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woven with the account given by an ancient author of some historical event, as to indicate precisely the interval of time between the eclipse, and the event, and at the same time completely to identify the eclipse, that date is recovered and fixed for ever.1·

(934.) The days thus parcelled out into years, the next step to a perfect knowledge of time is to secure the identification of each day, by imposing on it a name universally known and employed. Since, however, the days of a whole year are too numerous to admit of loading the memory with distinct names for each, all nations have felt the necessity of breaking them down into parcels of a more moderate extent; giving names to each of these parcels, and particularizing the days in each by numbers, or by some special indication. The lunar month has been resorted to in many instances; and some nations have, in fact, preferred a lunar to a solar chronology altogether, as the Turks and Jews continue to do to this day, making the year consist of 12 lunar months, or 354 days. Our own division into twelve unequal months is entirely arbitrary, and often productive of confusion, owing to the equivoque between the lunar and calendar month. The intercalary day naturally attaches itself to February as the shortest.

(935.) Astronomical time reckons from the noon of the current day, civil from the preceding midnight, so that the two dates coincide only during the earlier half of the astronomical, and the later of the civil day. This is an inconvenience which might be remedied by shifting the astronomical epoch to coincidence with the civil. There is, however, another inconvenience, and a very serious one, to which both are liable, inherent in the nature of the day itself, which is a local phænomenon, and commences at different instants of absolute time, under different meridians, whether we reckon from noon, midnight, sunrise, or sunset. In consequence all astronomical observations require, in addition to their date, to render them comparable with each other, the longitude of the place of observation from some meridian, commonly respected by all astronomers. For geographical longitudes, the Isle of Ferroe has been chosen by some as a common meridian, indifferent (and on that very account offensive) to all nations. Were astronomers to follow such an example, they would probably fix upon Alexandria, as that to which Ptolemy's observations

1 See the remarkable calculations of Mr. Baily relative to the celebrated solar eclipse which put an end to the battle between the kings of Media and Lydia, B. c. 610, Sept. 30. Phil. Trans. ci. 220.

"A month in law is a lunar month or twenty-eight days, (!!) unless otherwise expressed."-Blackstone, ii, chap. 9. "A lease for twelve months is only for forty-eight weeks."-Ibid.

and computations were reduced, and as claiming on that account the respect of all while offending the national egotism of none. But even this will not meet the whole difficulty. It will still remain doubtful, on a meridian 180° remote from that of Alexandria, what day is intended by any given date. Do what we will, when it is the Monday, the 1st of January, 1849, in one part of the world, it will be Sunday, the 31st of December, 1848, in another, so long as time is reckoned by local hours. This equivoque, and the necessity of specifying the geographical locality as an element of the date, can only be got over by a reckoning of time which refers itself to some event, real or imaginary, common to all the globe. Such an event is the passage of the sun through the vernal equinox, or rather the passage of an imaginary sun, supposed to move with perfect equality, through a vernal equinox supposed free from the inequalities of nutation, and receding upon the ecliptic with perfect uniformity. The actual equinox is variable, not only by the effect of nutation, but by that of the inequality of precession, resulting from the change in the plane of the ecliptic due to planetary perturbation. Both variations are, however, periodical; the one in the short period of 19 years, the other in a period of enormous length, hitherto uncalculated, and whose maximum of fluctuation is also unknown. This would appear, at first sight, to render impracticable the attempt to obtain from the sun's motion any rigorously uniform measure of time. A little consideration, however, will satisfy us that such is not the case. The solar tables, by which the apparent place of the sun in the heavens is represented with almost absolute precision from the earliest ages to the present time, are constructed upon the supposition that a certain angle, which is called "the sun's mean longitude," (and which is, in effect, the sum of the mean sidereal motion of the sun, plus the mean sidereal motion of the equinox in the opposite direction, as near as it can be obtained from the accumulated observations of twenty-five centuries,) increases with rigorous uniformity as time advances. The conversion of this mean longitude into time at the rate of 360° to the mean tropical year, (such as the tables assume it,) will therefore give us both the unit of time, and the uniform measure of its lapse which we seek. It will also furnish us with an epoch, not indeed marked by any real event, but not on that account the less positively fixed, being connected, through the medium of the tables, with every single observation of the sun on which they have been constructed and with which compared.

(936.) Such is the simplest abstract conception of equinoctial time. It is the mean longitude of the sun of some one approved set of solar tables, converted into time at the rate of 360° to the tropical year. Its unit is

the mean tropical year which those tables assume and no other, and its epoch is the mean vernal equinox of these tables for the current year, or the instant when the mean longitude of the tables is rigorously 0, according to the assumed mean motion of the sun and equinox, the assumed epoch of mean longitude, and the assumed equinoctial point on which the tables have been computed, and no other. To give complete effect to 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 2m 59s-05 mean time at Greenwich, and therefore at 1h 12m 20s.55 mean time at Paris, or 1h 56m 34.55 mean time at Berlin, at which instant, therefore, the equinoctial time was 0a 0h 0m 05.00, 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 0.956261 or 0a 22 57m 08.95, 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 1d, 2d, &c., for 0a, retaining the same decimals of a day, or the same hours, minutes, &c., up to and including March 22, 1829. Between Greenwich noon of the 22d and 23d of March, 1829, the 1828th equinoctial year terminates, and the 1829th commences. This happens at 04.286003, or at 6h 51m 50.66 Greenwich mean time, after which hour, and until the

next noon, the Greenwich hour added to equinoctial time 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 04.500000, 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, 12 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':

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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 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 04.01, 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 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.

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