happens to be in conjunction with the sun, or between the sun and the earth, viz. at the time of the new moons, the shadow of the moon falls upon the surface of the earth; hence, properly speaking, such eclipses should be called eclipses of the earth. But the whole disc of the earth cannot be involved in the shadow of the moon, because the moon is much smaller than the earth, and the shadow of the moon is conical. Thus, in Plate III. fig. 1, the rays of the sun, S, being intercepted by the moon, L, form the conical shadow CDG, which falling upon the surface of the earth, entirely deprives that portion of it upon which it falls of the sun's light, and of course the inhabitants of that part of the earth will have a total eclipse of the sun. Beyond the dense conical shadow CDG there is a diverging half shadow, or penumbra CDEF, which is occasioned by the moon's intercepting only a part of the sun's rays from those places which fall within this penumbral cone, and are out of the dense shadow. Thus from the part of the earth Z the portion Y Y B of the sun only can be seen; consequently the inhabitants of that part will have a partial eclipse. As the moon is not always at the same distance from the earth, it sometimes happens that the conical dense shadow does not reach the earth, as in fig. 2, and only the penumbral shadow falls upon it, the eclipse consequently is partial to every part of the earth. Those who are at the centre of the penumbra will lose sight of the centre of the sun by the interposition of the moon's body, which subtending a smaller angle than the sun, will not entirely cover its surface, so that there will be a ring of light all round. The eclipse is then said to be annular. The satellites, or moons, are often eclipsed by the planets to which they belong. The eclipses of Jupiter's moons, as we have already observed, are very useful in ascertaining the longitude. When any of the planetary bodies disappear by another coming before it, it is called an occultation. The occultations of the fixed stars by the moon are of great importance also in determining the longitudes of places. OF THE TIDES. The ebbing and flowing of the sea was first shewn by Kepler to be owing to the moon's attraction, and Newton demonstrated it upon the principles of gravitation. The attraction of the moon cannot alter the shape of the solid of the globe: but it has a considerable effect upon the fluid part, which VOL. I. it causes to assume a spheroidal figure, the longest axis being in the direction of the moon. It is therefore the highest tide at that place perpendicularly under the moon, or where the moon crosses the meridian. The sun also has some action upon the waters, though its attraction, on account of its distance, is not so strong as that of the moon. When the action of the sun and moon conspire together the tide rises higher, and produces what are called spring tides. On the contrary, when they counteract each other, they produce neap tides. The ocean, it is well known, covers more than one-half of the globe; and this large body of water is found to be in continual motion, ebbing and flowing alternately without the least intermission. What connection these motions have with the moon we shall see as we proceed; but at present it will be sufficient to observe, that they always follow a certain general rule. For instance, if the tide be now at high-water mark in any port or harbour which lies open to the ocean, it will presently subside, and flow regularly back for about six hours, when it will be found at low-water-mark. After this, it will again gradually advance for six hours, and then return back in the same time to its former situation; rising and falling alternately twice a day, or in the space of about twenty-four hours. And by observing the tides continually at the same place, they will always be found to follow the same rule; the time of high water upon the day of every new moon being nearly at the same hour, and three quarters of an hour later every succeeding day. Let M (fig. 3.) represent the moon, O the centre of ths earth, and A, B, C, &c. different points upon its surface, and let us suppose the earth to be entirely covered by the ocean. Then, because it is the property of a fluid for its parts to yield, and obey any force impressed upon them, it is clear that the moon M, acting upon the surface of the sea at the points A, B, C, &c. will elevate the waters in those parts, and draw them towards her, by her attractive power. But the point A being nearer to the moon than the point C, the attraction at A will be greater than at C; and because the points B and D are at equal distances from the moon, the attraction at those points will also be equal; and so at any other intermediate points the attractive force will be different, according to their different distances from the moon. From this example then, it is sufficiently evident, that the attractive force of the E e moon, acting unequally upon different parts of the ocean, must occasion it to assume a different figure from what it would other wise have, if there were no such unequal attractions. And since this attractive force is greatest on the part of the ocean which lies immediately under the moon, the waters will of course flow constantly to that part, and be elevated or depressed at different places, according as her situation changes with respect to those places. But, as the earth turns round on its axis, from the moon to the moon again, in about twenty-four hours and three quarters, the flux and reflux will be necessarily retarded from day to day about three quarters of an hour, which is agreeable to experience. It remains now to be explained, why they ebb and flow twice a day, or in the space of about twenty-four hours. When the moon passes the meridian of any place, or is at her greatest height above the horizon of that place, she will evidently attract and elevate the waters which lie immediately under her: but what is the reason, that twelve hours afterwards, when she passes the meridian below the horizon, the waters at the same place are then also elevated? We know, from experience, that, whether the moon be in the zenith or nadir, the phenomenon is nearly the same; it being high water with us at the same time that it is high water with our antipodes. Let M, (fig. 4.) represent the moon as before; O, the centre of the earth; and Z and N, those parts of the surface which are the nearest to the moon, and the farthest from her. Then because the point Z is nearer to the moon than any other part of the hemisphere HZ R, it is evident that the waters will be more strongly attracted by her, about that point, than at others which are more remote; and since this attraction acts in a contrary direction to that of the earth, the waters in all parts, from HR to Z, must have their gravity or tendency towards the centre O diminished; and as this tendency is the least at the point Z, they will consequently stand higher there than in any other part of the hemisphere. Again in the opposite hemisphere HNR, although the attraction of the moon conspires with that of the earth, yet as it is known to decrease in proportion as the squares of the distances increase, it is plain that the joint influence of the two forces, taken together, will be less at the point N, on the side opposite to the moon, than at those parts which lie nearer to HR, and consequently, as the gravity of the waters, or their tendency to wards the centre, is also the least at that point, they will be more elevated there thau in any other part of the hemisphere; so that the attractive force of the moon will evidently raise the waters, both at that point of the surface which is nearest to her, and at that which is farthest from her, at the same time, as was to be shewn. Following this system, then, it is to be observed, that at any port or harbour which lies open to the ocean, the action of the moon will tend to elevate the waters there, when she is on the meridian of that place, whether it be above the horizon or below it. But the water cannot be raised at one place, without flowing from and being depressed at another; and these elevations and depressions will obviously be the greatest at opposite points of the earth's surface. When the moon raises the waters at Z and N, they will be depressed at H and R; and when they are raised by her at H and R, they will be depressed at Z and N. And as the moon passes over the meridian, and is in the horizon twice every day, there will therefore be two tides of flood, and two of ebb, in that time, at the interval of about six hours and eleven minutes each; which is exactly conformable to theory and experience. From what has been hitherto said, it may be supposed, that the moon is the sole agent concerned in producing the tides. But it will be necessary to observe, before we quit the subject, that the influence of the sun would also produce a similar effect, though in a much less degree, than from his superior magnitude we should naturally be led to imagine. For it is not the entire actions of those bodies upon the whole globe of the earth that is here to be considered, but only the inequalities of those actions upon dirferent parts of it. The whole attractive force of the sun is far superior to that of the moon; but as his distance from the earth is nearly 400 times greater, the forces with which he acts upon different parts of it, will be much nearer to equality than those of the moon; and consequently will have a less effect in producing any change of its figure. For it is to be observed, that if all parts of the earth were equally attracted, they would suffer but little change in their mutual situations. That this doctrine may be still more clearly understood, let it be considered, that though the earth's diame ter bears a considerable proportion to the distance of the earth from the moon, yet this diameter is almost nothing when compared to the distance of the earth from the sun. The difference of the sun's attraction, the effect of the sun's influence in this case, For this purpose, let S (fig. 5) represent at the full; and in both cases they occasion what are called the spring tides. Pursuing the illustration in the same way, let now F and T (fig. 6) be the moon in her first and third quarters, and the rest as before. Then, since the sun and moon act in the right lines SH and FT, which are nearly perpendicular to each other, their forces will tend to produce contrary effects; because the one raises the waters in that part where the other depresses them. The sun's attraction at R and H, will diminish the effect of the moon's attraction at Z and N; so that the waters will rise a little at the points under and opposite to the sun, and fall as much at the points under and opposite to the moon; and of course the lunar tides will be diminished in those parts. This respects the moon only in her first quarter, at F; but the same reasoning will evidently hold, when applied to the moon in her third quarter at T; for as the sun and moon still act in lines which are perpendicular to each other, they must produce the same diminution as before; and in both these cases they occasion what are called the neap tides. But it must be observed, that neither the spring nor neap tides happen when the sun and moon have the precise situations here mentioned; because, in this case, as in others of a similar kind, the actions do not produce the greatest effect when they are the strongest, but some time afterwards. The effects of the disturbing forces of the sun and moon, depend likewise upon their respective distances from the earth, as well as upon their particular situations. For the less the distances are, the greater will be their effects; and, consequently, in winter, when the sun is nearer to the earth, the spring tides will be greater than in summer, when he is farther off; and the neap tides, on that account, will be less. For a like reason, as the moon moves in an elliptical orbit round the earth, and is nearer to us at some times than at others, the tides will at those times be greater, and at the opposite points of Some variations likeher orbit, less. wise take place in consequence of the different declinations of the sun and moon at different times. For if either of these luminaries were at the pole, it would occasion a constant elevation both there and at the opposite one, and a constant depression at the equator; so that as the sun and moon gradually decline from the equator, they lose their effect, and the tides become less ; and when they are both in the equator, the tides of course become greater. E e 2 Astronomy is sometimes divided in books, with respect to its different states, into "new" and "old." The former refers to the art as it stood under Ptolemy and his followers, with all the apparatus of solid orbs, epicycles, &c. &c. By new astronomy is meant the science as it has been cultivated since the period in which Copernicius flourished. By that great man the constitution of the heavens was reduced to more simple, natural, and certain principles. The substance of the old astronomy is given by Tacquet, and of the new by Whiston, in his "Prelectiones Astronomicæ, published in 1707. The whole doctrine, both according to the ancients and moderns, is explained by Mercator in his Institutiones Astron. Having concluded this brief sketch of a very important science, we shall refer to other articles, in which many subjects will be discussed, that usually find place in a treatise of astronomy. Under the word SUN will be found some interesting specula tions of Dr. Herschel ; under that of Moon, an account of the methods of measuring its mountains, an explication of the harvest moon and horizontal moon. For equation of time, see TIME; see also EARTH, figure of; ECLIPTIC; EQUINOXES, precession of; GALAXY; GRAVITATION; NEBULE; SATURN, ring of; ASTRONOMY, practical; and ASTONOMICAL instruments; see OBSERVATORY; SATELLITES; TRANSIT; &c. &c. &c. ASTROSCOPE, an instrument composed of two cones, having the constellations delineated on their surfaces, whereby the stars may be easily known. ASYMETRY, in a general sense, the want of proportion between the parts of any thing, being the contrary of symmetry. In mathematics it is used for what is more commonly called incommensurability, or the relation of two quantities which have no common measure, as between one and the square root of two, or as 1:2, or the side and diagonal of a square. ASYMPTOTE, in geometry, a line which continually approaches nearer to another; but, though continued infinitely, will never meet with it: of these there are many kinds. The term asymptotes is appropriated to right lines, which approach nearer and nearer to some curve, of which they are said to be the asymptotes; but if they and their curves are indefinitely continued they will never meet. Concerning asymptotes and asymptotical curves, it may be remarked, 1. That although snch curves as have asymptotes are of the number of those which do not include a space; yet it is not true, on the other hand, that wherever we have a curve of that nature, we have an asymptote also. 2. Of these curves that have an asymptote, some have only one, as the conchoid, cissoid, and logarithmic curve; and others two, as the hyperbola. 3. As a right line and a curve may be asymptotical to one another, so also may curves and curves such are two parabolas, whose axes are in the same right line. 4. No right line can ever be an asymptote to a curve that is every where concave to that right line. 5. But a right line may be an asymptote to a mixed curve, that is partly concave, and partly convex, towards the same line. And, 6. All curves that have one and the same common asymp tote, are also asymptotical to one another. See CONIC SECTIONS. ASYNDETON, in grammar, a figure which omits the conjunctions in a sentence, as in that verse of Virgil. Ferte citi flammas, date vela, impellite remos. ATCHIEVEMENT, in heraldry, denotes the arms of a person, or family, together with all the exterior ornaments of the shield, as helmet, mantle, crest, scrolls, and motto, with such quarterings as may have been acquired by alliances, all marshalled in order. ATHAMANTA, in botany, a genus of the Pentandria Digynia class of plants, the general corolla whereof is uniform; the partial one consists of five inflexo-cordateď unequal petals: there is no pericarpium ; the fruit is ovato-oblong, striated, and divisible into two parts; the seeds are two, oval, striated, and convex on the one side, and plane on the other. There are 10 species. ATHANASIA, in botany, a genus of the Syngenesia Polygamia Equalis class and order, and of the natural order of compound flowers. The essential character is calyx imbricate; down chaffy, very short; receptacle chaffy. There are 20 species. ATHEIST, is one who does not believe in the existence of a God. He attributes every thing to a fortuitous concourse of atoms. Plato distinguishes three sorts of Atheists. 1. Such as deny absolutely that there any gods. 2. Others who allow their existence, but deny that they have any concern with human affairs; and lastly, such as believe in gods and a providence, but think they are easily appeased, and remit the greatest of crimes for the smallest supplica |