next noon, the Greenwich hour added to equinoctial time 3644.956261 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 364-956261+ 0-500000 365-456261, which being greater than 365-242264, shows that the equinoctial year current has changed, and the latter number being subtracted, we get 04.213977 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 04.242264, 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':: : 1 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 38.68 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 tropical year of 365-2422175, for Delambre's. Thus the whole subject has fallen into confusion. [Note 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 001, the difference being 12 days, whose omission would have completely restored the ulian 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 9d-505, or, to the nearest whole number, 10 days.] APPENDIX. I. LISTS OF NORTHERN AND SOUTHERN STARS, WITH THEIR APPROXIMATE MAGNITUDES, ON THE VULGAR AND PHOTOMETRIC SCALE. II. SYNOPTIC TABLE OF THE ELEMENTS OF THE PLANETARY SYSTEM. Name of Body. Mean Distance from the Mean Sidereal Period in Mean Eccentricity in parts of Inclination of Orbit to the Sun or Semi-axis. Solar Days. the Semi-axis. Ecliptic. Longitude of the Ascending Node. ELEMENTS OF THE PLANETARY SYSTEM. at | Epoch of the Elements in M. T. Mass (denominator Diameter in 0.25 607 48 Flora... 40 22 15.1 Astræa... 135 20 47·0 318 45 3.3 55 4 49.7 1848. Jan. 1. 0h B. Jupiter. 11 8 34.6 47 12 56.7 ..... |