amount of this reduction is called parallax. Thus, the sun being seen from the earth's centre, in the direction CS, and from A on the surface in the direction AS, the angle A SC, included between these two directions, is the parallax at A, and similarly BSC is that at B.

Parallax, in this sense, may be distinguished by the epithet diurnal, or geocentric, to discriminate it from the annual, or heliocentric; of which more hereafter.

(300.) The reduction for parallax, then, in any proposed case, is obtained from the consideration of the triangle ACS, formed by the spectator, the centre of the earth, and the object observed; and since the side CA prolonged passes through the observer's zenith, it is evident that the effect of parallax, in this its technical acceptation, is always to depress the object observed in a vertical circle. To estimate the amount of this depression, we have, by plane trigonometry,

CS: CA: sine of CAS= sine of ZAS: sine of ASC.

(391.) The parallax, then, for objects equidistant from the earth, is proportional to the sines of their zenith distances. It is, therefore, at its maximum when the body observed is in the horizon. In this situation it is called the horizontal parallax; and when this is known, since small arcs are proportional to their sines, the parallax at any given altitude is easily had by the following rule:— Parallax= (horizontal parallax) x sine of zenith distance.

The horizontal parallax is given by this proportion :Distance of object: earth's radius:: rad. : sine of horizontal parallax.

It is, therefore, known, when the proportion of the object's distance to the radius of the earth is known; and vice versâ—if by any method of observation we can come at a knowledge of the horizontal parallax of an object, its distance, expressed in units equal to the earth's radius, becomes known.

(302.) To apply this general reasoning to the case of the sun. Suppose 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 CX, 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 whole amount of the two parallaxes, or by the angle A S B. This angle, then, is obtained by subducting the sum of the 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.

(303.) 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.

(304.) The horizontal parallax of the sun has been concluded from observations of the nature above de

scribed, 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 86. 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 23,984 times the length of the earth's radius, or about 95,000,000 miles.

(305.) That at so vast a distance the sun should appear to us 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 95,000,000 miles, and subtending an angle of 32' 3", must have a real diameter of 882,000 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 of 111 to 1, and in bulk in that of 1,384,472 to 1.

(306.) 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 inclined at a constant angle of 82° 40′ to the plane

of the ecliptic, performing one rotation in a period of 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 so 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 tie two stones together by a string, 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.

(307.) 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 its comparison. 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 teaches 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 354,936 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 part of its own diameter.

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(308.) 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 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.

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*See Cab. Cyc. MECHANICS, Centre of Gravity.