of other elements. In the latter case the combination of elements varies of course from one table to another. The values of g, for which each inequality is computed, head the table in a horizontal column; the corresponding values of the second argument are arranged in a vertical column at the margin. The inequalities are computed for every six hours of g, extending from god.25 to g= 29.75, or somewhat more than a period; and for successive values of each vertical argument differing by a unit of its respective period. In computing the moon's place for a given date the value of each inequality corresponding to its vertical argument is readily found by a process of simple interpolation, the differences of the successive numbers in the vertical columns being in all cases very small. In so far as the inequalities depend upon the horizontal argument g, the process for finding their values is different; for since they must all be determined for the same value of the argument, namely, that for which the moon's place is to be calculated, it suffices to take from the tables two values of each inequality corresponding to two values of g, one greater and the other less than the given argument, and then to interpolate once for all between the sums of the results. It is only the smaller inequalities which are arranged in tables of double entry. In the case of inequalities of considerable magnitude, it would be necessary to give the tables an enormous extension in order that the differences of the successive numbers in the vertical columns might be sufficiently small to admit of easy interpolation. In the tables of single entry the successive values of the arguments differ by the hundredth of a day, and the inequalities are accompanied by columns of differences to facilitate interpolation. In every case the tables are computed for a period of the inequality plus an anomalistic month. This arrangement affords great advantage in the computation of an ephemeris of the moon's place. Since the sines recur in regard both to quantity and direction, in the first and second, and again in the third and fourth quadrants; and since the cosines similarly recur in the first and fourth, and in the second and third quadrants, the tables, in most cases, admit of being reduced to half the extent they would otherwise occupy. When the inequalities represented by dz† are computed by the tables and added to g (expressed in time), the result constitutes z, upon which depend the true longitude, parallax, and latitude. This quantity is termed by Professor Hansen the fundamental argument. The following is the mode of computing the values of the arguments. The example is taken from the Introduction to the Tables: * The unit of the period is different for each vertical argument, being manifestly chosen so that for the successive values of the argument, the differences of the numbers in the vertical columns may be of inconsiderable amount. + nz and ndz are represented in time by z and dz. Let us suppose the date to be 1761, Feb. 2, 4h 4m 484 G.M.T. By Tables I. and II. this date is equivalent to Fundamental Argument. The column headed g does not require explanation. The fourth column exhibits the mode of computing one of the vertical arguments in the tables of double entry. The two first numbers in the column refer to the century and year. The third number exhibits the quantity to be added to the argument in consequence of g having completed two periods subsequently to the date (17610) for which it is in the first instance computed, for at the beginning of every new period the vertical argument must receive a new accession amounting to 5'432. The fourth number represents the period of the inequality corresponding to the argument. The anomalistic age of the moon for the given date is little more than three days. Now if the moon's place were to be calculated throughout the whole anomalistic month, the horizontal argument g would, of course, vary from day to day; but the vertical argument would remain constantly equal to 9.166, and it would be only when a new month commenced that the vertical argument would receive a fresh accession of 5'432, and would consequently become equal to 16·296, a value which it would continue to retain throughout the whole of the month, and so on similarly for each succeeding month. The arguments in the tables of single entry are found in the same way as g. First, the argument is ascertained for the beginning of the century, then for the beginning of the year in the century, and, lastly, underneath these values is placed the number of days of the current year which has elapsed, a number which is manifestly the same for all the tables. These three numbers being added together, their sum diminished by the greatest multiple of an entire period contained in it constitutes the value of the argument for the date. Professor Hansen remarks that when the place of the moon is calculated by the tables for every twelve hours, her place for any intervening period may be determined with equal accuracy by a 84 process of interpolation. To facilitate this object he has given tables of interpolation founded upon Stirling's Theorem. Tables are also given for converting longitudes and latitudes into right ascensions and north-polar distances, and vice versâ. Astronomers cannot fail to look forward with interest to the publication of the theory upon which these tables are founded. In the meantime, it is impossible to contemplate without admiration the consummate skill with which the results of so vast a subject have been adapted to the computation of the moon's place. An illustration of the satisfactory accordance which exists between the results of some of the best modern observations of the moon, and the corresponding places in these tables, has already appeared in the Monthly Notices for November, 1854. Mr. Pogson has forwarded an Ephemeris of the Variable Stars for 1858, which will be inserted in the Monthly Notices for March. ERRATA. Vol. XVIII., page 1, line 5 from bottom, for 0.28443 read 0·028443. In the annexed engraving of Jupiter, for Vol. XVIII. No. 2, read Vol. XVIII. No. 3. Mr. Drach has also forwarded the following Errata which he found in his transcript of Dr. Donati's letter respecting Comet VI., 1857:: Vol. XVIII., page 14, line 7 from the bottom, for for -1 21.99 read -I 21'97 8.14 Announcement respecting Mr. Johnson's Catalogue of Southern Stars ... ... ... Measurement of the Position-Angles of Double-Stars, Mr. Dawes ... ... Improvement of the Double-Image Micrometer, Mr. W. Simms, jun. ... Note on Prof. Smyth's Invention, Prof. Powell Observations of Small Planets at the Royal Observatory ... 71 72 On the relative Precision of Measures of Double Stars, taken Photographically, and by Direct Vision, Mr. G. P. Bond Miscellaneous Notes, Mr. Dawes ... ... ... Annular Eclipse of the Sun, 1858, March 14-15 Notice of the Annals of the Observatory of Harvard College, Mr. Bond Tables de la Lune, Prof. Hansen London:-Printed by G. BARCLAY, Castle St. Leicester Sq. and Published at the ROYAL ASTRONOMICAL SOCIETY. VOL. XVIII. February 12, 1858. No. 4. THE Annual General Meeting of the Society, MANUEL J. JOHNSON, Esq., V.P., in the Chair. Wm. Docg, Esq, Carlisle; Dr. Godfrey, Enfield; and William Keith Murray, Esq., H.M. 60th Rifles, were balloted for and duly elected Fellows of the Society. Report of the Council to the Thirty-eighth Annual General The Council present their Report for the past year with congratulations on the state and prospects of the Society. The Report of the Auditors, subjoined, will show the state of the finances: Tea, sugar, biscuits, &c. for evening meetings. 13 13 O Waiters attending meetings. Coals, wood, &c. Balance at Banker's Sundry disbursements by the Treasurer.. 3 17 O 12 O O 907 о Assets and present property of the Society on Feb. 8, 1858: £ s. d. 290 18 6 56 14 3I Various astronomical instruments, books, prints, &c. Balance of Turnor Fund (included in Treasurer's account)... |