this idea, it only remains to specify the particular tables fixed upon for the purpose, which ought to be of great and admitted excellence, since, once decided on, the very essence of the conception is that no subsequent alteration in any respect should be made, even when the continual progress of astronomical science shall have shown any one or all of the elements concerned to be in some minute degree erroneous (as necessarily they must), and shall have even ascertained the corrections they require (to be themselves again corrected, when another step in refinement shall have been made). (937.) Delambre's solar tables (in 1828) when this mode of reckoning time was first introduced*, appeared entitled to this distinction. According to these tables, the sun's mean longitude was 0°, or the mean vernal equinox occurred, in the year 1828, on the 22d of March at 1h 12m 59s-05 mean time at Greenwich, and therefore at 1h 12m 20.65 mean time at Paris, or 1h 56m 34s 55 mean time at Berlin, at which instant, therefore, the equinoctial time was Od Oh Om 08.00, being the commencement of the 1828th year current of equinoctial time, if we choose to date from the mean tabular equinox, nearest to the vulgar era, or of the 6541st year of the Julian period, if we prefer that of the first year of that period. (938.) Equinoctial time then dates from the mean vernal equinox of Delambre's solar tables, and its unit is the mean tropical year of these tables (365.242264). Hence, having the fractional part of a day expressing the difference between the mean local time at any place (suppose Greenwich) on any one day between two consecutive mean vernal equinoxes, that difference will be the same for every other day in the same interval. Thus, between the mean equinoxes of 1828 and 1829, the difference between equinoctial and Greenwich time is 0d-956261 or Od 22h 57m 0s-95, which expresses the equinoctial day, hour, minute, and second, corresponding to mean noon at Greenwich on March 23, 1828, and for the noons of the 24th, 25th, &c., we have only to substitute ld, 2d, &c. for 0a, retaining the same decimals of a day, or the same hours, minutes, &c., up to and including March 22, *On the instance of the author of these pages. 1829. Between Greenwich noon of the 22d and 23d of March, 1829, the 1828th equinoctial year terminates, and the 1829th commences. This happens at 0.286003, or at 6h 51m 50.66 Greenwich mean time, after which hour, and until the next noon, the Greenwich hour added to equinoctial time 364.956261 will amount to more than 365-242264, a complete year, which has therefore to be subtracted to get the equinoctial date in the next year, corresponding to the Greenwich time. For example, at 12h 0m 0s Greenwich mean time, or 0.500000, the equinoctial time will be 364.9562610+500000=365 456261, which being greater than 365-242264, shows that the equinoctial year current has changed, and the latter number being subtracted, we get Od-213977 for the equinoctial time of the 1829th year current corresponding to March 22, 12h Greenwich mean time. (939.) Having, therefore, the fractional part of a day for any one year expressing the equinoctial hour, &c., at the mean noon of any given place, that for succeeding years will be had by subtracting Od.242264, and its multiples, from such fractional part (increased if necessary by unity), and for preceding years by adding them. Thus, having found 0.198525 for the fractional part for 1827, we find for the fractional parts for succeeding years up to 1853 as follows*: 1828 1829 956261 1835 •260413 1842 .564565 1848 •110981 •713997 1836 018149 1843 322301 1849 .868717 1830 471793 1837 •775885 1844 ⚫080037 1850 *626453 1831 229469 1838 ⚫533621 1845 ⚫837773 1851 *384189 1832 *987205 1839 291357 1846 *595509 1852 141925 1833 744941 1840 *049093 1847 •953245 1853 *899661 1834 •502677 1841 .806829 These numbers differ from those in the Nautical Almanack, and would require to be substituted for them, to carry out the idea of equinoctial time as above laid down. In the years 1828 - 1833, the late eminent editor of that work used an equinox slightly differing from that of Delambre, which accounts for the difference in those years. In 1834, it would appear that.a deviation both from the principle of the text and from the previous practice of that ephemeris took place, in deriving the fraction for 1834 from that for 1833, which has been ever since perpetuated. It consisted in rejecting the mean longitude of Delambre's tables, and adopting Bessel's correction of that element. The effect of this alteration was to insert 3m 368 of purely imaginary time, between the end of the equinoctial year 1833 and the beginning of 1834, or, in other words, to make the interval between the noons of March 22 and 23, 1834, 24h 3m 3*68, when reckoned by equinoctial time. In 1835, and in all subsequent years, a further departure from the principle of the text took place by substituting Bessel's Y Y tropical year of 365-2422175 for Delambre's. Thus the whole subject fell into confusion. Under the present eminent superintendent of the Nautical Almanack a compromise has been effected-a fixed equinoctial year of 365-242216 mean solar days has been adopted (and it is to be hoped will henceforward be adhered to), and corrections stated by which the data in the Almanacks for 1828 -1894 may be brought into consistency with those in after years. According to this arrangement the fractional parts in question for 1828-1856 will run as follows: 1830 *473889 1838 ⚫536161 1831 *231673 1839 1832 1845 •840649 1852 145137 293945 1846 ⚫598433 1853 *989457 1840 *051729 1847 356217 1854 1833 ⚫747241 1841 809513 1848 •114001 1855 1834 505025 1842 ⚫567297 1849 871785 1856 1835 •262809 *902921 *660705 •418489 •176273 [Note (A) on Art. (916.) A rule proposed by Omar, a Persian astronomer of the court of Gelaleddin Melek Schah, in A.D. 1079, (or more than five centuries before the reformation of Gregory) deserves notice. It consists in interpolating a day, as in the Julian system, every fourth year, only postponing to the 33d year the intercalation which on that system would be made in the 32d. This is equivalent to omitting the Julian intercalation altogether in each 128th year (retaining all the others). To produce an accumulated error of a day on this system would require a lapse of 5000 years, so that the Persian astronomer's rule is not only far more simple, but materially more exact than the Gregorian.] [Note (B) on Table, Art. (926.) The civil epochs of the Metonic cycle, and the Hejira, are each one day later than the astronomical, the latter being the epochs of the absolute ne moons, the former those of the earliest possible visibility of the lunar crescent in a tropical sky. M. Biot has shown that the solstice and new moon not only coincided on the day here set down as the commencement of the Callippic cycle, but that, by a happy coincidence, a bare possibility existed of seeing the crescent moon at Athens within that day, reckoned from midnight to midnight.] [Note (C) on Art. (932.) The reformation of Gregory was, after all, incomplete. Instead of 10 days he ought to have omitted 12. The interval from Jan. 1, A. D. 1, to Jan. 1, A. D. 1582, reckoned as Julian years, is 577460 days, and as tropical, 577448, with an error not exceeding 0401, the difference being 12 days, whose omission would have completely restored the Julian epoch. But Gregory assumed for his fixed point of departure, not that epoch, but one later by 324 years, viz. Jan. 1, A.D. 325, the year of the Council of Nice; assuming which, the difference of the two reckonings is 94.505, or, to the nearest whole number, 10 days.] |