304 
GENERAL INDEX. 
determinant, 308 ; improper equivalence 
— ambiguous forms and classes, 310 ; 
positive or negative determinant, 312 ; 
the Pellian equation, 313 ; solution of 
the general indeterminate equation of 
the second degree, 319 ; distribution of 
classes into orders and genera, 320 ; on 
the determination of the number of 
quadratic forms of a given positive or 
negative determinant, 324 ; series ex¬ 
pressing the number of primitive classes, 
329 ; proof that each genus contains the 
same number of classes, 332 ; summa¬ 
tion of the series expressing the number 
of properly primitive classes , 336 
Numbers, Prof. JI. J. S. Smith’s report on 
the theory of, Part IV, 1862, general 
theorems relating to composition, 503 ; 
composition of quadratic forms — preli¬ 
minary lemmas , 505 ; Gauss’ six con¬ 
clusions, 506 ; solution of the problem of 
composition, 507 ; composition of several 
forms. 509 ; composition of forms—method 
of Pirichlet, 512 ; composition of classes 
of the same determinant, 514 ; compari¬ 
son of the numbers of classes of different 
orders, 515 ; composition of genera, 519 ; 
determination of the number of am¬ 
biguous classes, and demonstration of 
the lam of quadratic reciprocity, ib .; 
equality of the member of genera and of 
ambiguous classes, 521 ; arrangement 
of the classes of the principal genus, 
523 ; arrangement of the other genera, 
524 ; tabulation of quadratic for ms, 525 
- Part V., 1863, geometrical repre¬ 
sentation of forms of a negative deter¬ 
minant, 768 ; application of formula 
relating to the division of the circle to 
the theory of quadratic forms, 772 ; 
extension of the preceding theory by 
Eisenstein , 780 ; applications of con¬ 
tinued fractions to the theory of quad¬ 
ratic forms, 783 
- Part VI., 1865, 322 ; applica¬ 
tions of the theory of elliptic functions 
to quadratic forms, ib .; theorems of 
Jacobi on simultaneous quadratic 
forms, 339 ; the for mules of M. Kro- 
neclter, 347 , 349 ; connection of the 
formula of M. Kronecher with elliptic 
series, 359 ; arithmetical demonstrations 
of these formula, 365 ; equations satisfied’ 
by the modules which admit of complex 
multiplication, 369 ; application of the 
Theta functions to the Pellian equation, 
372 . [The previous reports are given 
in 1859, 228 - 267 ; 1860, 120 - 170 .] 
Numerical and philological relations of 
the Hebrew, Phoenician, or Canaanitic 
alphabet and the language of the 
Khita inscriptions, Hyde Clarke on the, 
1881, 698 
- results derived from observation, 
the adjustment of, V B. Sprague on, 
1883, 446 
Numerical science, some verbal expres¬ 
sions in, Prof. J. Thomson on, 1878, 451 
-theorem, with practical illustrations, 
W. H. Walenn on a, 1870, 16 
Numidian marbles, lost, in Algeria and 
Tunis, Lt.-Col. R. L. Playfair on the 
rediscovery of, 1885, 1018 
*Nunneley (T.) on the Calabar bean, 
1863, 192 
Nuplxar intermedium, Ledeb.. A. G. More 
on the occurrence in Ireland of, 1876, 
144 _ 
^Nutation of a solid shell containing 
liquid, Sir W. Thomson on the, 1876, 35 
Nutoscope, Prof. Zenger on the, an ap¬ 
paratus for showing graphically the 
curve of precession and nutation, 1871, 
36 
"‘Nutrition, various alterations of, due to 
nervous influence, Dr. Brown-Sequard 
on, 1870, 134 
-of muscular and pulmonary tissue 
in health and in phthisis, Dr. W. 
Marcet on the, with remarks on the 
colloid condition of matter, 1871, 40 
*- of embryos, certain adaptations 
for the, F. W. Oliver on, 1888, 710 
*Nyassa, Lake, Eastern Africa, Rev. Mr. 
Stewart on a voyage on the, 1862, 196 
Nyassaland and its commercial possi¬ 
bilities, Capt. Lugard on, 1889, 665 
OAKES (James) on a peculiar denudation 
of a coal-seam in Coates’s Park Col¬ 
liery, 1866, 64 
Oak-leaf, the shape of the, Sir J. Lubbock 
on, 1889, 626 
Oases of the Lybian Desert, Dr. G. 
Schweinfurth on the, 1874, 173 
*Oats, A. Stephen Wilson on the mea¬ 
sure and value of, 1867, 147 
Oban, Argyllshire, Prof. Turner on human 
and animal bones and flints found in a 
cave at, 1871, 160 
Objectives, large, H. Grubb on the test¬ 
ings of, 1876, 36 
O’Brien (M.) on the condition of small 
farmers, and their position with re¬ 
ference to the land question, 1878, 661 
Observatory, Lick, design for working the 
equatorial and dome of, by hydraulic 
power, H. Grubb on, 1886, 553 
Obsidian, W. Chandler Roberts on a 
specimen of, from Java, 1869, 74 
O’Callaghan (P.) on cromlechs and 
rocking-stones considered ethnologi- 
cally, 1861, 187 
- [Dr. P.] on a curious preserved 
specimen of the blackbird, 1865, 92 
- on science-lectures and organisation , 
1873 , 495, 507 
