sequently, the final expressions of these variables ought to include six constant arbitrary quantities, which we may regard as the elements of rotation, of which three relate to the rotation itself, and the three others to the plane to which we refer the rotation, as in the case of the movement of translation. These elements become variable by the perturbating forces of the other planets; and the determination of their variations, a problem which had never been attempted, is that which the learned author has proposed to investigate in some future memoir.
Supplement to the preceding Memoir. We have stated that the author, in his last paper, had very considerably simplified as well as generalized his formula: still, however, it occupied forty pages, and required an uncommon degree of attention in the reader to follow the author through all the steps of the investigation: but the memoir was scarcely printed before he discovered that his general result, at which he had arrived only by means of a long and complicated analysis, might be deduced immediately from the primitive equations, in such a manner as not to occupy more than two or three pages. This deduction is made the subject of the present supplement.
-General Formula for the higher Order of the Planetary Perturbations. By J. C. BURCKHARDT.-The purport of this memoir is sufficiently indicated in the title; and it is impossible to enter into any analysis of it within the limits of our article.
Memoir on various Means proper for perfecting Lunar Tables. By the Same.-We know that theory alone is not sufficient for determining, with the required degree of accuracy, the co-efficients of the lunar inequalities; and astronomers have therefore preferred to arrive at them by comparing a number of observations in which the inequality is the greatest; or, rather, the sum of the errors of the tables furnished by these observations, with a similar sum, where their greatest value is negative. The difference of the two sums, divided by the number of observations, will give the co-efficient sought: but, in order to use a greater number, we employ even those which are a little distant from the maximum, and search at the same time for each observation the sines of the argument; dividing the sum of the errors by the sum of the sines, instead of dividing by the number of observations. This is necessarily a very laborious computation; and M. BURCKHARDT's theorem for abridging it is all that we can give of the contents of this memoir; viz. The mean sum of the sines of an infinite series of arcs in arithmetical progression, from 90° to 90°-y, is equal to the sine of the arc y divided by the arc itself.
Vol. X. will be reported in our next Appendix.
To the REMARKABLE PASSAGES in this Volume,
N. B. To find any particular Book, or Pamphlet, see the
Table of Contents, prefixed to the Volume.
Ali Pacha, visit to, 340.
America, South, hazards of tra
velling in, 490.
Americans, their general mode of
living, 247. Character of the
American Presidents, 253-5.
Anesthesia, hist. of a case of,
300.
Anthologia inedita, obs. relative to,
452.
Appendix Vermiformis, case of a
diseased, 299.
Arcadia, account of, 3.
Archaia, description of, 3.
Argos, population of, 8.
Ash, on different kinds of that
tree, 535.
Athens, remarks on, and on the
inhabitants, 344.
Atmosphere, obs. on phænomena
of, 373
APP. REV. Vol. LXXIV.
Attention, its effect on intellectual
power, 403. 405.
Aubrey, John, specimen of his
biographies, 368.
Austin, Mr., on a new condenser
and air-pump, 157.
Bacon, Sir Francis, life of, by
Aubrey, 368. Apophthegms
of, 370.
Bank of England, its discounts not
confined to bonâ fide transac-
tions, 181.
of Ireland, amount of its
notes, 180.
Barlow, Joel, account of, 254.
Basalt, on the crystallization of,
Beattie, Dr., obs. on his style, 308.
Bell, Mr. C. on the muscles of
the Ureters, 301.
Benedict IV., anecdote of, 517.
Bernard, the French Anacreon,
account of, 528. His ode to
the Rose translated, 530.
Berthoud, F., memoir of, 541.
Berzelius, Dr., on the alcohol
of sulphur, 159. On animal
fluids, 301.
Betrothing, ceremony of, among
the modern Greeks, 351.
Billardiere, M. la, on a new genus
of the Palm, 536.
Biography, observations on the art
of, 356. Inferences drawn from
the study of, 358. Queries
prepared for the use of biogra-
Na
phers,
phers, 362. Observations on
French biography, 465.
Birds, habits of, poetically deli-
neated, 81. See Home.
Blagden, Sir C., on near-sighted-
ness, 77-
Blane, Sir Gilbert, on intermitting
fevers, 298.
Bonaparte supposed to be the
author of the Egyptian expe
dition, 493. His instruc-
tions to Kleber on quitting the
army, 498. His artful letter to
the Grand Vizier, 500. His
assassination of the Duke
d'Enghien, 505. His disas-
trous campaign of Moscow,
508. His fatal campaign of
Paris, 513
His character,
515. Stipulations for his fa-
mily, 516.
Book-keeping, observations on, 323.
Bosc, M., on different species of
the Ash, 535.
Bostock, Dr.,on Diabetes Insipidus,
300. On the Bark of the
Coccoloba Uvifera, 301.
Boston, in New England, descrip-
tion of, 252.
Brande, Mr., on alcohol in fer-
mented liquors, 75. On the
effects of magnesia, 160.
Bree, Dr., on Splenitis, 301.
Brewster, Dr., on properties of
light, 76.
Brinkley, Dr., on Newton's solu-
tion of the problem for finding
the relation between resistance
and gravity, 26. On the pro-
blem for clearing the moon's
apparent distance, 27.
Burckhardt, M., on a reflecting
sextant, 541. His formulæ
for planetary perturbations,
544. On perfecting Lunar
tables, ib.
Bullion, tracts relative to, 171.
Burke, Mr., on powers, 29.
Calvin, remarks on his opinions,
Canadians, their character and
manners, 245:
Canal, of magnificent size, in Scot-
land, 136.
Carolina, South, statistical parti-
culars relative to, 251.
Cassegrainian telescope, on the
light of, 155.
Casowary, observations on the
solvent glands of, 74.
Castlereagh,
Lord, supposed
poetic epistle from, to Lord
Liverpool, 429.
Catania, account of, 170.
Catherine, of Russia, her generous
conduct to Diderot, 519.
Catholics, obs. on the character
and conduct of, with reference
to the question of their eman-
cipation, 52-60. Portrait of
their religion, 256-268. Re-
marks on the emancipation of,
440.
Cavendish, the author of the life of
Wolsey, supposed to be George
and not Sir William C., 218.
Caulincourt, M., his attempted jus
tification respecting the murder
of the Duke d'Enghien, 504.
Chaptal, M., on the distillation of
Wines, 534. On colors found
at Pompeii, 535.
Charlemagne, supposed poetic ad-
dress to, 318.
Charlestown, account of, 249.
Chevalier, M., on ovarian dropsy,
299. On tying diseased tonsils,
ib. On spontaneous extravasa-
tion, 300. On a calculus,
301.
Child, illegitimate, verses on, by
its mother, 310.
Chinese, amount of their trade
with Japan, 280.
Church, antient, obs. on the go-
vernment of, 193..
Clanny, Dr., on lights in coal-
mines, 160.
Calculus, from the groin, case of, Claude, of Turin, obs. relative to,
![[ocr errors]](https://books.google.gl/books/content?id=R4oCAAAAYAAJ&hl=da&output=html_text&pg=PT2&img=1&zoom=3&q=editions:ISBN0344061817&cds=1&sig=ACfU3U1RPGpYayiP8rEI5zkk3wx4Dj7blQ&edge=0&edge=stretch&ci=78,541,10,9)
Cleanliness, its supposed effect in
improving the intellect, 404.
Clergy, of Ireland and Scotland,
See Ireland. See Scotland.
Coal-mines, on the lights in, 160.
Coccoloba Uvifera, on the bark of,
301.
Cold, on the production of, 162.
In Canada, described, 242.
Colors found at Pompeii, notice
of, 535-
Condamine, M. de la, anecdote
of, 518.
Condenser, and air-pump, new con-
struction of, 157:
Coray, M., obs. on his history of
medicine and translation of
Theophrastus, 453,454. Let
ter from, to M. Chardon de la
Rochette, 455-
Cork, account of that city, 129.
Corn-laws, discussion respecting
alterations in, 407–415.
Cotes's theorem, on an application
of, 78.
Country-Banker obliged to pay his
notes in cash, if demanded, 172.
Crickmore, Mr., his improved Cas-
segrainian and Gregorian Teles-
copes, 155.
Crystals, on the elementary par
ticles of, 72.
Curry, Dr., his case of remitting
ophthalmia, 302.
Cuvier, M., his report of dis-
coveries in natural philosophy,
&c., 532. On a memoir of
Dr. Gall on the brain, 533.
Cynanche laryngea, memoir on,
300..
D'Alembert, anecdotes relating
to, 526.
Davy, Sir H., on a new detonat-
ing compound, 69. 161. On
Fluor-spar, 163.
Debtors, among the Mahrattas,
forced to pay by the mode
called sitting dburna on them,
398.
Deity, on the character of, 295.
His glory, how promoted in
the lives of his creatures, 297,
Delambre, M., his report on the
mathematical sciences, 539.
54. On the life, &c., of
Berthoud, 541.
Deluge, observations on the Mosaic
account of, 227.
Depravity, of human nature, ob-
servations on, 294.
Desmarest, M., on a new stock-
ing-frame, 534.
Detonating Compound, memoir on
a new one, 69. 161.
Dhurna, See Debtors.
Diabetes Insipidus, obs. on, 300.
Dick, Sir James, his account of
the Duke of York's shipwreck,
384.
Diderot, M., generously treated
by the Empress of Russia, 519.
Differences, on finding the orders
of, 32.
Divorce, regulations relating to,
in the Code Napoleon, 66.
Drama, of the Germans, observa-
tions on, 269.
Duelling, its prevalence in Ame-
rica, 251.
Equations, on finding divisors of,
34.
Exports and imports of England
in the years 1805—9. 175.
Extravasation, spontaneous, on a
case of, 300.
Farewell verses by Mr. Moore,
186.
Farre, Dr. on eynarche laryngea,
300.
Fat in the intestines, on the for-
mation of, 158.
Fevers, intermittent, facts relative
to, 298.
Flowers, poetic enumeration of,
83.
Fluids, animal, essay on, 301.
Fluor-spar, on substances pro-
duced in processes on, 163.
Fourcroy, M., on animal mucus,
535.
France, obs. on the laws of, and
on the Code Napoleon, 62-68.
Franklin, Dr., anecdote of, 531.
Freezing, at a distance, on a me-
thod of, 73.
Fungus, See Earle, Lawrence,
Langstaff
Furs, on the trade in, by the
Canadians, 241.
Gall, Dr., report on his memoir
on the brain, 533.
Garrick, David, eulogized by a
foreigner, 520.
Gastric glands, on the coagula-
ting power of the secretion of,
75.
Geography, antient, plan for illus
trating, 19.
Geology, observations on the im-
portance of, 236.
Germany, observations on the liter-
ature of, 269-275.
Glammis, in Forfarshire, account
of that parish, 137.
Glands and gizzards of carnivo-
rous birds, obs. on. 74, 75.
Glands, bronchial, on the colour-
ing matter of, 158.
Glory of God, how promoted in
the lives of his creatures, 297.
Goethe, obs. on his dramas, 271.
Compared with Schiller, 272.
Gold-coin, tracts relative to, 171.
Golden-age compared to the
state of Adam and Eve in Pa-
radise, 226.
Goldoni, the dramatic writer, life
of, 467-476.
Government, free, alone suited to
the happiness and improvement
of man, 418.
Greeks, modern, character of, 9.
Their physicians, 12. Remarks
on their persons and habits,
349. Ceremony of betrothing
among, 351. On the language
of, 352.
Greenland, account of seamen left
there, 381.
Guyton, M., on Pyrometry, 538.
|