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put back one day in the calendar. Such inaccuracy, however, was suffered to remain till the year 1752, when Pope Gregory's reformation of the calendar was adopted in England. The alteration then made consisted in this-that whereas, in the common course of leap years, every hundredth year had been a leap year, it was now ordered, that only every four hundredth year should be a leap year; that is, three days were suppressed out of the Julian account in every four centuries, by cancelling the intercalary day in the first year of three of them; so that in one century of every four, the computation of time remained as it stood before the reformation of the calendar; but a day was omitted from each of the three other centuries.

This arrangement necessarily affected the method of determining the days of full moon by means of the Golden Numbers ; which, as has been shewn, was previously subject to a progressively increasing error. The following means therefore were devised for correcting both the former error and that now introduced, aud for keeping the Golden Numbers in future nearly to the true days of full moon.

It has been stated, that under the Julian computation the full moons take place sooner than they did nineteen years before, that is, in the same year of the former cycle, by about an hour and a half. This error amounts to nearly eight hours in a hundred years.

From this consideration, at the beginning of that century of the four, which has its first year bissextile,-The Julian computation having been alone used for a century previous,—the full moons will precede the time, at which they took place a hundred years before, by nearly eight hours.

But in the three centuries which have not their first year bissextile, one day being omitted, according to the Gregorian correction, the full moons, in the first year of each century, will fall later than the time at which they took place a hundred years before, by the difference between one day and eight hours, that is, sixteen bours.

These two deviations are thus provided for in the Tables con tained in the Book of Common Prayer. The Golden Number 14, for instance, prefixed to March 21, 1700, shews, that the full moon, for a century, takes place on that day in the fourteenth year of the lunar cycle. In the year 1800, not being bissextile in the

That the years denoted by any number of complete hundreds are the first years of the several centuries appears from this consideration :-the date being from ibe Christian cra, or nativity of Christ, (which, es in the case of the nativity of any other person, is by chronologers considered the year 0,) the year 1, at its commencement, marks one year passed since the nativity of Christ--the year ?, at its commencement, marks two years passed since the nativity of Christ: by continuing the same process, the year 1800, at iis commencement, nuaiks eighteen bundred years passed since the nativity of Christ, or it is the first year of the century.

usual

usual course, the full moons of the fourteenth year of the cycle will happen about sixteen hours later; which not amounting to a day, the Golden Number remains as before. But in the year 1900, the same full moons become about sixteen bours still later: the Golden Number 14 must therefore be put on one day to March 22d; and the full moon will be advanced in that day about eight hours. In the year 2000, being a bissextile year in the ordinary course, the full moons will fall nearly eight hours sooner; which might make it necessary to put back the Golden Number 14 to March 21st; if it were not that the full moon had been somewhat advanced in March 21st, previously to the first sixteen hours additional. And this, in fact, takes place afterwards, as appears from the numbers in the third column of the 2d Geveral Table, (by which the changes of the Golden Nambers in the calendar are indicated,) going for wards and backwards, thus, 3, 4, 3, 4; and again 8,9, 8, 9, &c.

The changes of the Golden Numbers in the calendar are indicated by the third column of numbers in the second General Table, thus : The situation of the Golden Numbers in the year 1600 being marked by o, in the year 1700 it will be marked by 1; that is, the Golden Numbers must be advanced one day in the calendar, to rectify the inaccuracy before mentioned. In the year 1800, no alteration need be made; but in the year 1900, to 2199 inclusive, the Golden Numbers must be again advanced; and again in the year 2200 : and after the Golden Numbers have been thus advanced twenty-nine days, they will again stand in their original order; that is, in the year 8500, they will be in the same situations as in the year 1600.

Upon an examination of the construction of the tables and rules for tinding the full moon on which Easter depends, and especially the second and third General Tables, it becomes obvious that they are not calculated to give the true time of full moon; because all the calculations are made from a consideration of the mean time of the several periodic revolutions.

The term of one lunation, or 29d. 12h. 44' 0" 48"", is not the true periodic time of the moon in the heavens, which continually varies ; it is merely the mean time of a syvodic revolution.

The term of nineteen years, also, is taken at an average, though evidently of different duration, according to the variable puber of leap years which enter into it. Then a comparison is instituted between this cycle and two hundred and thirty-tive lunations ; at the end of which, it appears, the moon returns again to its changes at the same time, within about an hour and a half. This difference is neglected till a hundred years have elapsed, when it causes the full moon to fall eight hours earlier, at the beginning of the century which has its first year bissextile, and sixteen hours later in those VOL. XVIII. NO. XXXVI.

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centuries centuries which have not their first year bissextile; and, then, an average correction is applied, which, on the whole, preserves a mean correspondence between nineteen years and two hundred and thirty-five lunations.

Such is the construction of the Tables, and such the method by which the full moon affecting Easter is determined from them. Though not so correct as they might be made, it does not strike us that any revision could render them perfect. In the present state, however, they are as accurate as ever they were supposed to be by those who understand them. It is expressly stated in the Table to find Easter from the year 1900,' that the corrections occasionally applied, are, in order that the ecclesiastical full moons may fall neurly on the same days with the real full moons.' Whence, then, this unusual and passionate attack on the present mode of computing the anniversaries of the Gospel History' as if a'conviction of the fallibility of the Tables' were something new—as if some 'progressively increasing error' were just now beginning to take effect, and that it was become absurd to argue in favour of a perseverance in our present scheme of computing ecclesiastical time!

No longer ago than the year 1815, the very same disagreement between the day of full moon given in the Almanack, and that determined by the ecclesiastical tables, took place, which has occurred in the present year. By an inspection of the Almanack for the year 1815, it appears that ihe Easter full moon fell on March 25th. This was the eleventh year of the lunar cycle, for which the day of the ecclesiastical full moon is given by the Golden Number 11, on March 24th, a difference in the tables precisely the same as that now so much noticed, but not producing the same effect, because the 25th of March, 1815, did not happen to be Sunday.

These obvious, though different effects of the same cause might easily have been predicted, in the year 1815: and it argues a want of knowledge of the subject, to give the alarm subsequently to the certain effect, by a tardy denunciation of the cause which accidentally produced it.

With respect to the writer's proposal of determining Easter from the astronomical full moon, such a method is liable to more material objection than that now in use. For, since the changes of the moon occur at the same point of absolute time throughout the world, but the account of time differs according to the longitude of the place, an bour for fifteen degrees,—the astronomical full moon may occur on different days, in two places of the same kingdom. If, for instance, the full moon happen at London on Sunday March 22d, so early as 0 h. 10 minutes A. M., the same will happen at Dublin on Saturday March 21st, at about 11 h. 45 minutes P.m. In this case,

Easter

Easter would be celebrated in England a week later than in Ireland. Such want of uniformity is, we conceive, far more objectionable than the defect which occurs under the present system of ecclesiastical computation.

As the consideration of the accuracy of our computed year, compared with the true periodic time of the sun, though unconnected with the fixing of Easter, has been introduced into the subject, and never rightly stated, we shall conclude this brief article with an account of the present state of the calendar, and of the further correction which would render it perfect.

The true annual period of the sun, or the time it takes to return to the same equinox, according to La Place, is 365.242222 days, or 365 days, 5 hours, 48 minutes, 48 seconds, within the fiftieth part of a second. This term is also stated by Vince, in his Astronomy, as the length of the year, from the best observations.

The Julian year, consisting of 365 days, with one day added every fourth year, is, on an average, 365 days 6 hours. If the correct time be subtracted from this, there will remain a balance of 11 minutes, 12 seconds annual excess, in the Julian computation above the true.

In the year 325, when the Council of Nice appointed Easter-day to be celebrated on the first Sunday after the first full moon next after the vernal equinox, this equinox fell on the 21st of March.' Such would, evidently, not continue to be the case, in subsequent years, on account of the excess, before mentioned, in the computed year, of 11 miứutes, 12 seconds. In the year 1582, 1257 years after the Nicene council, this error bad accumulated to 11' 12" X 1257, or 9 days, 18 hours, 38 minutes; nearly ten days. Therefore, to restore the equinox to the 21st of March, it was become necessary to omit ten days from the calendar, which was accordingly done, by order of Pope Gregory. And in the year 1752, 1427 years after the Nicene council

, when the Gregorian account was adopted in England, the error had accumulated to "l'12" X 1427, or 11 days, 2 hours, 22 minutes: eleven days were, therefore, rejected from the calendar; and the vernal equinox was restored to the 21st of March.

It is observable, that in the statute 24 Geo. II. ch.23, made for correcting the calendar then in use, the definition of Easter is so far changed, from that given of it at the Council of Nice, that the consideration of the vernal equinox is wholly omitted. It remains, however, a criterion of the accuracy of our computed year ; since the sun being at the vernal equinox, in one year on the 21st of March, if the computed year perfectly coincided with the solar year, it would always return to that equinox at the same instant. With the view of thus keeping the account of time correct, by 112

retaining

retaining the equinox at the 21st of March, another important región lation of Pope Gregory was adopted. The ordinary course of leap years was interrupted, by an omission of the intercalary day in every hundredth year except the four hundredth : thus three days were suppressed from the computation of time in four centuries, and the computed year became, on an average, three hundred and sixty-five days, five hours, forty-nine minutes, twelve seconds ;* leaving still a balance of twenty-four seconds annual excess, in the Gregorian computation above the true. They, however, so nearly coincide, that the excess will not amount to a day till 3600 years have elapsed; and the equinox will, upon the whole,+ not take place twenty-four hours sooner than it did in the year 1752, before the year 5352. This is, indeed, sufficiently accurate for all purposes; for a great number of centuries must elapse before the equinox will be so far removed from the 21st of March, as to be sensible to the agricnlturist.

The correction, which would have rendered the Julian computation perfect, will appear from the consideration, that the annual excess of eleven minutes, twelve seconds, exactly amounts to seven days in nine hundred years. If, therefore, when the calendar was reformed, it had been determined, instead of the present omission of three days in every four hundred years, six days in every eight hundred years, and so 011, that seven days should be omitted in the course of every nine hundred years, the computed average year would have exactly coincided with the solar, and the equinox been fixed to the same day for ever.

Art. XIII. The Secret and True History of the Church of Scot

land, from the Restoration to the yeur 1678. By the Rev.
Mr. James Kirkton, &c. With an Account of the Murder of
Archbishop Sharp: By James Russell, an actor therein.
Edited from the MS. by Charles Kirkpatrick Sharpe. 4to.
Edinburgh.
THIS work may be rather considered as containing valuable

materials for the bistory of a dark and turbulent period, than as being itself such. It has been repeatedly quoted by Wodrow, Laing, and other historians of the period, and carries with it a degree of authenticity scarcely pretended to by other authors of the

365 days 6 hours X 400 = 146100 days in 400 Julian years. From which three days being subtracted, as in the Gregorian account, there remain, in 400 Gregorian years, 146097 days, or 365 days 5 hours 49' 12'' in one average Gregorian year.

† On account of the correction of the year being applied on an average, the vernal equinox, in fact, takes place on the 20th of March in a leap year, and on the first year after leap year; and on the 21st in the two remaining years. 11' 12'' : 1440 x 7, the miuutes in 7 days :: 1 year : 900 years.

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