INDEX I. 



219 



Invertebrate fauna, British marine, list 

 of the, by R. M c Andrew, 217. 



Killiney Bay, shells obtained in, 29. 

 Kinahan (Prof.), report on dredging in 



Dublin Bay, 27. 

 Kingstown Bay, shells obtained in, 29. 



Lloyd (Rev. Dr. H.), report on the scien- 

 tific objects to be sought for by con- 

 tinuing balloon ascents, 43. 



Lowe (E. J.), report on observations of 

 luminous meteors, 1. 



Marine invertebrate fauna, British, list 

 of, by R. M c Andrew, 217. 



M c Andrew (Robert), list of the British 

 marine invertebrate fauna, 217- 



M c Connell (J. E.), report on steam-ship 

 performance, 193. 



Messageries Imperialesof France, table of 

 results of performances of steam-ships 

 in the service of, 200. 



Meteor, very remarkable, observations of 

 a, 12. 



Meteorites and fireballs, catalogue of, by 

 R. P. Greg, 48. 



Meteors, luminous, report on observa- 

 tions of, by J. Glaisher, Dr. Gladstone, 

 R. P. Greg, and E. J. Lowe, 1. 



, luminosity of, from solar reflexion, 



15 ; on the luminous trains left by, 15 ; 

 on the motion of the tail of, 17 ; on the 

 duration of, 17 ; on the hypothesis that 

 the intensity of the light of, is caused 

 by the oxygen in the atmosphere, 18; 

 list of 168 bolides observed from 1841 

 to 1853, 19 ; results of the most re- 

 markable as regards their general ob- 

 served direction, 21. 



Mollusca, British, list of, compiled by R. 

 M c Andrew, 218. 



Moorsom ( Vice-Admiral) on the perform- 

 ance of Steam-vessels, the functions 

 of the screw, and the relations of its 

 diameter and pitch to the form of the 

 vessel, 172. 



, chairman of the committee on steam 



ship performance, second report, 193. 



Napier (J. R.), report on steam-ship per- 

 formance, 193. 



Naval architecture, Admiral Moorsom 

 on, 172. 



Nicol (Prof. J.), report on the excavations 

 in Dura Den, 32. 



Numbers, Prof. Smith's report on the 

 theory of, 120 ; residues of the higher 

 powers, researches of Jacobi, 120 ; neces- 

 sity for the introduction of ideal primes, 



121 ; elementary definitions relating to 

 complex numbers, 122; complex units, 

 123; Gauss's equations of the periods, 

 125; the period-equations considered 

 as congruences, 127; conditions for 

 the divisibility of the norm of a com- 

 plex number by a real prime, 129; 

 elementary theorems relating to ideal 

 factors, 131 ; classification of idealnum- 

 bers, 132; representation of ideal num- 

 bers as the roots of actual numbers, 

 133 ; the number of classes of ideal 

 numbers, 134 ; criterion of the divisi- 

 bility of H by X, 136 ; " exceptional " 

 primes, 138; Fermat's theorem for 

 complex primes, 139 ; M. Rummer's 

 law of reciprocity, 140 ; the theorems 

 complementary to M. Rummer's law 

 of reciprocity, 141 ; complex numbers 

 composed of roots of unity, of which 

 the index is not a prime, 145; appli- 

 cation to the theory of the division of 

 the circle, 147 ; application to the last 

 theorem of Fermat, 148 ; application 

 to the theory of numerical equations, 

 152; tables of complex primes, 153; 

 solution of binomial congruences, 155 ; 

 solution of the congruence nfl 1 — 1, 

 mod p, 155; cubic and biquadratic 

 congruences, 158; quadratic congru- 

 ences — indirect methods of solution, 

 159 ; general theory of congruences, 

 161 ; extension of Fermat's theorem, 

 163 ; imaginary solutions of a congru- 

 ence, 165; congruences having powers 

 of primes for their modules, 165 ; bi- 

 nomial congruences having a power of 

 a prime for their modulus, 167; primi- 

 tive roots of the powers of a prime, 

 1 68 ; case when the modulus is a power 

 of 2, 168 ; composite modulus, 168; 

 binomial congruences with composite 

 modulus, 169; primitive roots of the 

 powers of complex primes, 170 ; addi- 

 tions to Part I., 170. 



Page (D.), report on the excavations in 

 Dura Den, 32. 



Paris (Admiral), report on steam-ship 

 performance, 193. 



Plants, Professor Buckman's report on 

 the growth of, in the Botanical Garden 

 of the Royal Agricultural College, 

 Cirencester, 34. 



Polvzoa, British marine, list of, compiled 

 by R. M c Andrew, 230 :— Infundibulata, 

 230. 



Porifera, British marine, list of, compiled 

 by R. M c Andrew, 235. 



Protozoa, British marine, list of, compiled 

 by R. M c Andrew, 234. 



