_ ON THE RECENT PROGRESS OF ANALYSIS. 85 
Apex. Addition au Mémoire Précédent—Schumacher’s Astronomische 
Nach. No. 147, vii. 33. V. Abel’s works, i. 275; also R. whi supra. 
_. . The following papers were published for the first time in Abel's col- 
- lected works. ‘The references are to the second volume :— 
——. Propriétés remarquables de la Fonction y=¢ 2, etc., p. 51. The 
- multiple periodicity of a function inverse to a hyper-elliptic integral is 
here mentioned. V. R. p.77. 
—. Sur une Propriété remarquable d'une Classe trés étendue de Fone- 
tions Transcendantes, p. 54. This paper contains a generalisation of a 
theorem relating to elliptic functions. 
—. Extension de la Théorie Précédente, p. 58. 
_——. Sur la Comparaison des Fonctions Transcendantes, p. 66. This paper 
contains a somewhat fuller development of his general theory than that 
which is inserted in the fourth volume of Crelle’s Journal, p. 200. 
V. R. p. 40. 
——. Théorie des Transcendantes Elliptiques, p. 93. V. R. p. 66. 
_ — +. Démonstration de quelques Formules Elliptiques, p. 210. 
_ Brocu. Sur quelques Propriétés d’une certaine classe des Fonctions Trans- 
cendantes.—C. xx. 178. An extension of Abel’s theorem. V. R. p.40. 
Mémoire sur les Fonctions de la forme 
§ 
SSS 
SJ—7?-" F(a?) (Ra?) "? da, ete.—C. xxiii. 145 and 201. 
This memoir, of which the first part may be considered a generalisation 
of the preceding, is accompanied by a report of MM. Liouville and 
Cauchy. V.R.p.41. 
Bronwin. On Elliptic Functions—Camb. Mathematical Journal, iii. 123. 
Mr. Bronwin puts the transcendental formula of transformation in a 
very neat form. 
——. On M. Jacobi’s Theory of Elliptic Functions.—Lond., Ed. and Dub. 
Phil. Mag. xxii. 258. V. R. p. 53. 
-——. Reply to Mr. Cayley’s Remarks.—L., E. & D. Phil. Mag. xxiil. 89. 
e:: V. R. ubi supra. 
 Caratan. Surla Réduction d’une Classe d’Intégrales Multiples.—L. iv. 323. 
_—. Sur les Transformations des Variables dans les Intégrales Multiples. 
Mémoires Couronnés par Académie Royale de Bruxelles, xiv. ade 
partie, p.1. The third part contains a transformation of a multiple 
integral leading to properties of hyper-elliptic integrals analogous to 
é known properties of elliptic integrals. 
Caucuy. Comptes Rendus, xvii. 825.—V. R. p. 69. 
Cavtry. Mémoire sur les Fonctions doublement Périodiques.—L., x. 385. 
An enlargement of his paper on the inverse elliptic functions, published 
in the fourth volume of the Cambridge Mathematical Journal. V. R. 
iy p-:'69. 
_——. Remarks on the Rev. B. Bronwin’s paper.—L., E. and D. Phil. Mag. 
xxii. 358. 
—. Investigation of the Transformation of certain Elliptic Functions.— 
L., E. and D. Phil. Mag. xxv. 352. V. R. p. 69. ; 
5, a the Inverse Elliptic Functions—Camb. Math. Journal, iv. 257. 
- KR. p. 69. 
‘Cuastxes. Comptes Rendus de l'Institut, xvii. 838, and xix. 1239. M. 
-_ Chasles in these two communications presents to the Institute notices 
of his geometrical researches illustrative of the theory of elliptic func- 
tions. V. R. p. 74. 
