render a rational account of the appearances they successively present, — that is to say, an account of which the several parts, postulates, propositions, deductions, intelligibly cohere, without contradicting each other or the nature of things as concluded from experience. In this view of the Copernican doctrine it is rather a geometrical conception than a physical theory, inasmuch it simply assumes the requisite motions, without attempting to explain their mechanical origin, or assign them any dependence on physical causes. The Newtonian theory of gravitation supplies this deficiency, and, by showing that all the motions required by the Copernican conception must, and that no others can, result from a single, intelligible, and very simple dynamical law, has given a degree of certainty to this conception, as a matter of fact, which attaches to no other creation of the human mind.

(78.). To understand this conception in its further developments, the reader must bear steadily in mind the distinction between relative and absolute motion. Nothing is easier to perceive than that, if a spectator at rest view a certain number of moving objects, they will group and arrange themselves to his eye, at each successive moment, in a very different way from what they would do were he in active motion among thein, if he formed one of them, for instance, and joined in their dance. This is evident from what has been said before of parallactic motion; but it will be asked, How is such a spectator to disentangle from each other the two parts of the apparent motions of these external objects,—that which arises from the effect of his own change of place, and which is therefore only apparent (or, as a German metaphysician would say, subjective - having reference only to him as perceiving it), and that which is real (or objective— having a positive existence, whether perceived by him or not)? By what rule is he to ascertain, from the appearances presented to him while himself in motion, what would be the appearances were he at rest? It by no means follows, indeed, that he would even then at once obtain a clear conception of all the motions of all the objects. The appearances so presented to him would have still something subjective about them.

They would be still appearances, not geometrical realities. They would still have a reference to the point of view, which might be very unfavourably situated (as, indeed, is the case in our system) for affording a clear notion of the real movement of each object. No geometrical figure, or curve, is seen by the eye as it is conceived by the mind to exist in reality. The laws of perspective interfere and alter the apparent directions and foreshorten the dimensions of its several parts. If the spectator be unfavourably situated, as, for instance, nearly in the plane of the figure (which is the case we have to deal with), they may do so to such an extent, as to make a considerable effort of imagination necessary to pass from the sensible to the real form.

(79.) Still, preparatory to this ultimate step, it is first necessary that the spectator should free or clear the appearances from the disturbing influence of his own change of place. And this he can always do by the following general rule or proposition :

The relative motion of two bodies is the same as if either of them were at rest, and all its motion communicated to the other in an opposite direction.

Hence, if two bodies move alike, they will, when seen from each other (without reference to other near bodies, but only to the starry sphere), appear at rest. Hence, also, if the absolute motions of two bodies be uniform and rectilinear, their relative motion is so also.

(80.) The stars are so distant, that as we have seen it is absolutely indifferent from what point of the earth's surface we view them. Their configurations inter se are identically the same. It is otherwise with the sun, moon, and planets, which are near enough (especially the moon) to be parallactically displaced by change of station from place to place on our globe. In order that astronomers residing on different points

* This proposition is equivalent to the following, which precisely meets the case proposed, but requires somewhat more thought for its clear apprehension than can perhaps be expected from a beginner :

PROP. If two bodies, A and B, be in motion independently of each other, the motion which B seen from A would appear to have if A were at rest is the same with that which it would appear to have, A being in motion, if, in addition to its own motion, a motion equal to A's and in the same direction were communicated to it.

of the earth's surface should be able to compare their observations with effect, it is necessary that they should clearly understand and take account of this effect of the difference of their stations on the appearance of the outward universe as seen from each. As an exterior object seen from one would appear to have shifted its place were the spectator suddenly transported to the other, so two spectators, viewing it from the two stations at the same instant, do not see it in the same direction. Hence arises a necessity for the adoption of a conventional centre of reference, or imaginary station of observation common to all the world, to which each observer, wherever situated, may refer (or, as it is called, reduce) his observations, by calculating and allowing for the effect of his local position with respect to that common centre (supposing him to possess the necessary data). If there were only two observers, in fixed stations, one might agree to refer his observations to the other station; but, as every locality on the globe may be a station of observation, it is far more convenient and natural to fix upon a point equally related to all, as the common point of reference; and this can be no other than the centre of the globe itself. The parallactic change of apparent place which would arise in an object, could any observer suddenly transport himself to the centre of the earth, is evidently the angle C S P, subtended at the object S by that radius CP of the earth which joins its centre and the place P of observation.

S

CHAPTER II.

TERMINOLOGY AND ELEMENTARY GEOMETRICAL CONCEPTIONS AND RELATIONS.— TERMINOLOGY RELATING TO THE GLOBE OF THE ΤΟ THE CELESTIAL SPHERE. CELESTIAL PERSPEC

EARTH
TIVE.

(81.) SEVERAL of the terms in use among astronomers have been explained in the preceding chapter, and others used anticipatively. But the technical language of every subject requires to be formally stated, both for consistency of usage and definiteness of conception. We shall therefore proceed, in the first place, to define a number of terms in perpetual use, having relation to the globe of the earth and the celestial sphere.

(82.) DEFINITION 1. The axis of the earth is that diameter about which it revolves, with a uniform motion, from west to east; performing one revolution in the interval which elapses between any star leaving a certain point in the heavens, and returning to the same point again.

(83.) DEF. 2. The poles of the earth are the points where its axis meets its surface. The North Pole is that nearest to Europe; the South Pole that most remote from it.

(84.) DEF. 3. The earth's equator is a great circle on its surface, equidistant from its poles, dividing it into two hemispheres a northern and a southern; in the midst of which are situated the respective poles of the earth of those names. The plane of the equator is, therefore, a plane perpendicular to the earth's axis, and passing through its centre.

(85.) DEF. 4. The terrestrial meridian of a station on the earth's surface, is a great circle of the globe passing through both poles and through the place. The plane of the meridian is the plane in which that circle lies.

(86.) DEF. 5. The sensible and the rational horizon of any station have been already defined in art. 74.

(87.) DEF. 6. A meridian line is the line of intersection of the plane of the meridian of any station with the plane of the sensible horizon, and therefore marks the north and south points of the horizon, or the directions in which a spectator must set out if he would travel directly towards the north or south pole.

(88.) DEF. 7. The latitude of a place on the earth's surface is its angular distance from the equator, measured on its own terrestrial meridian: it is reckoned in degrees, minutes, and seconds, from 0 up to 90°, and northwards or southwards according to the hemisphere the place lies in. Thus, the observatory at Greenwich is situated in 51° 28′ 40′′ north latitude. This definition of latitude, it will be observed, is to be considered as only temporary. A more exact knowledge of the physical structure and figure of the earth, and a better acquaintance with the niceties of astronomy, will render some modification of its terms, or a different manner of considering it, necessary.

(89.) DEF. 8. Parallels of latitude are small circles on the earth's surface parallel to the equator. Every point in such a circle has the same latitude. Thus, Greenwich is said to be situated in the parallel of 51° 28' 40".

(90.) DEF. 9. The longitude of a place on the earth's surface is the inclination of its meridian to that of some fixed station referred to as a point to reckon from. English astronomers and geographers use the observatory at Greenwich for this station; foreigners, the principal observatories of their respective nations. Some geographers have adopted the island of Ferro. Hereafter, when we speak of longitude, we reckon from Greenwich. The longitude of a place is, therefore, measured by the arc of the equator intercepted between the meridian of the place and that of Greenwich; or, which is the same thing, by the spherical angle at the pole included between these meridians.

(91.) As latitude is reckoned north or south, so longitude is usually said to be reckoned west or east. It would add