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Examples of this nature might be easily multiplied; but we have given more than enough to shew that previously to the attack of the plague, or other epidemical diseases, a temporary delirium generally affects those in whom the malady is lurking, or who are predisposed to receive the contagion. Whilst this hallucination lasts it conjures up the spectres of the dead before them.
Our scientific readers will receive with indulgence the observations which we have added in attempting to elucidate the wonders of Thorgill's Saga. They know that the miracles of the monk, or the tales of the village fireside, are not to be wholly or hastily rejected by the philosophical inquirer. They now command the electric aura which gleamed with portentous lustre on the point of the lance, or burnt round the helmet-crest, the omen of defeat or the harbinger of victory. By them is traced the eccentric path of the stone which fell from heaven itself in the days of the awe-stricken chronicler. Truth is often to be learnt from the liar, and wisdom from the fool. Superstition may give a false colouring to facts, ignorance may distort them; but on the whole, pyrrhonism and scepticism oppose greater obstacles to the knowledge of nature than credulity. We may not be able to unlock the casket at our first attempt, but because we are so foiled at first, should we therefore cast the key despitefully into the deep?
Art. XII.—Investigation of the Came of Easter, 1818, being appointed to be celebrated on a Wrong Day, #c. fyc. By a Member of the University of Oxford. T3Y the definition given in the Tables and Rules prefixed to the 'Book of Common Prayer,' ' Easter-day is always the first Sunday after the full moon which happens upon, or next after, the 21st day of March; and, if the full moon happens on a Sunday, Easter-day is the Sunday after.' This full moon is given in the tables on the •I I st of March; according to which Sunday the is Easter-day; but, as appears by the Nautical Almanack, the real full moon happened on Sunday, March 22d, and therefore, according to the above definition; Easter-day should have been fixed for the 29th.
From the well-known accuracy of astronomical observations, the occasion of this inconsistency is, of course, attributed to some error in the ecclesiastical method of computation. Without any attempt to point out the precise nature of the error, it has been supposed that the 'Tables and Rules for finding Easter' were originally constructed on a false principle, and have at length failed in the object for which they were intended.
Anxious to olitain some more satisfactory account of a fact so generally interesting, we took up the pamphlet before us, hoping,
from its title, and the respectable source whence it professedly, comes, to see the matter at once set at rest, and the public instructed in the true state of the case. Great, however, was our disappointment when, instead of a correct statement, we found a mere repetition of the imputed false principle in the original construction of the Tables—rendered indeed more intricate and confused by the introduction of another fact which has no connexion whatever with the subject, namely, the disagreement between our computed year and the true periodic time of the sun.
Leaving these misrepresentations, (from the consideration of which our readers could derive no benefit whatever,) we shall proceed to an examination of the method on which the 'Rules for finding Easter' are constructed; from which it will appear that in their nature they are, and always were known to be, liable to the inaccuracy of giving the full moon on a day different from that determined by astronomical observation; and that this inaccuracy, with the accidental concurrence of another fact, namely, that the latter of the two days, thus differently determined, falls on a Sunday, has occasioned the incorrect appointment of Easter in the present year.
It was discovered by Meton, an Athenian astronomer, that, after nineteen years, the moon completes two hundred and thirty-five lunations, and returns again to its changes on the same day of the month; which term of nineteen years is therefore called the Metonic or lunar cycle. If, in the first year of this cycle, all the days on which the full moons happen be marked throughout the calendar with the number 1, in the second year with the number 2, and so on progressively to the nineteenth, or last year, with the number 19, the days on which the full moons happen, for any given year of a succeeding cycle, will be found by looking to what days in the calendar the number of such year is prefixed. These nineteen numbers, thus pointing out the days of all the full moons in the year, ,and especially that full moon on which Easter depends, having been printed in characters of gold, are denominated ' Golden Numbers.'
In process of time it appeared that the cycle of the moon, or the' term of two hundred and thirty-five lunations, is less than nineteen average Julian years of three hundred and sixty-five days six hours by about an hour and a half ;* and when this progressively increasing disagreement amounts to a day, the Golden Numbers would of course cease to give the true day of the full moon, unless they were
days hrs. days hrs. / n llt
* 19 Julian years of 365 6 = 6939 18 0 0 0
236 lunations of 29 12 44' 2" 48'" . = 6939 16 30 58 45
Solar excess at the end ef the cycle . . = 1 29 nearly.
^fut back one day in the calendar. Such inaccuracy, however, waj 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, and 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 hours.
These two deviations are thus provided for in the Tables contained 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 tin- first years of the several centuries appears from this consideration :—the Hate being from the Christian era, or nativity of Christ, (which, as ill the case of the nativity of any other person, is by chtonologers considered the year 0,") tb« year 1, at its commencement, marks one year passed since the nativity of Christ—the year 2, at its commencement, marks two years passed since the nativity of Christ: by continuing the same process, the year 1800, at its commencement, ma: ks eighteen hundred years passed since the nativity of Christ, •r it ii the first year of the century.
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 hours 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, lit the year 2000, being a bissextile year in the ordinary course, the full moons will fall nearly sight 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 General Table, (by which the changes of the Golden Numbers in the calendar are indicated,) going forwards and backwards, thus, 3,4, o, 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 0, 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 8.J00, they will be in the same situations as in the year 1600.
Upon an examination of the construction of the tables and rules for finding 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. 44'2" 48"', is not Ae true periodic time of the moon in the heavens, which continually varies; it is merely the mean time of a synodic revolution.
The term of nineteen years, also, is taken at an average, though evidently of different duration, according to the variable number of leap years which enter into it. Then a comparison is instituted between this cycle and two hundred and thirty-five 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. 1 1 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 nearly 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 Easier 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 II, 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 determinmg 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 w orld, but the account of time differs according to the longitude of the place, an hour 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 2'id, so early as Oh. 10 minutes A. M., the same will happen at Dublin on Saturday March 21st, at about 11 h. 45 minutes F. M. In this case,