REPORTS, ETC. INDEX OF SUBJECTS. 



63 



Numbers, theory of, continued. 



Elementary definitions relating to com- 

 plex numbers, 122. 



Complex units, 123. 



Gauss's equations of the periods, 125. 



The period-equations considered as con- 

 gruences, 127. 



Conditions for the divisibility of the 

 norm of a complex number by a real 

 prime, 129. 



Definition of ideal prime factors, 130. 



Elementary theorems relating to ideal 

 factors, 131, 



Classification of ideal numbers, 132. 



Eepresentation of ideal numbers as the 

 roots of actual numbers, 133. 



The number of classes of ideal num- 

 bers, 134. 



Criterion of the divisibility of H by \, 

 136. 



"Exceptional" primes, 138. 



Fermat's theorem for complex primes, 



139- 



M. Kummer's law of reciprocity, 140. 



The theorems complementary to M. 

 Kummer's law of reciprocity, 141. 



Complex numbers composed of roots of 

 unity, of which the index is not a 

 prime, 145. 



Application to the theory of the di- 

 vision of the circle, 147. 



Application to the last theorem of For- 

 mat, 148. 



Application to the theory of numerical 

 equations, 152. 



Tables of complex primes, 153. 



Solution of binomial congruences, 155. 



Solution of the congruence o;"^!, mod 



P^ 155- 

 Cubic and biquadratic congruences, 158. 

 Quadratic congruences — ^indirect me- 

 thods of solution, 159. 

 Gbneral theory of congruences, 161. 

 Extension of Fermat's theorem, 163. 

 Imaginary solutions of a congruence, 



165. 

 Congruences having powers of primes 



for their modules, 165. 

 Binomial congruences having a power 



of a prime for their modulus, 167. 

 Primitive roots of the powers of a 



prime, 168. 

 Case when the modulus is a power 



of 2, 168. 

 Composite modules, 168. 

 Binon^ial congruences with composite 



modules, 169. 

 Primitive roots of the powers of complex 



primes, 170. 

 Additions to Part I., 170. 

 Nutation, constant of. Rev. Dr. T. R, Ro- 

 binson on the determination of the, by 

 the Greenwich observations, 1837, 127. 

 Nutrition of animals, J. Blake on an im- 

 portant chemical law in the, 1846, 

 30- 



Nymphaceae, Dr. Carpenter on the micro- 

 scopic structure of the shells of the, 1847, 



Oats, on the transmutation of, by Prof. 

 Buckman, 1857, 206 ; 1859, 30. 



Observatory of Armagh and of Dublin, 

 determination of the arc of longitude be- 

 tween the, 1839, 19. 



, Bombay, 1845, 75. 



, Cambridge, 1831-32, 129, 181. 



, Cape of Good Hope, 1831-32, 129 ; 



1839, 172; 1841, 351 ; 1842,4; 1844, 144. 



, Dublin, 1831-32, 129, 131. 



, Greenwich, 1831-32, 126, 129, 131. 



, Kew, 1843, xxxix; 1844, xUx, 120; 



1845, 341; 1846, xvii; 1848, xvii; 1849, 

 xvi, 80, 113; 1850, XX, 176; 1851, xxvii, 

 325, 328, 335; 1852, xxviii; 1853, xxix ; 

 1854, xxvii ; 1855, xxx ; 1856, xxx ; 1857, 

 xxxi ; 1858, xxxiii ; 1859, xl, 200 ; 1860, 

 xxxi ; short description of the, xli. 



, Liverpool, report of the committee on 



the establishment of, 1838, 316. 



, Paramatta, 1831-32, 130. 



, Philadelphia, 1842, 209. 



, Senftenberg, 1845, 108. 



, Simla, 1845, 4. 



, St. Helena, 1841, 349, 352 ; 1844, 144. 



, Toronto, 1841, 340 ; 1842, 5 ; 1844, 



144; 1848, 99. 



, Trevandrum, 1841, 347. 



, electrical, for transport, 1851, 338. 



Observatories, a short general historv of, by 

 G. B. Airy, 1831-32, 126. 



, public. Prof. J. D. Forbes on, 1840, 



143- 



, magnetic, British Colonial, on some 



of the results obtained at the, 1854, 355. 



, magnetic, of Russia, 1840, 432. 



Odorin, Prof. Johnston on, 1831-32, 526. 



OEnone, Dr. T. Williams on the genus, 

 1851, 210, 230. 



Oil of bitter almonds, metamorphic, 1831- 

 32, 503. 



of turpentine, artificial camphor, analy- 

 sis of, 1831-32, 512. 



■ , animal, substances obtained from, 



1831-32, 526. 



Oils, essential, Dr. Daubeny on the nomen- 

 clature of the, 1851, 127. 



Olanin, Prof. Johnston on, 1831-32, 526. 



Olbers's comet, 1831-32, 161. 



Oliva, Dr. Carpenter on the microscopic 

 structure of the shell of the, 1847, 109. 



Onchus, fossil. Prof. Agassiz on, 1842, 87 ; 

 1843, 194, 195. 



Oolitic Echinodermata, Dr. T. Wright on 

 the stratigraphical distribution of the, 

 1856, 396. 



system. Prof. Agassiz on the British 



fossil fishes of the, 1843, 199. 



Opheliadse, Dr. T. Williams on the, 1851, 

 216, 236. 



, British, 1860, 228. 



Ophidia, American, 1836, 200. 



