The second kind of year is called the tropical year, and it is measured by the period taken by the sun to pass round the sky from one conjunction with the vernal equinox to the next. This period differs slightly from the first, because, owing to the precession of the equinoxes, the vernal equinox is slowly shifting westward, as if to meet the sun in its annual course, from which it results that the sun overtakes the equinox a little before it has completed a sidereal year. The tropical year is about twenty minutes shorter than the sidereal year. It is, however, more convenient for ordinary purposes, because we naturally refer the progress of the year to that of the seasons, and, as we have seen, the seasons depend upon the equinoxes.
But yet the tropical year is not entirely satisfactory as a measure of time, because the number of days contained in it is not an even one. Its length is 366 days, 5 hours, 48 minutes, 46 seconds. Accordingly, as the irregularities of apparent solar time were avoided by the invention of mean solar time, so the difficulty presented by the tropical year is gotten rid of, as far as possible, by means of what is called the civil year, or the calendar year, the average length of which is almost exactly equal to that of the tropical year. This brings us to the consideration of the calendar, which is as full of compromises as a political treaty—but there is no help for it since nature did not see fit to make the day an exact fraction of the year, or, in other words, to make the day and the year commensurable quantities of time.
Without going into a history of the reforms that the calendar has undergone, which would demand a great deal of space, we may simply say that the basis of the calendar we use to-day was established by Julius Cæsar, with the aid of the Greek astronomer Sosigenes. This is the Julian calendar, and the reformed shape in which it exists at present is called the Gregorian calendar. Cæsar assumed 365¼ days as the true length of the year, and, in order to get rid of the quarter day, ordered that it should be left out of account for three years out of every four. In the fourth year the four quarter days were added together to make one additional day, which was added to that particular year. Thus the ordinary years were each 365 days long and every fourth year was 366 days long. This fourth year was called the bissextile year. It was identical with our leap year. The days of both the ordinary and the leap years were distributed among the twelve months very much as we distribute them now.
But Cæsar's assumption of 365¼ days as the length of the year was erroneous, being about 11 min. 14 sec. longer than the real tropical year. In the sixteenth century this error had accumulated to such a degree that the months were becoming seriously disjointed from the seasons with which they had been customarily associated. In consequence, Pope Gregory XIII, assisted by the astronomer Clavius, introduced a slight reform of the Julian calendar. The accumulated days were dropped, and a new start taken, and the rule for leap year was changed so as to read that “all years, whose date-number is divisible by four without a remainder are leap years, unless they are century years (such as 1800, 1900, etc.). The century years are not leap years, unless their date number is divisible by 400, in which case they are.” And this is the rule as it prevails to-day, although there is now (1912) serious talk of undertaking a new revision. But the Gregorian calendar is so nearly correct that more than 3000 years must elapse before the length of the year as determined by it will differ by one day from the true tropical year.
The subject of the reform of the calendar is a very interesting one, but, together with that of the rules for determining the date of Easter, its discussion must be sought in more extensive works.
There is one other measure of time, depending upon the motion of a heavenly body, which must be mentioned. This is the month, or the period required for the moon to make a revolution round the earth. Here we encounter again the same difficulty, for the month also is incommensurable with the year. Then, too, the length of the month varies according to the way in which it is reckoned. We have, first, a sidereal revolution of the moon, which is measured by the time taken to pass round the earth from one conjunction with a star to the next. This is, on the average, 27 days, 7 hours, 43 minutes, 12 seconds. Next we have a synodical revolution of the moon, which is measured by the time it takes in passing from the phase of new moon round to the same phase again. This seems the most natural measure of a month, because the changing phases of the moon are its most conspicuous peculiarity. (These will be explained in Part III.) The length of the month, as thus measured, is, on the average, 29 days, 12 hours, 44 minutes, 3 seconds. The reason why the synodical month is so much longer than the sidereal month is because new moon can occur only when the moon is in conjunction with the sun, i.e. exactly between the earth and the sun, and in the interval between two new moons the sun moves onward, so that for the second conjunction the moon must go farther to overtake the sun. It will be observed that both of the month measures are given in average figures. This is because the moon's motion is not quite regular, owing partly to the eccentricity of its orbit and partly to the disturbing effects of the sun's attraction. The length of the sidereal revolution varies to the extent of three hours, and that of the synodical revolution to the extent of thirteen hours.
But, whichever measure of the month we take, it is incommensurate with the year, i.e. there is not an even number of months in a year. In ancient times ceaseless efforts were made to adjust the months to the measure of the year, but we have practically given up the attempt, and in our calendar the lunar months shift along as they will, while the ordinary months are periods of a certain number of days, having no relation to the movements of the moon.
It has been thought that the period called a week, which has been used from time immemorial, may have originated from the fact that the interval from new moon to the first quarter and from first quarter to full moon, etc., is very nearly seven days. But the week is as incorrigible as all its sisters in the discordant family of time, and there is no more difficult problem for human ingenuity than that of inventing a system of reckoning, in which the days, the weeks, the months, and the years shall be adjusted to the closest possible harmony.
Spiral Nebula in Ursa Major (M 101)
Photographed at the Lick Observatory by J. E. Keeler, with the Crossley reflector. Exposure four hours.
Note the appearance of swift revolution, as if the nebula were throwing itself to pieces like a spinning pin-wheel.