Let us begin with that time of the year when the sun arrives at the vernal equinox. This occurs about the 21st of March. The sun is then perpendicular over the equator, daylight extends, uninterrupted, from pole to pole, and day and night (neglecting the effects of twilight and refraction) are of equal length all over the earth. Everywhere there are about twelve hours of daylight and twelve hours of darkness. This is the beginning of the astronomical spring. As time goes on, the motion of the sun in the ecliptic carries it eastward from the vernal equinox, and, at the same time, owing to the inclination of the ecliptic, it rises gradually higher above the equator, increasing its northern declination slowly, day after day. Immediately the equality of day and night ceases, and in the northern hemisphere the day becomes gradually longer in duration than the night, while in the southern hemisphere it becomes shorter. Moreover, because the sun is now north of the equator, daylight no longer extends from pole to pole on the earth, but the south pole is in continual darkness, while the north pole is illuminated.

You can illustrate this, and explain to yourself why the relative length of day and night changes, and why the sun leaves one pole in darkness while rising higher over the other, by suspending a small terrestrial globe with its axis inclined about 23½° from the perpendicular, and passing a lamp around it in a horizontal plane. At two points only in its circuit will the lamp be directly over the equator of the globe. Call one of these points the vernal equinox. You will then see that, when the lamp is directly over this point, its light illuminates the globe from pole to pole, but when it has passed round so as to be at a point higher than the equator, its light no longer reaches the lower pole, although it passes over the upper one.

Now, with the lamp thus elevated above the equator, set the globe in rotation about its axis. You will perceive that all points in the upper hemisphere are longer in light than in darkness, because the plane dividing the illuminated and the unilluminated halves of the globe is inclined to the globe's axis in such a way that it lies beyond the upper pole as seen from the direction of the lamp. Consequently, the upper half of the globe above the equator, as it goes round, has more of its surface illuminated than unilluminated, and, as it turns on its axis, any point in that upper half, moving round parallel to the equator, is longer in light than in darkness. You will also observe that the ratio of length of the light to the darkness is greater the nearer the point lies to the pole, and that when it is within a certain distance of the pole, corresponding with the elevation of the lamp above the equator, it lies in continual light—in other words, within that distance from the pole night vanishes and daylight is unceasing. At the same time you will perceive that round the lower pole there is a similar space within which day has vanished and night is unceasing, and that in the whole of the lower hemisphere night is longer than day. Exactly on the equator, day and night are always of equal length.

Endeavour to represent all this clearly to your imagination, before actually trying the experiment, or consulting a diagram. If you try the experiment you may, instead of setting the axis of the globe at a slant, place it upright, and then gradually raise and lower the lamp as it is carried round the globe, now above and now below the equator.

We return to our description of the actual movements of the sun. As it rises higher from the equator, not only does the day increase in length relatively to the night, but the rays of sunlight descend more nearly perpendicular upon the northern hemisphere. The consequence is that their heating effect upon the ground and the atmosphere increases and the temperature rises until, when the sun reaches its greatest northern declination, about the 22d of June (when it is 23½° north of the equator), the astronomical summer begins. This point in the sun's course through the circle of the ecliptic is called the summer solstice (see Part I, Sect. 8). Having passed the solstice, the sun begins to decline again toward the equator. For a short time the declination diminishes slowly because the course of the ecliptic close to the solstice is nearly parallel to the equator, and in the meantime the temperature in the northern hemisphere continues to increase, the amount of heat radiated away during the night being less than that received from the sun during the day. This condition continues for about six weeks, the greatest heats of summer falling at the end of July or the beginning of August, when the sun has already declined far toward the equator, and the nights have begun notably to lengthen. But the accumulation of heat during the earlier part of the summer is sufficient to counterbalance the loss caused by the declension of the sun.

About the 23d of September the sun again crosses the equator, this time at the autumnal equinox, the beginning of the astronomical autumn, and after that it sinks lower and lower (while appearing to rise in the southern hemisphere), until about the 22d of December, when it reaches its greatest southern declination, 23½°, at the winter solstice, which marks the beginning of the astronomical winter. It is hardly necessary to point out that the southern winter corresponds in time with the northern summer, and vice versa. From the winter solstice the sun turns northward once more, reaching the vernal equinox again on the 21st of March.

Thus we see that we owe the succession of the seasons entirely to the inclination of the earth's axis out of a perpendicular to the plane of the ecliptic. If there were no such inclination there would be climate but no seasons. There would be no summer heat, except in the neighbourhood of the equator, while the middle latitudes would have a moderate temperature the year round. Owing to the effects of refraction, perpetual day would prevail within a small region round each of the poles. The sun would be always perpendicular over the equator.

Two things remain to be pointed out with regard to the effect of the sun's annual motion in the ecliptic. One of these is the circles called the tropics. These are drawn round the earth parallel to the equator and at a distance of 23½° from it, one in the northern and the other in the southern hemisphere. The northern one is called the tropic of Cancer, because its corresponding circle on the celestial sphere runs through the zodiacal sign Cancer, and the southern one is called the tropic of Capricorn for a similar reason. The tropics run through the two solstices, and mark the apparent daily track of the sun in the sky when it is at either its greatest northern or its greatest southern declination. The sun is then perpendicular over one or the other of the tropics. That part of the earth lying between the tropics is called the torrid zone, because the sun is always not far from perpendicular over it, and the heat is very great.

The other thing to be mentioned is the polar circles. These are situated 23½° from each pole, just as the tropics are situated a similar distance on each side of the equator. The northern is called the arctic, and the southern the antarctic circle. Those parts of the earth which lie between the tropics and the polar circles are called respectively the northern and the southern temperate zone. The polar circles mark the limits of the region round each pole where the sun shines continuously when it is at one or the other of the solstices. If the reader will recall the experiment with the globe and the lamp, he will perceive that these circles correspond with the borders of the circular spaces at each pole of the globe which are alternately carried into and out of the full light as the lamp is elevated to its greatest height above the equator or depressed to its greatest distance below it. At each pole, in turn, there are six months of continual day followed by six months of continual night, and when the sun is at one of the solstices it just touches the horizon on the corresponding polar circle at the hour that marks midnight on the parts of the earth which lie outside the polar circles. This is the celebrated phenomenon of the “midnight sun.” At any point within the polar circle concerned, the sun, at the hour of midnight approaches the horizon but does not touch it, its midnight elevation increasing with nearness to the pole, while exactly at the pole itself the sun simply moves round the sky once in twenty-four hours in a circle practically parallel to the horizon. It is by observations on the daily movement of the sun that an explorer seeking one of the earth's poles during the long polar day is able to determine when he has actually reached his goal.

The reader will have remarked in these descriptions how frequently the angle of 23½° turns up, and he should remember that it is, in every case, due to the same cause, viz., the inclination of the earth's axis from a perpendicular to the ecliptic.

A very remarkable fact must now be referred to. Although the angular distance that the sun has to travel in passing first from the vernal equinox to the autumnal equinox, on the northern side of the equator, and then back again from the autumnal equinox to the vernal equinox, on the southern side of the equator, is the same, the time that it occupies in making these two half stages in its annual journey is not the same. Beginning from the 21st of March and counting the number of days to the 23d of September, and then beginning from the 23d of September and counting the number of days to the next 21st of March, you will find that in an ordinary year the first period is seven days longer than the second. In other words, the sun is a week longer above the equator than below it. The reason for this difference is found in the fact that the orbit of the earth about the sun is not a perfect circle, but is a slightly elongated ellipse, and the sun, instead of being situated in the centre, is situated in one of the two foci of the ellipse, 3,000,000 miles nearer to one end of it than to the other. Now this elliptical orbit of the earth is so situated that the earth is nearest to the focus occupied by the sun, or in perihelion, about December 31st, only a few days after the winter solstice, and farthest from the sun, or in aphelion, about July 1st, only a few days after the summer solstice. Thus the earth is nearer the sun during the winter half of the year, when the sun appears south of the equator, than during the summer half of the year, when the sun appears north of the equator. Now the law of gravitation teaches that when the earth is nearer the sun it must move more rapidly in its orbit than when it is more distant, from which it follows that the time occupied by the sun in its apparent passage from the vernal equinox to the autumnal equinox is longer than that occupied in the passage back from the autumnal to the vernal equinox.

But while the summer half of the year is longer than the winter half in the northern hemisphere, the reverse is the case in the southern hemisphere. There the winter is longer than the summer. Moreover, the winter of the southern hemisphere occurs when the earth is farthest from the sun, which accentuates the disadvantage. It has been thought that the greater quantity of ice about the south pole may be due to this increased length and severity of the southern winter. It is true that the southern summer, although shorter, is hotter than the northern, but while, theoretically, this should restore the balance as a whole, yet it would appear that the short hot summer does not, in fact, suffice to arrest the accumulation of ice.

However, the present condition of things as between the two hemispheres will not continue, but in the course of time will be reversed. The reader will recall that the precession of the equinoxes causes the axis of the earth to turn slowly round in space. At present the northern end of the earth's axis is inclined away from the aphelion and in the direction of the perihelion point of the orbit, so that the northern summer occurs when the earth is in the more distant part of its orbit, and the winter when it is in the nearer part. But the precession swings the axis round westward from its present position at the rate of 50″.2 per year, while at the same time the position of the orbit itself is shifted (by the effects of the attraction of the planets) in such a manner that the aphelion and perihelion points, which are called the apsides, move round eastward at the rate of 11″.25 per year. The combination of the precession with the motion of the apsides produces a revolution at the rate of 61″.45 per year, which in the course of 10,500 years will completely reverse the existing inclination of the axis with regard to the major diameter of the orbit, so that then the northern hemisphere will have its summer when the earth is near perihelion and its winter when it is near aphelion. The winter, then, will, for us, be long and severe and the summer short though hot.

It has been thought possible that such a state of things may cause, in our hemisphere, a partial renewal of what is known in geology as a glacial period. A glacial period in the southern hemisphere would probably always be less severe than in the northern, because of the great preponderance of sea over land in the southern half of the globe. An ocean climate is more equable than a land climate.

10. The Year, the Calendar, and the Month. A year is the period of time required for the earth to make one revolution in its orbit about the sun. But, as there are three kinds, or measures, of time, so there are three kinds, or measures, of the year. The first of these is called the sidereal year, but although, like sidereal time, it measures the true length of the period in question, it is not suitable for ordinary use. To understand what is meant by a sidereal year, imagine yourself to be looking at the earth from the sun, and suppose that at some instant you should see the earth exactly in conjunction with a star. When, having gone round the sun, it had come back again to conjunction with the same star, precisely one revolution would have been performed in its orbit, and the period elapsed would be a sidereal year. Practically, the length of the sidereal year is determined by observing when the sun, in its apparent annual journey round the sky, has come back to conjunction with some given star.

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.