The Joints of Time

I

THE reason that the year begins on January 1 is a ‘pretty reason,’as Lear’s poor fool would say. Julius Cæsar, when he reformed the calendar in the year 46 B.C., evidently had in mind to begin the year with the shortest day. The winter solstice at Rome occurred in that year on the twenty-fourth of December of the Julian calendar; consequently the first day of the year would have fallen on December 25. But he delayed it seven days out of regard for prevailing customs and the superstitions of the people. As they had been accustomed to a lunar calendar, they would be better satisfied if the first year of the new calendar came in with the new moon. Accordingly the mean new moon was carefully computed and the new calendar had its beginning on the first of January, 45 B.C., at sixteen minutes past six in the afternoon.

Among all peoples, in all ages, it has been the custom to start the year, whether civil or ecclesiastical, with either the winter or summer solstice or the vernal or autumnal equinox. These times seem to mark the natural beginnings for reckoning the circuit of the seasons. The result of Cæsar’s little stroke of diplomacy is that our year now has no relation to astronomic fact or logical reason. It has relation only to superstitions and political considerations which no longer exist.

That this year is 1926 A.D. is an opinion that would be questioned by few. But there is very good reason to feel dissatisfied with these figures. The church chronologist who set to work one day in the sixth century to find out how far back it was to the birth of Christ made a mistake of about four years.

The custom of numbering the years in the present manner did not, of course, begin immediately upon the birth of Christ. His birth and life made so little impression upon the world in general that the Greeks continued to count the years from the time of the first Olympic games, and the Romans from the mythical date when their city was founded. These dates represented their ideas as to what constituted the most memorable events in their history. As the centuries passed the world’s ideas changed; and in 527 A.D. Dionysius Exiguus, who compiled the first regular ecclesiastical code for the Western Church, conceived the idea of dating time with reference to the birth of Christ. In this connection an error was made. Herod died in the seventieth year of his age and in the very year in which Jesus of Nazareth was born; and this has been discovered to have occurred four years earlier than the date from which our chronology is reckoned, or the year 4 B.C. It seems rather inconsistent to say that Christ was born in the fourth year B.C.; but chronologists quite generally agree that such was the case. The present number of the Atlantic pretends to be making its appearance in 1926. It ought to be dated 1930.

If both the year and the epoch are so open to question, we need hesitate no longer to ask what is the matter with the months. What happened to them that some should have thirty-one days, while others have thirty, and one veers between twenty-eight and twenty-nine?

Here also there is a reason. The Romans believed there was luck in odd numbers; and seven of the months have thirty-one days each out of a desire to have as much good luck as possible. When Cæsar abolished the old lunar calendar and established in its place the form of calendar which we now have, he was adopting the absolute solar calendar of the Egyptians. In this calendar the year was made up of twelve months of thirty days each; and a supplementary period of five days, which was accounted a time of festival, completed the 365 days. To the Roman mind, here ware twelve unlucky months. In their old, or lunar, calendar, which was supposed to observe carefully the phases of the moon, all the months but one had been given an odd number of days. They had twenty-nine or thirty-one days each; and this in spite of the fact that the moon knows nothing whatever of a thirty-one-day period of revolution. They had tried to disagree with Nature for the sake of good luck; and the final result was such utter chaos and confusion in the keeping of time that they had to throw over the lunar scheme entirely and try the calendar of the Egyptians. As this was one hundred per cent unlucky, they proceeded to alter the month-periods somewhat to correspond to the old calendar. They took the five festival days and distributed them among the months so as to give five of them thirty-one days each. Then two more lucky months were created at the expense of February, thus making the number of thirty-oneday months which we now have. They did not hesitate to reduce the Egyptian number of thirty days to twenty-eight in the case of February because that had always been an unlucky month with them. It had originally been left with only twenty-eight as a matter of arithmetical necessity in making all the months odd.

There were two months to which the odd number of days was most important— July and August. July was named in honor of Julius Cæsar; and he saw to it, of course, that that month was made lucky. His successor, Augustus Cæsar, needed to have a month named for him; his birth-month was therefore called August and given thirty-one days. Not a great while after this distribution of days was made it was found that there was too great a disparity between the quarters of the year; and in the new shifting about to remedy this defect it was proposed to take a day from August. Augustus Cæsar put his foot down promptly on the idea. He would have no unlucky month named after him. Consequently a day was taken from September, which had been given thirty-one in the first distribution, and transferred to October. It is because of such considerations as these that seven of our months have thirty-one days each, and four of them thirty, while February ‘hath but twenty-eight.’

Openly and flagrantly wrong, or else mysteriously mistaken, are the names of the months. September is the ninth month; but a little knowledge of Latin is sufficient to inform us that it lays claim to being the seventh — from septem, seven. Likewise October, November, and December announce themselves as being the eighth, ninth, and tenth months respectively; all of which they are not.

The reason for this discrepancy between name and number is that the old Roman year, having some regard for the spring equinox, began in March. When the calendar was changed, and a new sort of year was begun, the old months continued to run in their accustomed succession, and mostly with their old names. The new solar year, breaking in at a certain stage of the moon, fell on the first day of their eleventh lunar month, which was January. January thus became the first month of the newly adopted year. February had been their twelfth month under the lunar calendar; and it was because it occupied this position that it lost its days. When days were needed by the other months, it seemed logical to pick them off the end of the year.

Our months are not lying to us; they are simply remembering the truth as it was in the old lunar calendar. While our present calendar, in all its various details, comes down to us from the forty-sixth year before Christ, the names of the months and their relative places run back to a time still more remote — so ancient, in fact, that it is a most uncertain period of history.

The month of January was named in honor of Janus, the god of beginnings, He is the god of two faces, looking behind and before. All gates and doors were under his sacred jurisdiction; so were the morning, the opening of all solemnities, the month of January, and beginnings generally. Of his two faces, one is youthful, the other aged. The aged countenance, looking behind, reflects upon the past; the youthful one looks forward and smiles, seeing happiness in the future. How appropriate to have the first month of the year named after such a god! It is a most striking symbolism, perfect in its poetry.

The reader who has been watching my statements closely will note in this connection that they do not hang together very well. Did I not say that January came from the old Roman year, and that it was the eleventh month of that year? How then do I get this artful appositeness to the beginning of the year?

This is just one more thing that has a reason. The month was originally dedicated to Janus because the labors of the husbandman in Southern Italy began anew at that time. This was a beginning that was quite as important as the beginning of the year. And so it becomes evident that the one month of our year whose name seems perfectly appropriate is only so by chance. In the very places where the calendar seems to run with an oily smoothness the time is most sadly out of joint.

When the sun Was made the standard of measurement of the year, the moon, along with the lunar year, was thrown utterly aside. Since that time she has been wandering through the months in the lost and aimless way that is familiar to anyone who refers to the calendar on the wall. The ancient Greek or Jew or Roman had a much easier time with the moon than we have. The new moon always fell on the first; and the full moon came in on the fourteenth. These facts, written as plainly on the sky as print on paper, constituted the calendar itself. Nowadays it takes an expert to tell us on which days of the month the principal phases of the moon are going to occur. And in consequence of this abandonment of the moon to her own peculiar notions of timekeeping, those church festivals whose dates are determined by the phases of the moon have had to go wandering with her. Hence the Movable Festivals.

Easter, in reference to which all the other movable festivals are determined, comes on the Sunday following the first full moon of spring — which is to say, the first full moon after the twentyfirst of March. The Book of Common Prayer, in those first few pages which contain all that a rector needs to know about arithmetic, tells us about the Golden Number, the Dominical Letter, and the Epact, and furnishes therewith a table by which to ascertain the time of that first full moon of spring. And, strange to say, the results are usually wrong when compared with any reliable calendar. In this connection the prayer book makes mention of a fact which would seem important to take heed of: ‘But Note, That the Full Moon, for the purposes of these Rules and Tables, is the Fourteenth Day of a Lunar Month, reckoned according to an ancient Ecclesiastical computation, and not the real or Astronomical Full Moon.’

It is not the actual moon in the heavens, nor yet the mean moon of the astronomers, that determines the time of Easter; though it is theoretically so. It is an altogether imaginary moon. But yet it is not wholly arbitrary when you consider that it comes in two or three days after the real full moon.

The reason — or at least one reason — for this way of computing the phases of the moon was to keep Easter from falling on the same date as the Jewish Passover. In an early day the Eastern Church contended that Easter had the same date as Passover, and they celebrated Easter as if the two holidays were identical; but the Western Church did not approve of this practice. The authorities favored the observance of the Sunday following the full moon which marked Passover. It was no doubt necessary in an early day to take some step to keep converts from getting the two festivals and their significance confused.

The Jewish Passover comes in on the fourteenth day of the month Nisan, which date, being the middle of a lunar month, marks the time of the full moon. It is the first full moon of spring. So it would seem that the early Church, by setting Easter for the Sunday following the springtime full moon, would be effectually avoiding the Jewish holiday for all time. But it so happens that if the Christians were to go by the regular astronomical calendar while the Jews continued (as they still do) to go by the old lunar, or Metonic, calendar, Easter would frequently fall on Passover in spite of such arrangement; hence the following of the ancient Ecclesiastical rule which pays little attention to the real moon in the sky. Notwithstanding all this care, the two festivals sometimes occur together. They will come on the same date in 1927, on the seventeenth of April. After that they will not come together again till 1981.

I think I have now said enough about the calendar to satisfy, or rather to dissatisfy, any rational reader. Certainly anyone must have come to the conclusion by this time that the calendar is in need of reform. And there is such a large element of human nature in it, rather than mere arithmetical error, that reform would seem to be the right word for what is needed.

II

But what man or body of men is going to decide what changes are advisable, among the many plans proposed, and then enforce observance upon the nations? Heretofore the sweeping changes of calendar correction have been accomplished only under some supreme mental or military authority of general acclaim. The Metonic calendar came in with Pericles; the solar calendar found its sponsor in Julius Cæsar; the corrected solar calendar was proclaimed by Gregory, a still powerful Pope. These names stand for the Golden Age of Greece, the Golden Age of Rome, and the great intellectual reawakening of the Renaissance. They are the high points in history. There seems, indeed, to be that in the nature of the calendar which requires for its making and its adoption all the activities and forces of a people at their best. War, conquest, mental and material progress — and then, at a point or pause in history when peace and prosperity give opportunity for intellectual stock-taking, and the times are dominated by some vigorous character or new racial spirit, a new calendar is born. But these are not the days of universal empire or of nations knit together by sentiment or religion. What would be needed now would be a congress of nations; or some body of men, not merely scientific or political, but of general prestige. Put in that way, the question suggests its own answer — the League of Nations.

That calendar reform should come under such jurisdiction would seem inevitable; and such is the case with the calendar at the present time. The League of Nations, acting through its Economic Section, which has been working in coöperation with the International Chamber of Commerce and taking advice from ecclesiastical authorities who are versed in the requirements of the church calendar, has been making progress toward some final recommendation in regard to calendar reform.

The League began with a Calendar Inquiry Committee appointed in 1922; and this committee confined its activities in 1923 chiefly to consultation with officially appointed representatives of ecclesiastical authority — Roman Catholic, Eastern Orthodox, and Anglican. The year 1923 was made notable in calendar history by the decision of the Russo-Greek and other Eastern Orthodox authorities to forsake the old-style Julian calendar and adopt the one in general use in the rest of the world. Russia, clinging religiously to the Julian calendar, was thirteen days behind the rest of the world. Commercial transactions and communications between Russia and other countries had to be carried on under a double set of dates. I he official church sanction of the change came subsequent to the decision of the Russian (Soviet) Government to abolish the much-cherished old calendar, regardless of its effects on saints days, and adopt the corrected form. Accordingly, September 30, old style, was immediately followed by October 14, new style. Thirteen uneventful days had brought themselves to pass in one night, and thirteen needless numbers were dropped quietly overboard upon ‘the sea of time’! Thus was healed a great cleavage in chronology, and the Gregorian calendar, already adopted in China and Japan, has become almost universal. The Soviet. Government, if it has nothing else to its credit, may be said to have put Russia in step with the sun.

The League invited proposals for calendar reform to reach Geneva by March 1, 1924. Of nearly one hundred proposed plans, from twenty nationalities, which were carefully grouped and analyzed in the following three months and largely rejected by the committee as being manifestly impractical, two seem to have taken the ascendancy; and these two are now making rival claims for final approval.

The so-called Astronomer’s or Swiss Plan, taking account of the fact that our year consists of fifty-two weeks and one day, abolishes the one day, or keeps it out of the reckoning, by making it January 0. By this simple step the week days are kept from rotating through the year. The same day of the week occurs on the same day of the month every year, which at present it does not.

As the calendar now is, every year ends on the same day of the week that it began on. This is due to the one day over the fifty-two weeks. As a consequence, each regular year begins a day later in the week than the one before, and is, of course, different all the way through. And as every fourth year, or leap year, has still another day at the end, the days of the week rotate through the years in a still more complicate way. But if the year consisted of an unbroken number of weeks, each year would begin on the same day of the week and thus be the same all the way through; and the calendar in that regard would become perpetual. The extra day of leap year would be taken care of by inserting it to follow June 31 as a summer holiday. As such it would be given a name but no date.

Another advantage of this plan would be to make the year divisible into exact quarters, not only in days but in unbroken weeks. With 365 days in the year and our present distribution of thirtyand thirty-one-day months, this is not the case. A year consisting of fifty-two weeks is exactly divisible by four, giving quarter-years of thirteen weeks each. The fifty-two weeks contain 364 days, and this number of days is exactly divisible into quarters of ninety-one days. The next problem is to divide the months of the year into quarters that shall be equal. As this ninety-one-day period could be made up of two thirty-day months and one of thirty-one days, it is proposed to adopt such a uniform distribution of month-lengths and do away with our present illogical system. It is considered desirable to have the year begin on Monday, which it would do if it were inaugurated, for instance, in 1928. This calendar could be printed in such form as to be perpetual. The equal quarters would present a desirable mathematical ideal for the purposes of the business man, accountant, or renter, or whoever has to do with quarter-years.

An objection to the plan is that it does not meet the ideal of having the month made up of a certain number of unbroken weeks. Like the present calendar it breaks up the weeks in relation to the beginning and end of the month. Another undesirable feature, especially from the religious standpoint, is that, by setting aside the extra days of the year and making a fiction of them, the continuity of the weeks, which has so long been kept inviolate, would be broken.

In this plan it is also proposed to revert January 1 to the time of the winter solstice. Beginning the year with December 22 would cause the seasons and the quarters to coincide more exactly than they do now. Julius Cæsar, had he not been preoccupied with public sentiment toward the moon, would no doubt have given January 1 a different position with regard to the seasons, reverting the date to the time of the shortest day. This new beginning of the year would be ideal from the astronomer’s standpoint, but it would have no practical advantages to recommend it very strongly to the business man or the general public; and it is doubtful whether this break with the past would not make it unwelcome to the nations. However, the rest of the plan does not necessarily include this. The other features may be considered upon their own merits.

The other plan, which has strong partisans in both America and Europe, is known as the International Fixed Calendar, or the Equal-Month Calendar. Here we have thirteen months of twenty-eight days each, accounting for 364 days of the year. The extra day of the regular year would be put down as January 0 or considered simply as an international Sabbath or stock-taking day. Leap year would have a midsummer holiday with no name; that is, it would come in between two regular week-days — like Capulet’s daughter it would ‘stand in number, though in reckoning none.’

In this plan the calendar for each month would be the same as for every other month throughout the year. The whole nature of the plan, with its more apparent advantages, may be seen at once by looking at its model month: —

The advantages claimed for it are as follows: (a) In every year, each of the 365 dates would recur on the same day of the week as in every other year. (b) Yearly, half-yearly, and quarterly events could be permanently fixed on recurring dates, (c) The year’s fiftytwo weeks would be twenty-six in each half-year and thirteen each quarteryear. (d) Appreciable economy would be gained in printing and circulating calendars.

In explaining the Astronomer’s Plan I pointed out that the dropping of one day from the regular year not only made the year divisible into quarters of equal length but also caused each year for all time to begin on some certain day of the week.

The present plan, by having months of equal length, and with no remainder of broken weeks to lap over from one month to another, carries this advantage even further. Supposing the year to begin on Monday, every week, every month, and every quarter-year would begin on Monday for all time. If the reformed year came in on some other day, a corresponding consistency would hold. As for the claim of economy in the printing of calendars, I think this needs no emphasis. It is likely that most of us would have the simple scheme of the month so thoroughly memorized that reference to a printed calendar would be hardly necessary. For the consolation of the printing fraternity it is pointed out that diaries would continue to be used. But as no one keeps a diary very long, and a new one has to be bought every year under the old system, this consolation is of little avail. The same diary would do for any year.

The principal objection to this plan is that thirteenth month. Human nature does not take readily to such radical invasions upon long-established custom. And when it is found that a transposition table (which has already been worked out) will be needed to put the time into joint again and show us our true relation with any former date, the people might rebel. Furthermore it is feared by those who have this plan in mind that the world may not take kindly to the number thirteen! Whether this will be enough to stop the League of Nations I cannot say; but it would be enough to give a Cæsar pause.

That the calendar could be improved is a growing opinion among business men belonging to associations affiliated directly or indirectly with the Economic Section of the League. ‘The International Chamber is on record favoring reform of the calendar, including a fixed date for Easter.’ So the secretary of the American section of that organization informs me. The matter has been given favorable consideration by the United States Chamber of Commerce. There are, too, societies in this country and Europe organized purely upon the basis of calendar reform.

What, let us now ask, are the prospects that some final solution of this perplexing problem will be arrived at? Are we the generation of generations to whom future peoples will look back when they tell the story of the calendar?

III

The question leads us to a reconsideration of certain fundamental facts. The history of the calendar is a struggle between human nature and arithmetic, the former not wanting to give in to the conclusions of the latter. This history, philosophically considered, not only serves to give us our bearings with regard to the problem of time measurement, but is a subject of considerable interest in itself.

A year consists of 365 days, 5 hours, 48 minutes, and 45.51 seconds. From the standpoint of one who is trying to equip the universe with some practical system of time measurement, this sort of year is manifestly ridiculous. In a practical system of measurement each larger unit should be exactly divisible by the smaller unit next below it.

A month has a mean length of 29 days, 12 hours, 44 minutes, and 2.7 seconds. This is equally absurd. We cannot very well deal with months and years which begin and end with such utter disregard of the smaller units that we have these fractions of a day on our hands.

What, then, is a day, let us ask. That it is not an acknowledged part of a month or a year is a fact which the above figures make sufficiently plain. Nature did not intend it to be such. A day is a day. It is sufficient unto itself, and it is wholly unconcerned about any other unit of time.

In a foot there are a certain number of inches of equal size; and in a bushel the pecks are of like content. But what is a month? There are said to be twelve months in a year, but this statement means little when you consider that the months do not fit into the year except by being altered to a variety of sizes!

As man did not make days, months, and years he is not, of course, to be held accountable for them. But he did make hours, minutes, and seconds, and so it would seem that as a matter of convenience and common sense he would have chosen such smaller time units as would fit in with and be a common divisor of the units already established. And no doubt he would have done so if he could. But evidently there were difficulties in the way; for when we state the length of a year or of a month in fractions of a second we are simply saying that these larger units are not divisible into any sort of time that man has been able to discover or invent.

Doing as best he could, man divided the day into parts which were equal but which fitted nothing further; and while his work might seem careless, inconsistent, and entirely incompetent, it is not so bad by comparison. For neither do days fit into months, nor months into years, nor years into any astronomical cycle which the heavens exhibit. It is all as bad as our English system of weights and measures; and the whole world knows how illogical and inconsistent and altogether incompetent that is.

Contrary to what any mortal member of any Academy would expect, the heavens are not constructed on the metric system! They do not countenance or make possible any such mechanical notions of perfection upon the part of man. Consequently the time is out of joint; and as man is a measuring and record-keeping animal there has been constant challenge to his intellect to set it right.

The whole truth of the matter is that Nature has offered us three different standards of time measurement — the day, the month, and the year. We have got to make a choice and abide by it. We may not accept them all as if they were harmonious facts and parts of a heavenly clockwork. That is just what they are not. Sun and moon revolve and rotate as they please; each is true to its own appointments. But the sun takes no care that years shall be divisible into months; and neither does the sun or moon time its evolutions to fit in with that standard of measurement which we call a day.

And this is a fact which is totally unacceptable to the mind of man. There is something about it which is obnoxious to human nature. If man, instead of God, had made the universe he would surely have made months that were exactly divisible into the year. This is a safe assertion in view of the fact that for ages he stuck to the moon as a standard of measurement while at the same time he tried to drive the chariot of the sun. We like to think that the universe is all working together, cogged and clocklike, with wheels that are proper multiples of one another — the whole acting as one big time system. If it is not so, then it ought to be so, and it is for us to bring the stars into harmony.

Of course there is but one way. That is to assume that they rotate and revolve thus and so. Consequently we have made the year a convenient length; and we have invented a system of leap years, leap months, and leap centuries to put us periodically into step with the facts. Finding ourselves compelled to deal in fractions of a day, we borrow from time, or extend credit to it, and then set things approximately right on a clearing-house system. We save up our scraps of time till we have enough to make a day, and we add it to a year; but as this is too liberal we pause once in a hundred years to take a day back; and as this is just a little too parsimonious we remember every four-hundredth year not to take the day that was coming to us. And for this temporizing with time we are hardly to be blamed. For the day and the year are each important to us; and when each insists upon being the sole standard of measurement, what else are we going to do about it?

Up to the time when our present form of calendar was adopted, all peoples, with the exception of the Egyptians, went strictly by the moon. A month was a month, an average duration of 29½ days; and it was of no very vital concern to them that twelve of those months amounted to only 354 days instead of a proper year.

To a people adopting a form of calendar the exact length of the year seems to be of no great importance. The year, with its four seasons, is supposed to bring a progressive change of climate; but when we consider that mere spells of weather make irruptions upon the seasonable climate and set the year backward or forward by days and weeks, an astronomer’s information as to the exact number of days in a year would seem to be of mere academic interest.

But an exact foreknowledge of the phases of the moon is of immediate and practical importance. Besides lighting the way for travelers and holy pilgrims, and thus making itself of prime importance in the regulations of religion and commerce, the moon was so obvious a timepiece, and so easily determined in its comings and goings, that it naturally became the first standard of measurement. A discrepancy of a week or two between twelve lunar months and the length of a solar year would appear to make no great difference in practical life.

But such a discrepancy is cumulative. The error keeps growing; it adds to itself year after year; and pretty soon it amounts to months. The inevitable result is that the months rotate through the seasons. And no people, whether herdsmen or planters, can afford to go by dates that are completely out of harmony with the solar year.

It was a puzzling prospect that opened up before the eyes of our forefathers when, after much effort to construct a satisfactory calendar, they discovered the true nature of the difficulty. They made use of months that lasted from moon to moon; but no particular number of moons fitted into a year! When they tried twelve there was a considerable remainder of time which that twelvemonth did not fill out; consequently, their first month of the year, starting eleven days before the actual solar year was ended, would cause a falling behind of the season with regard to the supposed date. Each year would fall farther behind, the result being that the months revolved rapidly through the year. The practical effect of this was that a winter holiday, such as our Christmas, would get around to midsummer; and all the while they were carefully observing its month and date! And a summer festival would work its way, perforce, to the middle of winter! This was very embarrassing. It not only made an undesirable state of affairs with regard to religious and other holidays, but it was confusing to the planter, a certain day of the month meaning nothing in his line of endeavor.

This harassing state of affairs prevailed among the early Greeks and Romans and troubled the mind of the world generally. It continued to work confusion at Rome up to the time the present form of calendar was adopted. When Julius Cæsar took over the solar year from the Egyptians, computed time at Rome had gained eighty days on actual time. And yet the priests had been accustomed to throwing an extra month into the year whenever it seemed to need it, after the manner of a crew dressing the ballast in a ship.

One might easily suggest that, if a lunar twelvemonth is eleven days short of the actual year, it would only be necessary to add these eleven days to the end of the year or distribute them among the months. This suggestion is really foolish. It would put the month out of step with the moon; and what use would a lunar calendar be in that case? It must be borne in mind that a calendar must go absolutely by the moon or absolutely by the sun, else it will run completely astray and be no calendar at all. The ancients managed very cleverly so far as the moon was concerned. A complete lunation is approximately 29½ days. Their months therefore had twenty-nine and thirty days alternately. By following this rule strictly they struck an average that kept in close step with the moon and only needed a day thrown in at long intervals to correct the slight error. This was the practice of the Greeks. The problem was to find a way to correct this calendar to correspond with the annual journey of the sun and yet not get out of step with the moon. They could have lunar months which rambled through the seasons in a most confusing way, or they could have a year which was fairly true to the sun, but with months that had no relation to the moon. And it is not in human nature to be satisfied with either.

It was a great day in the history of humanity when the astronomer Meton, of Athens, made his observation that once in nineteen years the sun and moon come round to the same relative position in the heavens. This means that the new moon, or any other phase of the moon, falls upon the same time or season that it did nineteen years before.

Here was an astronomic fact that was due to be taken advantage of. In this total time of nineteen years he counted just 235 lunations. This was a happy coincidence for the purposes of a lunar calendar. At last it was found that the sun does do something, complete, in exactly the same time that it takes the moon to do it. As a matter of fact, the 235 lunations take nineteen years and two hours; but the coincidence was sufficient for the purpose.

The problem had always been to get the moon into step with the sun without breaking a month to do it, and thus getting out of step with the moon. And when it is noted that any certain number of lunations equals any certain number of solar years, the problem is on its way to solution.

The period consisted of 6940 days. All that remained was to divide this period into years of twelve and thirteen lunar months. As twelve lunar months are less than a solar year, and thirteen are in excess of a solar year, either one is approximately correct. And the problem was to mix these years in such proportion that their total would come out even with the lunisolar period. It was found that by having seven of these thirteen-month years, or leap years, distributed among the nineteen the proper total was made up. Through all these years, whether of twelve or thirteen months, the moon was strictly followed by the alternation of twenty-nine-day and thirty-day months, except at intervals when an extra thirty-day month was used by way of correction.

To the modern mind such years would be far from satisfactory; for twelve of them in each nineteen-year period had 354 days, while the seven leap years had 384 days, due to the extra thirty-day month. But they were not trying to have solar years. This is a mathematical impossibility so long as you are observing lunar months. Their problem was simply to have a system of correction, on a true astronomical basis, which would hold them in an approximate relation to the sun and would keep their months from rotating through the seasons.

Heretofore a month had been but an uncertain craft for a man to trust himself to upon the sea of time. It had a way of floating clean off its bearing so that man and month were lost together. And when the date belied the season there was no certain and set formula to bring them into some recognized relation again. But this nineteen-year coincidence — a recurring basis of correction — was like having a row of stakes driven for you all across the blue of eternity. It was only necessary to figure out a formula for getting from one to the other; and this was done by having the thirteen-month years to hold the months and the seasons in approximate relation till the nineteen-year goal was reached. After that the formula could be repeated, and the problem was solved forever!

This calendar, a memorable invention, was made public at the Olympic games on July 16 of the year 432 B.C. and acclaimed by the people. Thereafter the number of each year, from one to nineteen, was engraved ‘on pillars of marble in letters of gold’; and in church calendars after the beginning of the Christian era the Metonic number of each year was printed in golden ink. It is the same Golden Number which we find in the modern prayer-book in connection with the rule for finding the date of Easter. The calendarmaker could hardly get along without it.

The Jewish calendar is essentially the same as this old Greek calendar, being based upon the Metonic cycle and the alternating months of twentynine and thirty days. It differs a little in the management of the leap years and common years, there being three lengths of each; but the end attained and the principle are the same. The Mohammedans cling to it religiously.

The Romans, if they had strictly observed the rules of the Metonic calendar, instead of altering figures upon the basis of superstition, would no doubt have found it fairly satisfactory. But they made a complete mess of it; and Julius Cæsar solved the problem by adopting the Egyptian method, which makes the sun the standard. When this was done the moon was cast utterly aside — necessarily. A solar calendar cannot serve two masters.

In establishing the solar calendar Cæsar took advice from the astronomers at Alexandria and made the length of the year 365¼ days, which is slightly in excess of the true period. In 1582 the error of about eleven minutes per year had accumulated until it amounted to ten days. This shifting of the date away from the season became undesirable because it brought Easter and all the other movable festivals at a wrong time. Pope Gregory XIII corrected it, making the fifth of October the fifteenth, 1582. And in order that the error might not grow to such size again he ordained that every year of even hundreds should not be counted a leap year, excepting every fourhundredth, beginning with the year 2000. In Catholic countries the change was promptly adopted; but in the Protestant world the people refused to take advice from the Pope even though he was dealing with a mere matter of arithmetic. It was not till 1751, after nearly two centuries of inconvenience, that Great Britain and her dependencies gave in. By that time the error was eleven days; and September 3, 1752, was called September 14.

IV

Viewing our present proposals for calendar reform in the light of history, we cannot but be struck by the fact that there is no call for astronomical correction. Our scheme of time measurement, substantially the same as it was in the year 45 B.C., and only slightly corrected in 1582, is astronomically perfect.

When Julius Cæsar made months of thirty-one days purely upon a basis of superstition, it really was no great matter from a scientific standpoint. The month was no longer an astronomical unit; the moon had utterly passed out as a standard of measurement. Of our present proposed plans, that known as the Astronomer’s has great standing in Europe; and that has a thirty-oneday month in every quarter. Its advantage over the present calendar is that a difference of from one to two days in the lengths of the quarter-years is done away with; and that is all. It is a difference which would probably be taken account of by statisticians or in certain business transactions. While many of the features of calendar reform win our assent at once, we scarcely know what attitude to take when we find the continuity of the week broken into and our relations with the past again put out of joint. The length of the month is of no importance astronomically; it is purely a matter of taste or business convenience. Astronomically the calendar is perfect; and it was made so by astronomers who had no observatories in the modern sense, and who made all their discoveries with the naked eye.

Of the great naked-eye astronomers I hardly know whether to give my admiration to Meton, who made the moon practical for human use, or to Hipparchus or to Copernicus. Meton was very useful to the world, but beyond his connection with the lunar calendar we know little about him. Hipparchus, who lived in the second century before Christ, was the first of whom we have reliable record; and he is accounted the founder of scientific astronomy. He explained the precession of the equinoxes, and was the first to discover from direct observation of the sun that the length of the year is somewhat less than 365¼ days. Copernicus was of the modern speculative type, which strikes out and concerns itself with God’s own business. Purely in his mind’s eye, and with no proof beyond appearances that were open to all, he saw a world-machine which, as was proved by later discovery, was very much like the one which God Himself had invented.

We are so accustomed to think of astronomy in connection with the modern observatory that when we read of Copernicus and his discoveries we naturally see him viewing the heavens through a telescope — forgetting, of course, that he never heard of such a thing. It is difficult for us to imagine an astronomer as mere ‘unaccommodated man ‘ standing forth and searching the sky on his own two feet, as it were. Even the astronomers who helped Gregory XIII to correct the system of leap years in 1582, when Shakespeare and Cervantes were living and Luther had not long been dead, had no notion of such a thing as a telescope. Their only lenses were the ones God gave them; and so it was with all the great astronomers who lived and died before them.

Consider well, then, the calendar on the wall. It came down to us, just as it is, from the days of paganism! It owes little to modern astronomy and nothing whatever to the telescope. And, except for the fact that Cæsar did not start it on the day of the winter solstice, it is astronomically perfect!