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during an entire period. It was not, therefore, without much painful and laborious calculation, that it was discovered by Kepler (who was also the first to ascertain the elliptic form of the orbit), and announced in the following terms :- Let a line be always supposed to connect the sun, supposed in motion, with the earth, supposed at rest; then, as the sun moves along its ellipse, this line (which is called in astronomy the radius vector) will describe or sweep over that portion of the whole area or surface of the ellipse which is included between its consecutive positions: and the motion of the sun will be such that equal areas are thus swept over by the revolving radius vector in equal times, in whatever part of the circumference of the ellipse the sun may be moving.
(353.) From this it necessarily follows, that in unequal times, the areas described must be proportional to the times. Thus, in the figure of art. 349. the time in which the sun moves from A to B, is to the time in which it moves from C to D, as the area of the elliptic sector A O B is to the area of the sector D O C.
(354.) The circumstances of the sun's apparent annual motion may, therefore, be summed up as follows:- It is performed in an orbit lying in one plane passing through the earth's centre, called the plane of the ecliptic, and whose projection on the heavens is the great circle so called. In this plane its motion is from west to east, or to a spectator looking down on the plane of the elliptic from the northern side, in a direction the reverse of that of the hands of a watch laid face uppermost. In this plane, however, the actual path is not circular, but elliptical ; having the earth, not in its center, but in one focus. The excentricity of this ellipse is 0.01679, in parts of a unit equal to the mean distance, or half the longer diameter of the ellipse; i. e. about one sixtieth
; part of that semi-diameter; and the motion of the sun in its circumference is so regulated, that equal areas of the ellipse are passed over by the radius vector in equal times.
(355.) What we have here stated supposes no knowledge of the sun's actual distance from the earth, nor, consequently, of the actual dimensions of its orbit, nor of the body of the sun itself. To come to any conclusions on these points, we must first consider by what means we can arrive at any knowledge of the distance of an object to which we have no access. Now, it is obvious, that its parallar alone can afford us any information on this subject. Suppose P A B Q to
B represent the earth, C its centre, and S the sun, and A, B
two situations of a spectator, or, which comes to the same thing, the stations of two spectators, both observing the sun S at the same instant. The spectator A will see it in the direction A Sa, and will refer it to a point a in the infinitely distant sphere of the fixed stars, while the spectator B will see it in the direction BSI, and refer it to b. The angle included between these directions, or the measure of the celestial arc a b, by which it is displaced, is equal to the angle A SB; and if this angle be known, and the local situations of A and B, with the part of the earth's surface A B included between them, it is evident that the distance C S may be calculated. Now, since ASC (art. 339 ) is the parallax of the sun as seen from A, and B SC as seen from B, the angle A S B, or the total apparent displacement is the sum of the two parallaxes. Suppose, then, two observers — one in the northern, the other in the southern hemisphere- at stations on the same meridian, to observe on the same day the meridian altitudes of the sun's centre. Having thence derived the apparent zenith distances, and cleared them of the effects of refraction, if the distance of the sun were equal to that of the fixed stars, the sum of the zenith distances thus found would be precisely equal to the sum of the latitudes north and south of the places of observation. For the sum in question would then be equal to the angle Z C X, which is the meridional distance of the stations across the equator.
But the effect of parallax being in both cases to increase the apparent zenith distances, their observed sum will be greater than the sum of the latitudes, by the sum of the two parallaxes, or by the angle A SB. This angle, then, is obtained by subducting
, the sum of the north and south latitudes from that of the zenith distances; and this once determined, the horizontal parallax is easily found, by dividing the angle so determined by the sum of the sines of the two latitudes.
(356.) If the two stations be not exactly on the same meridian (a condition very difficult to fulfil), the same process will apply, if we take care to allow for the change of the sun's actual zenith distance in the interval of time elapsing between its arrival on the meridians of the stations. This change is readily ascertained, either from tables of the sun's motion, grounded on the experience of a long course of observations, or by actual observation of its meridional altitude on several days before and after that on which the observations for parallax are taken. Of course, the nearer the stations are to each other in longitude, the less is this interval of time, and, consequently, the smaller the amount of this correction; and, therefore, the less injurious to the accuracy of the final result is any uncertainty in the daily change of zenith distance which may arise from imperfection in the solar tables, or in the observations made to determine it.
(357.) The horizontal parallax of the sun has been concluded from observations of the nature above described, performed in stations the most remote from each other in latitude, at which observatories have been instituted. It has also been deduced from other methods of a more refined nature, and susceptible of much greater exactness, to be hereafter described. Its amount so obtained, is about 8":6. Minute as this quantity is, there can be no doubt that it is a tolerably correct approximation to the truth; and in conformity with it, we must admit the sun to be situated at a mean distance from us, of no less than 23984 times the length of the earth's radius, or about 95000000 miles.
(358.) That at so vast a distance the sun should appear to as of the size it does, and should so powerfully influence our condition by its heat and light, requires us to form a very
grand conception of its actual magnitude, and of the scale on which those important processes are carried on within it, by which it is enabled to keep up its liberal and unceasing supply of these elements. As to its actual magnitude we can be at no loss, knowing its distance, and the angles under which its diameter appears to us. An object, placed at the distance of 95000000 miles, and subtending an angle of 32' l", must have a real diameter of 882000 miles. Such, then, is the diameter of this stupendous globe. If we compare it with what we have already ascertained of the dimensions of our own, we shall find that in linear magnitude it exceeds the earth in the proportion 111} to 1, and in bulk in that of 1384472 to 1.
(359.) It is hardly possible to avoid associating our conception of an object of definite globular figure, and of such enormous dimensions, with some corresponding attribute of massiveness and material solidity. That the sun is not a mere phantom, but a body having its own peculiar structure and economy, our telescopes distinctly inform us. They show us dark spots on its surface, which slowly change their places and forms, and by attending to whose situation, at different times, astronomers have ascertained that the sun revolves about an axis nearly perpendicular to the plane of the ecliptic, performing one rotation in a period of about 25 days, and in the same direction with the diurnal rotation of the earth, i. e. from west to east. Here, then, we have an analogy with our own globe; the slower and more majestic movement only corresponding with the greater dimensions of the machinery, and impressing us with the prevalence of similar mechanical laws, and of, at least, such a community of nature as the existence of inertia and obedience to force may argue. Now, in the exact proportion in which we invest our idea of this immense bulk with the attribute of inertia, or weight, it becomes difficult to conceive its circulation round s0 comparatively small a body as the earth, without, on the one hand, dragging it along, and displacing it, if bound to it by some invisible tie; or, on the other hand, if not so held to it, pursuing its course alone in space, and leaving the earth behind. If we connect two solid masses by a rod, and fling them aloft, we see them circulate about a point between them,
which is their common centre of gravity ; but if one of them be greatly more ponderous than the other, this common centre will be proportionally nearer to that one, and even within its surface; so that the smaller one will circulate, in fact, about the larger, which will be comparatively but little disturbed from its place.
(360.) Whether the earth move round the sun, the sun round the earth, or both round their common centre of gravity, will make no difference, so far as appearances are concerned, provided the stars be supposed sufficiently distant to undergo no sensible apparent parallactic displacement by the motion so attributed to the earth. Whether they are so or not must still be a matter of enquiry; and from the absence of any measureable amount of such displacement, we can conclude nothing but this, that the scale of the sidereal universe is so great, that the mutual orbit of the earth and sun may be regarded as an imperceptible point in comparison with the distance of its nearest members. Admitting, then, in conformity with the laws of dynamics, that two bodies connected with and revolving about each other in free space do, in fact, revolve about their common centre of gravity, which remains immoveable by their mutual action, it becomes a matter of further enquiry, whereabouts between them this centre is situated. Mechanics teach us that its place will divide their mutual distance in the inverse ratio of their weights or masses *; and calculations grounded on phenomena, of which an account will be given further on, inform us that this ratio, in the case of the sun and earth, is actually that of 354936 to 1,- the sun being, in that proportion, more ponderous than the earth. From this it will follow that the common point about which they both circulate is only 267 miles from the sun's centre, or about 3;'ooth part of its own diameter.
(361.) Henceforward, then, in conformity with the above statements, and with the Copernican view of our system, we must learn to look upon the sun as the comparatively motionless centre about which the earth performs an annual elliptic orbit of the dimensions and excentricity, and with a velocity,
• Principia, lib. i. lex. iii. cor. 14.