divisible, but is not divisible by 100, of 366; every year divisible by 100, but not by 400, again of 365; and every year divisible by 400, again of 366. For ex

ample, the year 1833, not being divisible by 4, consists of 365 days; 1836 of 366; 1800 and 1900 of 365 each; but 2000 of 366. In order to see how near this rule will bring us to the truth, let us see what number of days 10000 Gregorian years will contain, beginning with the year 1. Now, in 10000, the numbers not divisible by 4 will be of 10000, or 7500; those divisible by 100, but not by 400, will in like manner be of 100, or 75; so that, in the 10000 years in question, 7575 consist of 366, and the remaining 2425 of 365, producing in all 3652425 days, which would give for an average of each year, one with another, 365d 2425. The actual value of the tropical year (art. 327.) reduced into a decimal fraction, is 365-24224, so the error of the Gregorian rule on 10000 of the present tropical years is 2.6, or 2d 14h 24m; that is to say, less than a day in 3000 years; which is more than sufficient for all human purposes, those of the astronomer excepted, who is in no danger of being led into error from this cause. Even this error might be avoided by extending the wording of the Gregorian rule one step farther than its contrivers probably thought it worth while to go, and declaring that years divisible by 4000 should consist of 365 days. This would take off two integer days from the above-calculated number, and 2.5 from a larger average; making the sum of days in 100000 Gregorian years, 36524225, which differs only by a single day from 100000 real tropical years, such as they exist at present.

(633.) As any distance along a high road might, though in a rather inconvenient and roundabout way, be expressed without introducing error by setting up a series of milestones, at intervals of unequal lengths, so that every fourth mile, for instance, should be a yard longer than the rest, or according to any other fixed rule; taking care only to mark the stones, so as to

leave room for no mistake, and to advertise all travellers of the difference of lengths and their order of succession; so may any interval of time be expressed correctly by stating in what Gregorian years it begins and ends, and whereabouts in each. For this statement coupled with the declaratory rule, enables us to say how many integer years are to be reckoned at 365, and how many at 366 days. The latter years are called bissextiles, or leap-years, and the surplus days thus thrown into the reckoning are called intercalary or leap-days.

(634.) If the Gregorian rule, as above stated, had always been adhered to, nothing would be easier than to reckon the number of days elapsed between the present time and any historical recorded event. But this is not the case; and the history of the calendar, with reference to chronology, or to the calculation of ancient observations, may be compared to that of a clock, going regularly when left to itself, but sometimes forgotten to be wound up; and when wound, sometimes set forward, sometimes backward, and that often to serve particular purposes and private interests. Such, at least, appears to have been the case with the Roman calendar, in which our own originates, from the time of Numa to that of Julius Cæsar, when the lunar year of 13 months, or 355 days, was augmented at pleasure, to correspond to the solar, by which the seasons are determined, by the arbitrary intercalations of the priests, and the usurpations of the decemvirs and other magis. trates, till the confusion became inextricable. To Julius Cæsar, assisted by Sosigenes, an eminent Alexandrian astronomer and mathematician, we owe the neat contrivance of the two years of 365 and 366 days, and the insertion of one bissextile after three common years. This important change took place in the 45th year before Christ, which was the first regular year, commencing on the 1st of January, being the day of the new moon immediately following the winter solstice of the year before. We may judge of the state into which the reckoning of time had fallen, by the fact, that, to in

troduce the new system, it was necessary to enact that the previous year (46 B. c.) should consist of 455 days, a circumstance which obtained it the epithet of "the year of confusion."

(635.) 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 365, 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 elapsed) the difference

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

(636.) 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.*

(637.) 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

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.

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 13 lunar months, or 355 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.

* The Metonic cycle, or the fact, discovered by Meton, a Greek mathematician, that 19 solar years contain just 235 lunations (which in fact they do to a very great degree of approximation), was duly appreciated by the Greeks, as ensuring the correspondence of the solar and lunar years, and honours were decreed to its discoverer.

NOTE

On the Constitution of a Globular Cluster, referred to in page 401.

If we suppose a globular space filled with equal stars, uniformly dispersed through it, and very numerous, each of them attracting every other with a force inversely as the square of the distance, the resultant force by which any one of them (those at the surface alone excepted) will be urged, in virtue of their joint attractions, will be directed towards the common center of the sphere, and will be directly as the distance therefrom. This follows from what Newton has proved of the internal attraction of a homogeneous sphere. Now, under such a law of force, each particular star would describe a perfect ellipse about the common center of gravity as its center, and that, in whatever plane and whatever direction it might revolve. The condition, therefore, of a rotation of the cluster, as a mass, about a single axis would be unnecessary. Each ellipse, whatever might be the proportion of its axes, or the inclination of its plane to the others, would be invariable in every particular, and all would be described in one common period, so that at the end of every such period, or annus magnus of the system, every star of the cluster (except the superficial ones) would be exactly re-established in its original position, thence to set out afresh, and run the same unvarying round for an indefinite succession of ages. Supposing their motions, therefore, to be so adjusted at any one moment as that the orbits should not intersect each other, and so that the magnitude of each star, and the sphere of its more intense attraction, should bear but a small proportion to the distance separating the individuals, such a system, it is obvious, might subsist, and realise, in great measure, that abstract and ideal harmony, which Newton, in the 89th Proposition of the First Book of the Principia, has shown to characterise a law of force directly as the distance. See also Quarterly Review, No. 94. p. 540.- Author.