 101, and in. 

 160 [1827]. Y. Abel's works, i. 141 ; also R, p. 273. 



. -- Remarques sur quelques Proprietes Generales d'une certaine 

 sorte de Fonctions Transcendantes. G. in. 313. This paper 

 contains the theorem commonly known as 'Abel's Theorem.' 

 V. Abel's works, i. 288 ; also R. p. 247. 



-- Sur le Nombre de Transformations Differentes qu'on pent 

 faire subir a une Fonction Elliptique par la Substitution d'une 

 Fonction donnee du premier desse. C. in. 394. V. Abel's 

 works, i. 309. 



-- Theorem e General sur la Transformation des Fonctions Ellip- 

 tiques de la seconde et de la troisieme espece. C. in. 402. The 

 theorem is stated without demonstration. Y. Abel's works, 

 i. 317. 



-- Note sur quelques Formules Elliptiques. C. iv. 85. This 

 paper contains developments of elliptic functions, &c. Y. Abel's 

 works, I. 299. 



-- Theore~rnes sur les Fonctions Elliptiques. C. rv. 194. They 

 relate to the demonstration of the theorem stated by M. Jacobi 

 in the third volume of Crelle's Journal, p. 86, by means of which 

 Abel's method for the division of elliptic integrals is greatly sim- 

 plified. Y. Abel's works, i. 318 ; also R p. 277. 



-- Demonstration d'une Propriety Generale d'une certaine Classe 

 de Fonctions Transcendantes. C. iv. 200. This short paper 

 contains the fundamental idea of the memoir presented to the In- 

 stitute in 1826. Y. Abel's works, i. 324 ; also R. p. 246. 



-- Precis d'une Theorie des Fonctions Elliptiques. C. iv. 236 

 and 309. This precis was left unfinished. Y. Abel's works, I. 

 326 ; also R. p. 286. 



- Extracts from Letters to M. Crelle, one of which relates to 

 the comparison of Transcendents. C. v. 336. Y. Abel's works, 

 ii. 253. 



- A Letter to M. Legendre. C. vi. 73. Works, n. 256. It 



