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° 28'103° 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.) The elliptic form of the earth's orbit has but a very trifling share in producing the variation of temperature corresponding to the difference of seasons. This assertion may at first sight seem incompatible with what we know of the laws of the communication of heat from a luminary placed at a variable distancc. Heat, like light, being equally dispersed from the sun in all 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. 350.) that this is also the proportion in which the angular velocity of the earth about the sun varies. Hence it appears, 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; APMQ 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 ASM the aris of the ellipse. Now, suppose the orbit divided into two segments by a straight line PSQ, drawn through the sun, and anyhow situated as to direction; then, if we

B

E

Q

M

suppose the earth to circulate in the direction PMQAP, 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

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 inquire 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, 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.

(372.) 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 reversely named; 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.

(373.) The position of the longer axis of the earth's orbit is a point of great importance. In the figure (art. 368.) let ECLI be the ecliptic, E the vernal equinox, L the autumnal (i. e. the points to which the earth is referred from the sun when its heliocentric longitudes are 0° and 180° respectively). Supposing the earth's motion to be performed in the direction

(370.) A conclusion of a very remarkable kind, recently drawn by Professor Dove from the comparison of thermometric observations at different seasons in very remote regions of the globe, may appear on first sight at variance with what is above stated. That eminent meteorologist has shown, by taking at all seasons the mean of the temperatures of points diametrically opposite to each other, that the mean temperature of the whole earth's surface in June considerably exceeds that in December. This result, which is at variance with the greater proximity of the sun in December, is, however, due to a totally different and very powerful cause, the greater amount of land in that hemisphere which has its summer solstice in June (i. e. the northern, see art. 362.); and the fact is so explained by him. The effect of land under sunshine is to throw heat into the general atmosphere, and so distribute it by the carrying power of the latter over the whole earth. Water is much less effective in this respect, the heat penetrating its depths, and being there absorbed; so that the surface never acquires a very elevated temperature even under the equator.

(371.) 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 tions for the eye of reason and theory. 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, when embarrassed

advantageous staHaving learned to

lucifer match does not ignite when simply pressed upon a smooth surface at 212°, but in the act of withdrawing it, it takes fire, and the slightest friction upon such a surface of course ignites it.

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 inquire 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, 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.

(372.) 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 reversely named; 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.

(373.) The position of the longer axis of the earth's orbit is a point of great importance. In the figure (art. 368.) let ECLI be the ecliptic, E the vernal equinox, L the autumnal (i. e. the points to which the earth is referred from the sun when its heliocentric longitudes are 0° and 180° respectively). Supposing the earth's motion to be performed in the direction

ECLI, the angle E.S A, 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 20984 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.

(374.) 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 elliptic motion according to Kepler's law above stated, areas not angles are described uniformly, the proportion must now be stated 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 (ASP, fig. art. 368.), which corresponds to any proposed fractional area of the whole ellipse supposed to be