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elapsed of the Julian period, the number of which increased. by 1 gives the day current.

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EXAMPLE.What is the current day of the Julian period corresponding to the last day of Old Style in England, on Sept. 2., A. D. 1752.

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(930.) To find the same for any given date, New Style. Proceed as above, considering the date as a Julian date, and disregarding the change of style. Then from the resulting days, subtract as follows:

For any date of New Style, antecedent to March 1. A. D. 1700
After Feb. 28. 1700 and before March 1. A. D. 1800

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10 days.

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11 days.

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12 days.

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13 days, &c.

(931.) To find the interval between any two dates, whether

of Old or New Style, or one of one, and one of the other. Find

the day current of the Julian period corresponding to each date, and their difference is the interval required. If the dates contain hours, minutes, and seconds, they must be annexed to their respective days current, and the subtraction performed as usual.

*

(932.) The Julian rule made every fourth year, without exception, a bissextile. This is, in fact, an over-correction; it supposes the length of the tropical year to be 36514, which is too great, and thereby induces an error of 7 days in 900 years, as will easily appear on trial. Accordingly, so early as the year 1414, it began to be perceived that the equinoxes were gradually creeping away from the 21st of March and September, where they ought to have always fallen had the Julian year been exact, and happening (as it appeared) too early. The necessity of a fresh and effectual reform in the calendar was from that time continually urged, and at length admitted. The change (which took place under the popedom of Gregory XIII.) consisted in the omission of ten nominal days after the 4th of October, 1582, (so that the next day was called the 15th, and not the 5th,) and the promulgation of the rule already explained for future regulation. The change was adopted immediately in all catholic countries; but more slowly in protestant. In England, "the change of style," as it was called, took place after the 2d of September, 1752, eleven nominal days being then struck out; so that, the last day of Old Style being the 2d, the first of New Style (the next day) was called the 14th, instead of the 3d. The same legislative enactment which established the Gregorian year in England in 1752, shortened the preceding year, 1751, by a full quarter. Previous to that time, the year was held to begin with the 25th March, and the year A. D. 1751 did so accordingly; but that year was not suffered to run out, but was supplanted on the 1st January by the year 1752, which it was enacted should commence on that day, as well as every subsequent year. Russia is now the only country in Europe in which the Old Style is still adhered to, and (another secular year having

See note at the end of this chapter, p. 644.

elapsed) the difference between the European and Russian dates amounts, at present, to 12 days.

(933.) It is fortunate for astronomy that the confusion of dates, and the irreconcilable contradictions which historical statements too often exhibit, when confronted with the best knowledge we possess of the ancient reckonings of time, affect recorded observations but little. An astronomical observation, of any striking and well-marked phænomenon, carries with it, in most cases, abundant means of recovering its exact date, when any tolerable approximation is afforded to it by chronological records; and, so far from being abjectly dependent on the obscure and often contradictory dates, which the comparison of ancient authorities indicates, is often itself the surest and most convincing evidence on which a chronological epoch can be brought to rest. Remarkable eclipses, for instance, now that the lunar theory is thoroughly understood, can be calculated back for several thousands of years, without the possibility of mistaking the day of their occurrence. And, whenever any such eclipse is so interwoven 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.*

(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 especial indication. The lunar month has been resorted to in many instances; and some nations have, in fact, preferred a lunar to a solar

* 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.

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 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 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

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.

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

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