regulated according to the law above assigned; the sun occupying one of the foci of the ellipse, and from that station quietly disseminating on all sides its light and heat; while the earth travelling round it, and presenting itself differently to it at different times of the year and day, passes through the varieties of day and night, summer and winter, which we enjoy; its motion (art. 354.) being from west to east.

(362.) In this annual motion of the earth, its axis preserves, at all times, the same direction as if the orbitual movement had no existence; and is carried round parallel to itself, and pointing always to the same vanishing point in the sphere of the fixed stars. This it is which gives rise to the variety of seasons, as we shall now explain. In so doing, we shall neglect (for a reason which will be presently explained) the ellipticity of the orbit, and suppose it a circle, with the sun in the center and the four quadrants of its orbit to be described in equal times, the motion in a circle being uniform.

(363.) Let, then, S represent the sun, and A, B, C, D, four positions of the earth in its orbit 90° apart, viz. A that which it has at the moment when the sun is opposite to the intersection of the plane of the ecliptic B G, with that of the equator F E, B that which it has a quarter of a year subsequently or 90° of longitude in advance of A; C, 180° and D, 270° in advance of A.* In each of these positions

The figure by a mistake of the engraver is inverted right and left, so that the earth is made to move the wrong way round the sun — a point of no consequence to the reasoning, and which the reader will rectify in imagination.

let P Q represent the axis of the earth, about which its diurnal rotation is performed without interfering with its annual motion in its orbit. Then, since the sun can only enlighten one half of the surface at once, viz. that turned towards it, the shaded portions of the globe in its several positions will represent the dark, and the bright, the enlightened halves of the earth's surface in these positions. Now, 1st, in the position A, the sun is vertically over the intersection of the equinoctial F E and the ecliptic H G. It is, therefore, in the vernal equinox; and in this position the poles P, Q, both fall on the extreme confines of the enlightened side. In this position, therefore, it is day over half the northern and half the southern hemisphere at once; and as the earth revolves on its axis, every point of its surface describes half its diurnal course in light, and half in darkness; in other words, the duration of day and night is here equal over the whole globe : hence the term equinox. The same holds good at the autumnal equinox on the position C.

(364) B is the position of the earth at the time of the northern summer solstice. (See art. 389.) Here the north pole P, and a considerable portion of the earth's surface in its neighbourhood, as far as B, are situated within the enlightened half. As the earth turns on its axis in this position, therefore, the whole of that part remains constantly enlightened; therefore, at this point of its orbit, or at this season of the year, it is continual day at the north pole, and in all that region of the earth which encircles this pole as far as B- that is, to the distance of 23° 27′ 30′′ from the pole, or within what is called in geography the arctic circle. On the other hand, the opposite or south pole Q, with all the region comprised within the antarctic circle, as far as 23° 27' 30" from the south pole, are immersed at this season in darkness during the entire diurnal rotation, so that it is here continual night.

(365.) With regard to that portion of the surface comprehended between the arctic and antarctic circles, it is no less evident that the nearer any point is to the north pole, the

larger will be the portion of its diurnal course comprised within the bright, and the smaller within the dark hemisphere; that is to say, the longer will be its day, and the shorter its night. Every station north of the equator will have a day of more and a night of less than twelve hours' duration, and vice versa. All these phænomena are exactly inverted when the earth comes to the opposite point D of its orbit.

(366.) Now, the temperature of any part of the earth's surface depends mainly on its exposure to the sun's rays. Whenever the sun is above the horizon of any place, that place is receiving heat; when below, parting with it, by the process called radiation; and the whole quantities received and parted with in the year (secondary causes apart) must balance each other at every station, or the equilibrium of temperature (that is to say, the constancy which is observed to prevail in the annual averages of temperature as indicated by the thermometer) would not be supported. Whenever, then, the sun remains more than twelve hours above the horizon of any place, and less beneath, the general temperature of that place will be above the average; when the reverse, below. As the earth, then, moves from A to B, the days growing longer, and the nights shorter in the northern hemisphere, the temperature of every part of that hemisphere increases, and we pass from spring to summer; while, at the same time, the reverse obtains in the southern hemisphere. As the earth passes from B to C, the days and nights again approach to equality the excess of temperature in the northern hemisphere above the mean state grows less, as well as its defect in the southern; and at the autumnal equinox C, the mean state is once more attained. From thence to D, and, finally, round again to A, all the same phænomena, it is obvious, must again occur, but reversed, it being now winter in the northern and summer in the southern hemisphere.

(367.) All this is consonant to observed fact. The continual day within the polar circles in summer, and night in winter, the general increase of temperature and length of

day as the sun approaches the elevated pole, and the reversal of the seasons in the northern and southern hemispheres, are all facts too well known to require further comment. The positions A, C of the earth correspond, as we have said, to the equinoxes; those at B, D to the solstices. This term must be explained. If, at any point, X, of the orbit, we draw XP the earth's axis, and X S to the sun, it is evident that the angle P X S will be the sun's polar distance. Now, this angle is at its maximum in the position D, and at its minimum at B: being in the former case=90° +23° 28′=113° 28', and in the latter 90° - 23° 28′ = 66° 32′. At these points the sun ceases to approach to or to recede from the pole, and hence the name solstice.

(368 a.) Let us next consider how these phænomena are modified by the ellipticity of the earth's orbit and the position of its longer axis with respect to the line of the solstices. This ellipticity (art. 350.) is about one sixtieth of the mean distance, so that the sun, at its greatest proximity is about one thirtieth of its mean distance nearer us than when most remote. Since light and heat are equally dispersed from the sun in all directions, and are spread, in diverging, over the surface of a sphere enlarging as they recede from the center, they must diminish in intensity according to the inverse proportion of the surfaces over which they are spread, i. e. in the inverse ratio of the squares of the distances. Hence the hemisphere opposed to the sun will receive in a given time, when nearest, two thirtieths or one fifteenth more heat and light than when most remote, as may be shown by an easy calculation. Now, the sun's longitude when at its least distance from the earth (at which time it is said to be in perigee and the earth in its perihelion †) is at present 280° 28′ in which position it is on the 1st of January, or eleven days after the time of the winter solstice of the northern hemisphere; or, which is the same thing, the summer solstice of the southern (art. 364.), while on the other hand the sun is most remote (in apogee or the earth in its aphelion ‡), when

(9})2=(83)2 very nearly,=(31)2 = 361=36 very nearly, = 18.

tep, about or in the neighbourhood of; yn, the earth; os, the sun. anó, away from.

in longitude 100° 28′ or on the 2nd of July, i. e. eleven days after the epoch of the northern summer or southern winter solstice. We shall suppose, however, for simplicity of explanation, the perigee and apogee to be coincident with the solstice. At and about the southern summer solstice then, the whole earth is receiving per diem the greatest amount of heat that it can receive, and of this the southern hemisphere receives the larger share, because its pole and the whole region within the antarctic circle is in perpetual sunshine, while the corresponding northern regions lie in shadow. On the other hand, at and about the northern summer solstice, although it is true that the reverse conditions as to the regions illuminated prevail, yet the whole earth is then receiving per diem less heat owing to the sun's remoteness: so that on the whole if the seasons were of equal duration, or in other words, if the angular movement of the earth in its elliptic orbit were uniform, the southern hemisphere would receive more heat per annum than the northern, and would consequently have a warmer mean temperature.

(368b.) Such, however, is not the case. The angular velocity of the earth in its orbit, as we have seen (art. 350.), is not uniform, but varies in the inverse ratio of the square of the sun's distance, that is, in the same precise ratio as his heating power. The momentary supply of heat then received by the earth in every point of its orbit varies exactly as the momentary increase of its longitude, from which it obviously follows, that equal amounts of heat are received from the sun in passing over equal angles round it, in whatever part of the ellipse those angles may be situated. Supposing the orbit, then, to be divided into two segments by any straight line drawn through the sun, since equal angles in longitude (180°) are described on either side of this line, the amount of heat received will be equal. In passing then from either equinox to the other, the whole earth receives equal amount of heat, the inequality in the intensities of solar radiation in the two intervals being precisely compensated by the opposite inequality in the duration of the intervals them