ascertained to be about 365 days; and as the moon, apparently, made near 12 revolutions around the earth in that time the year was subdivided into 12 months, which, in reference to the phases of the moon, were again subdivided into weeks, of seven days each. The time occupied by the sun in the departure from any particular meridian, until its return to that meridian again, is called a Solar day, and a similar revolution, a star being the object, is called a Siderial day. We have already shown that the Solar day was longer than the Siderial day, on account of the apparent backward motion of the sun among the stars; but it is obvious, that the Siderial day, is the true measure of the time of revolution of the earth on its axis. Now if the earth made an exact number of revolutions on its axis, during the time in which it moves from a particular part of the heavens, back to that particular position again, it is evident we would have an exact number of siderial days to a year.

It is found, however, that the siderial year does not consist of an exact number of days, but contains, also, a fractional part of a day. When a long interval of time elapses between different observations, so that the earth makes a great number of revolutions around the sun, the length of the year may be very correctly ascertained. Thus- On the 1st day of April, 1669, at Oh. 3m. 47s., mean solar time, (which we shall explain presently,) Picard observed the distance of the sun from the star Procyon, measured on a parallel of latitude, to be 98° 59' 36". In 1745, which was 76 years after, La Caille observed the sun, to determine exactly the time when his difference of longitude should be the same from the star, as in Picard's observation. Now the day of the month in which La Caille observed, had been reckoned on from Picard's time, just as if the year had consisted of exactly 365 days, except every leap year, when a day had been added, for a reason that will appear presently. It was not until April 2d, at 11h. 10m. 45s., mean solar time, that the difference of longitude was the same as when Picard observed. Now here it was obvious that the earth had in reality, made just exactly 76 revolutions. The number of days however, was as follows, viz : 58 years, of 365 days each, and 18 leap years, of 366 days each,

LENGTH OF THE YEAR.

55

and 1d. 11h. 6m. 58s. more, or in all, 27759d. 11h. 6m. 58s., which being divided by 76, gives 365d. 6h. 8m. 47s. for the length of the Siderial year. More recent and exact observations give 365d. 6h. 9 m. 11s.

There are various kinds of years. First, the Siderial year, or the time which it takes the earth to perform exactly one revolution around the sun. This year it is not expedient to use, for the seasons being dependant on the position of the earth with regard to the sun, it is more convenient to have for the length of a year, the time from the commencement of spring to the commencement of spring again, and this is a period which, for a reason we will soon explain, is shorter than a siderial year. This year is called a Tropical or Equinoctial year. Again, inasmuch as this year does not consist of an exact number of days, and as it would be excessively inconvenient to have a year begin at any other time except the commencement of a day, we have the Civil year, which consists of exactly 365 days, and every fourth year, of 366. We have already given the length of the Siderial year, which is the time of a true revolution of the earth in its orbit, but the length of the equinoctial year, or year from beginning of spring, to spring again, is shorter than this. It is obvious that the equinoctial year is the one which most intimately concerns us, all agricultural, and other operations, being entirely dependant upon the seasons.

When we explain, in the next chapter, the cause of the seasons, we shall show why this year, must be shorter than the Siderial year. Meantime we may suppose one of the early philosophers detecting it in this manner. The path of the sun in the heavens being ascertained, it was soon observed that it was inclined at a certain angle, with the apparent diurnal paths of the stars. Thus, if we observe a certain star to-night, (mid-summer,) which rises due east, and watch its diurnal path, or the line which it traces in its apparent motion over the heavens, we will find it a part of a circle, whose centre is the pole of the heavens, near which the pole star is situated, and the star will set due west at a certain point midway between east and west, it will reach its highest altitude, after which it will begin to set, this highest altitude is

when it is in the meridian, or mid-heaven, and the meridian of a place, is a plane, or direction, which passes through the spectator, and the north and south point. If we observe another star which rises 10 south of east, we will find it arriving to the meridian something more than 100 lower down than the other star, according to our latitude. If we were at the equator, it would be just 100. This star would set 10° south of west, and so of any stars whatever, they would all apparently describe diurnal circles, or parts of such circles, all having the pole of the heavens for their grand centre. Now at the time of the summer solstice, or mid-summer, 21st of June, the sun rises directly east, and sets due west, describing apparently a diurnal circle in the heavens, after a few days, however, he will rise a little south of east, and set a little south of west, and in a few days more he will rise still farther south of east, and set so much south of west, until at the time of the winter solstice, or mid-winter, he will, in our northern latitude, rise very far towards the south, and come to the meridian very low down, and set at as great a distance south of the west point, as he arose south of the east. Now, if the backward motion of the sun in the heavens, had been performed in a diurnal circle, he would rise later and later each day, but always just at the same distance from the east. Hence we infer, that this backward motion of the sun, is not in a diurnal circle but inclined to it. This is the case, the ecliptic, or sun's apparent path, instead of corresponding with the equator, or with any particular diurnal circle parallel to the equator, cuts them all at a certain angle, which angle is called the inclination of the ecliptic. In order to make this part of our subject clear, we must have reference to a diagram.

Let P P', be the poles of the celestial vault or concave, having the earth A, within it, its poles being in the line P P'. As the earth turns around on its axis, let its equator reach the heavens, marking E E' as the celestial equator. Through a point B, at the distance of 231° from the equator, suppose a line B S, which also passes through the centre of the earth, to reach the sky at S. As the earth turns around, this line, B S, will mark out a circle in the heavens, C S, called, for a reason which will soon be given,

the tropic of Cancer. A similar line D S, which passes through

the centre of the earth, and a point 234° south of the equator, will trace out the circle C' S', called the tropic of Capricorn. The circle P E' PE, will represent a meridian, or a great circle which passes through the poles and the centre of the earth. Let S S', be a great circle, (of course seen edgewise in the diagram) this will represent the ecliptic which is inclined 2310 to the equator E E'. When the sun is at S in the ecliptic, his apparent diurnal path in the heavens, as the earth turns around, will be the circle C S; and to a spectator at B, the sun would be directly vertical, or overhead, at noon. If we suppose a little circle marked on the earth, corresponding with C S, we can readily perceive, that, as the sun is fixed, while the earth turns around, all those places upon the earth which lie in this circle, will have the sun vertical at noon. But a spectator at A, nearer the north pole of the earth, would have his Zenith, or highest point of the heavens, as at Z, hence the sun would come to the meridian below the Zenith. This is the case at all places north of the tropic of Cancer, or south of the tropic of Capricorn. Suppose now the sun to have moved in his orbit from S to O, he would then appear to rise at the same time with the star O, and describe the diurnal circle F Ġ in the heavens, parallel to the equator, arriving at the meridian

considerably lower than in the first case.

The dotted line POP will here represent the meridian, which, it must be remembered, is not a fixed direction in space, but simply a plane, extending from the earth to the heavens, and passing through the spectator, wherever he may be, and the poles of the earth. When the sun, after moving through one fourth of his orbit, arrives at the point where the equator and ecliptic cross each other, and which is called the equinoctial point, the days and nights are equal all over the world, and the sun is vertical at noon, at the equator. His apparent diurnal circle will now be the equator E E'. The sun, still moving on in its orbit, finally arrives at S' its greatest southern limit, describing the diurnal circle S'C' at the time of the winter solstice; after which it again moves northward, rising higher, and higher, each day, until after a tropical year, it arrives at the point S, where we commenced. Now if the points S and S', were fixed points in the heavens, the length of a tropical, or equinoctial year, would be the same as the length of a siderial year, for the equinoctial points are fixed with regard to the tropical points. It is, for many reasons, more convenient to reckon this year from equinox to equinox, and hence this is generally termed the equinoctial year.

Let A B C D, represent the sun's path, inclined 23° 28′ to the equator E D F B, and suppose B, the position of the vernal equi