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,
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.
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