directions, and being spread over the surface of a sphere continually enlarging as we recede from the centre, must, of course, diminish in intensity according to the inverse proportion of the surface of the sphere over which it is spread; that is, in the inverse proportion of the square of the distance. But we have seen (art. 293.) that this is also the proportion in which the angular velocity of the earth about the sun varies. Hence it ap

pears, that the momentary supply of heat received by the earth from the sun varies in the exact proportion of the angular velocity, i. e. of the momentary increase of longitude: and from this it 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. Let, then, S represent the sun ;

AQM-P the earth's orbit; A its nearest point to the sun, or, as it is called, the perihelion of its orbit; M the farthest, or the aphelion; and therefore A S M the axis of the ellipse. Now, suppose the orbit divided into two segments by a straight line PS Q, drawn through the sun, and any how situated as to direction; then, if we suppose the earth to circulate in the direction PAQMP, it will have passed over 180° of longitude in moving from P to Q, and as many in moving from Q to P. It appears, therefore, from what has been shown, that the supplies of heat received from the sun will be equal in the two segments, in whatever direction the line PSQ be drawn. They will, indeed, be described in unequal

CHAP. V. 'EQUAL DISTRIBUTION OF HEAT.

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times; that in which the perihelion A lies in a shorter, and the other in a longer, in proportion to their unequal area but the greater proximity of the sun in the smaller segment compensates exactly for its more rapid description, and thus an equilibrium of heat is, as it were, maintained. Were it not for this, the excentricity of the orbit would materially influence the transition of seasons. The fluctuation of distance amounts to nearly 3th of its mean quantity, and, consequently, the fluctu_ ation in the sun's direct heating power to double this, or 1th of the whole. Now, the perihelion of the orbit is situated nearly at the place of the northern winter solstice; so that, were it not for the compensation we have just described, the effect would be to exaggerate the difference of summer and winter in the southern hemisphere, and to moderate it in the northern; thus producing a more violent alternation of climate in the one hemisphere, and an approach to perpetual spring in the other. As it is, however, no such inequality subsists, but an equal and impartial distribution of heat and light is accorded to both.*

(316.) The great key to simplicity of conception in astronomy, and, indeed, in all sciences where motion is concerned, consists in contemplating every movement as referred to points which are either permanently fixed, or so nearly so, as that their motions shall be too small to interfere materially with and confuse our notions. In the choice of these primary points of reference, too, we must endeavour, as far as possible, to select such as have simple and symmetrical geometrical relations of situation with respect to the curves described by the moving parts of the system, and which are thereby fitted to perform the office of natural centres-advantageous stations for the eye of reason and theory. Having learned to attribute an orbitual motion to the earth, it loses this advantage, which is transferred to the sun, as the fixed centre about which its orbit is performed. Precisely as,

* See Geological Transactions, 1832, "On the Astronomical Causes which may influence Geological Phenomena,"-by the author of this work.

when embarrassed by the earth's diurnal motion, we have learned to transfer, in imagination, our station of observation from its surface to its centre, by the application of the diurnal parallax; so, when we come to enquire into the movements of the planets, we shall find ourselves continually embarrassed by the orbitual motion of our point of view, unless, by the consideration of the annual or heliocentric parallax, as it may be termed, we consent to refer all our observations on them to the centre of the sun, or rather to the common centre of gravity of the sun, and the other bodies which are connected with it in our system. Hence arises the distinction between the geocentric and heliocentric place of an object. The former refers its situation in space to an imaginary sphere of infinite radius, having the centre of the earth for its centre- the latter to one concentric with the sun. Thus, when we speak of the heliocentric longitudes and latitudes of objects, we suppose the spectator situated in the sun, and referring them, by circles perpendicular to the plane of the ecliptic, to the great circle marked out in the heavens by the infinite prolongation of that plane.

(317.) The point in the imaginary concave of an infinite heaven, to which a spectator in the sun refers the earth, must, of course, be diametrically opposite to that to which a spectator on the earth refers the sun's centre; consequently, the heliocentric latitude of the earth is always nothing, and its heliocentric longitude always equal to the sun's geocentric longitude + 180°. The heliocentric equinoxes and solstices are, therefore, the same as the geocentric; and to conceive them, we have only to imagine a plane passing through the sun's centre, parallel to the earth's equator, and prolonged infinitely on all sides. The line of intersection of this plane and the plane of the ecliptic is the line of equinoxes, and the solstices are 90° distant from it.

(318.) The position of the longer axis of the earth's orbit is a point of great importance. In the figure (art. 315.) let ECLI be the ecliptic, E the vernal

MEAN AND TRUE LONGITUDE OF THE SUN. 201

equinox, L the autumnal (i. e. the points to which the earth is referred from the sun when its heliocentric lon-14 gitudes are 0° and 180° respectively). Supposing the earth's motion to be performed in the direction E C L I, the angle ESA, or the longitude of the perihelion, in the year 1800 was 99° 30′ 5′′: we say in the year 1800, because, in point of fact, by the operation of causes hereafter to be explained, its position is subject to an extremely slow variation of about 12" per annum to the eastward, and which, in the progress of an immensely long period of no less than 20,984 years carries the axis A S M of the orbit completely round the whole circumference of the ecliptic. But this motion must be disregarded for the present, as well as many other minute deviations, to be brought into view when they can be better understood.

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(319.) Were the earth's orbit a circle, described with a uniform velocity about the sun placed in its centre, nothing could be easier than to calculate its position at any time, with respect to the line of equinoxes, or its longitude, for we should only have to reduce to numbers the proportion following; viz. One year: the time elapsed: 360° the arc of longitude passed over. The longitude so calculated is called in astronomy the mean longitude of the earth. But since the earth's orbit is neither circular, nor uniformly described, this rule will not give us the true place in the orbit at any proposed moment. Nevertheless, as the excentricity and deviation from a circle are small, the true place will never deviate very far from that so determined (which, for distinction's sake, is called the mean place), and the former may at all times be calculated from the latter, by applying to it a correction or equation (as it is termed), whose amount is never very great, and whose computation is a question of pure geometry, depending on the equable description of areas by the earth about the sun. For since, in the elliptic motion, according to Kepler's law above stated, areas not angles are described uniformly, the proportion must now be stated

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thus; One year: the time elapsed :: the whole area of the ellipse the area of the sector swept over by the radius vector in that time. This area, therefore, becomes known, and it is then, as above observed, a problem of pure geometry to ascertain the angle about the sun (A S P, fig. art. 315.), which corresponds to any proposed fractional area of the whole ellipse supposed to be contained in the sector A P S. Suppose we set out from A the perihelion, then will the angle A S P at first increase more rapidly than the mean longitude, and will, therefore, during the whole semi-revolution from A to M, exceed it in amount; or, in other words, the true place will be in advance of the mean: at M, one half the year will have elapsed, and one half the orbit have been described, whether it be circular or elliptic. Here, then, the mean and true places coincide; but in all the other half of the orbit, from M to A, the true place will fall short of the mean, since at M the angular motion is slowest, and the true place from this point begins to lag behind the mean to make up with it, however, as it approaches A, where it once more overtakes it.

(320.) The quantity by which the true longitude of the earth differs from the mean longitude is called the equation of the centre, and is additive during all the half-year in which the earth passes from A to M, beginning at 0° 0′ 0′′, increasing to a maximum, and again diminishing to zero at M; after which it becomes subtractive, attains a maximum of subtractive magnitude between M and A, and again diminishes to O at A. Its maximum, both additive and subtractive, is 1° 55' 33"-3.

(321.) By applying, then, to the earth's mean longitude, the equation of the centre corresponding to any given time at which we would ascertain its place, the true longitude becomes known; and since the sun is always seen from the earth in 180° more longitude than the earth from the sun, in this way also the sun's true place in the ecliptic becomes known. The cal