32. It must first be premised, that the Sun will always be vertical to that point of the Earth, where a right line drawn from the centre of the Sun to the centre of the Earth cuts the surface of the latter. Thus, when the Earth is in the beginning of Capricorn, the Sun will be vertical to the Northern Tropic T. R.; because, a right line drawn from the Sun to the beginning of Capricorn will cross the surface of the Earth at T. So also, when the Earth is in Aries, the Sun will be vertical to the Equator or EQ; because, a right line drawn from the Sun to Aries will cross the surface of the Earth in a point of E Q. Hence, it is easy to apprehend how the various lengths of day and night, as well as the various seasons of the year, are produced by the annual motion of the Earth. 33. Vernal Equinox. Suppose, then, the Earth to be at Libra, the Sun will appear in Aries, and so in one of the Equinoctial points, and in the middle between the poles of the Earth A. X.; consequently, he will enlighten from Pole to Pole, that hemisphere of the Earth, which is opposite to him. Hence it follows, that every place on the Earth, being carried round the Axis of the Earth in a uniform manner by the diurnal motion of the Earth, will be as long in the light as in darkness, i. e. the day and night will be then equal all over the Earth. 34. Summer Solstice. The Earth having moved by its Annual motion from Libra to Capricorn, the Sun will appear in Cancer, where is his greatest Declination (i. e. distance from the Equator) Northward: whence it is evident, that his rays," which always enlighten one half of the Earth at once, will reach beyond the North Pole A to P, but will not reach nearer the South Pole X than the point S. From this it follows, that the portion of the Earth within the North Polar Circle N P, will at this time of the year enjoy day-light during the whole diurnal revolution of the Earth; whilst, on the contrary, it will be continual night during the same period, in that portion of the Earth lying within the South Polar Circle S P. It follows also, that the greater part of the Northern Hemisphere enjoys the light of the Sun, whilst the greater part of the Southern Hemisphere is in darkness; and this proportion of light is greater or less, according as any place may be nearer or farther from the North Pole, one half of the Equator being always enlightened, and the other not. Hence it is, that in this position of the Earth, the days are longest and the nights shortest in the Northern Hemisphere, and so it is Summer there; wherefore we, who live in the Northern Hemisphere, call this the Summersolstice: whereas, in the Southern Hemisphere, the days are then shortest and the nights longest, and so it is Winter there. And the longest day is so much the longer as the place is nearer to the North Pole, for at the Equator itself day and night are equal to each other throughout the whole year. 35. Autumnal Equinox. The Earth having moved by its Annual motion from Capricorn to Aries, the Sun will appear to be in Libra, or one of those points where the Ecliptic and Equator cross each other, and so produce equal day and night all over the world; as was the case when the Earth was in the opposite direction (that is, when it was in Libra, and the Sun in Aries), and for the same reasons. 36. Winter Solstice. In like manner, the Earth having moved by its Annual motion from Aries to Cancer, the Sun will appear to be in Capricorn, where is its greatest Declination (i. e. distance from the Equator) Southward. And, consequently, at this time of the year, the same phænomena will happen to the inhabitants of the * Τὸ δὲ τὸν ἥλιον, ἐπειδὰν ἐν χειμῶνι τράπηται, προσιέναι τὰ μὲν ἁδρύνοντα, τὰ δὲ ξηραίνοντα, ὧν καιρὸς διελήλυθεν· καὶ ταῦτα διαπραξάμενον μηκέτι ἐγγυτέρω προσιέναι, ἀλλ' ἀποτρέπεσθαι, φυλαττόμενον μή τι ἡμᾶς μᾶλλον τοῦ δέοντος θερμαίνων βλάψη· καὶ ὅταν αὖ πάλιν ἀπιὼν γένηται, ἔνθα καὶ ἡμῖν δῆλόν ἐστιν, ὅτι, εἰ προσωτέρω ἄπεισιν, ἀποπαγησόμεθα ὑπὸ τοῦ ψύχους, πάλιν αὖ τρέπεσθαι καὶ προσχωρειν, καὶ ἐνταῦθα τοῦ ὀυρανοῦ ἀναστρέφεσθαι, ἔνθα ὢν μάλιστα ἡμᾶς ὠφελοίη; νὴ τὸν Δί ̓, ἔφη, καὶ ταῦτα παντάπασιν ἔοικεν ἀνθρώπων ἕνεκα γιγνομένοις. Τὸ δ ̓ αὖ (ἐπειδὰν καὶ τοῦτο φανερὸν, ὅτι οὐκ ἂν ὑπενέγκοιμεν οὔτε τὸ καῦμα, οὔτε τὸ ψύχος, ἐι ἐξαπίνης γίγνοιτο), οὕτω μὲν κατὰ μικρὸν προσιέναι τὸν ἥλιον, οὕτω δὲ κατὰ μικρὸν ἀπιέναι, ὥστε λανθάνειν ἡμᾶς εἰς ἑκάτερα τὰ ἰσχυρότατα καθισταμένους; ἐγὼ μὲν, ἔφη ὁ Εὐθύδημος, ἤδη τοῦτο σκόπω, εἰ ἄρα τί ἐστι τοῖς θεοῖς ἔργον, ἤ ἀνθρώπους θεραπεύειν. C Xenoph. Memorab. IV. 3. Southern Hemisphere, that happened to those of the Northern Hemisphere when the Earth was in Capricorn, that is to say, they will then have longer days than nights, and will be enjoying their Summer; whilst we in the Northern Hemisphere, shall have longer nights than days, and be suffering the inclemencies of Winter, wherefore we call this the Winter Solstice 35. 37. The different distances of the Sun from the Earth at different parts of the year, as also its appearing of a different magnitude, and seeming to move at a different rate, are all owing to the elliptical orbit of the Earth, and to the Earth not being in the centre of this ellipsis but in one of its foci. For, as the Sun's diameter appears less about the middle of June, and greater about the middle of December, so, the Sun is more distant from us in our Summer than in our Winter, and also seems to move quicker in the latter than in the former 36; insomuch, that he takes up about eight days more in seeming to pass from the Vernal to the Autumnal Equinox, than from the Autumnal to the Vernal-although in both intervals of time, he seems to pass over exactly one half of the Ecliptic. This is explained in Plate II. fig. 5, where the circle represents the Ecliptic, the ellipsis represents the Orbit of the Earth, and S. the Sun, in that focus of the ellipsis next the sign Cancer. Now, about the middle of June, the Sun appearing to us in the beginning of Cancer, the Earth is consequently in the beginning of Capricorn, and so at the point A of its elliptical orbit; that is, at its Aphelium or greatest distance from the Sun, for which reason, he then appears less to us. Again, about the middle of December, the Sun appearing to us in the beginning of Capricorn, the Earth is consequently in the beginning of Cancer, and so at the point P of its elliptical orbit; that is, at its Perihelium or least distance from the Sun, for which reason, he then appears greatest to us. The terms Aphelium and Perehelium are derived from the Greek (and from, og the sun; and εpì near, iλoç), and signify distance from, or approximation to, the Sun.-Farther, a line drawn from Aries to Libra, through the centre of the Sun, divides the Ecliptic into two halves; but it unequally divides the orbit of the earth, the greater segment of it answering to the six signs of the Ecliptic which the Earth passes under, between the Vernal and Autumnal equinoxes, and the less segment answering to the other six signs, which the Earth passes under, between the Autumnal and Vernal equinoxes. Whence it comes to pass, that the Earth taking up more time (about eight days more) to go along the greater segment of its orbit than along the less, the Sun also seems to take up more time, and, consequently, to move more slowly under the six signs of the Ecliptic between the Vernal and Autumnal, than between the Autumnal and Vernal Equinoxes. 38. As it is evident from this, that the Sun is nearer to us in Winter than in Summer, it appears at first sight singular, that we should feel his heat so much more in Summer, than in Winter. But it must be recollected, that we feel the Sun's heat not only as he is nearer to, or farther from us, but as his rays fall directly or indirectly upon us; whence it happens, that though the Sun is farthest from us in Summer, yet, because his rays are then much more nearly perpendicular to us than in Winter, therefore, they are hotter to us in the former, than in the latter season. This may be seen at once, by referring to Plate II. fig. 4. For, when in summer, the Earth is in the beginning of Capricorn, the rays of the Sun then fall perpendicularly upon the Northern Tropic T R, and are hottest to all the inhabitants of the Earth, North of this Tropic: but on the other hand, when in winter the Earth is in the beginning of Cancer, the perpendicular rays of the Sun 35 Mysterious round! what skill, what force divine, Thomson, Hymn to the Seasons. Virg. En. I. 745. fall upon the Southern Tropic T N, and are hottest to all the inhabitants South of this Tropic-whilst they only reach us in this part of the globe in a very oblique direction, as is evident, by supposing the right line X drawn from the Sun to the Northern Tropic. 39. It would, likewise, at first appear that the Annual motion of the Earth in its orbit, will prevent its always retaining the same situation in respect to the fixed stars; but this orbit is so very small, when compared with the immense sphere of the fixed stars, that it can make no sensible difference in the situation of the Earth with respect to them. 40. THE MOON is a secondary planet, inasmuch as she moves round the Earth, though she derives all her light from the Sun. A single revolution of the Moon round the Earth from one Synod, or conjunction, with the Sun to another, is called the Moon's Synodical Month, and consists of 29 days, 12 hours: it is this month " which is principally used in the computation of time, for its several parts are easily distinguished by the several Phases (or appearances) of the Moon belonging respectively to it. The several Phases of the Moon arise from her being an opacous body receiving her light from the Sun, and from her spherical figure, in consequeuce of which one half of her is always enlightened, namely, that Hemisphere which is towards the Sun. Now, this Hemisphere being seen by us, sometimes more, sometimes less (according to her position with respect to the Earth), causes the several Phases of the Moon. 41. This will be best understood by referring to Plate II. fig. 6, in which S represents the Sun, E the Earth, O R part of the Earth's orbit, and ABCD the orbit of the Moon. On the several most remarkable points of this last, is represented the Moon with its enlightened and darkened hemispheres, which, though they are always equal to each other, do not appear so to us, but rather like the several little circular draughts respectively adjoining them. Thus, the Moon being at A, all its enlightened hemisphere is towards the Earth, and therefore seen by us; for which reason, we say the Moon is full, because she appears to us with a full orb, or with all her surface enlightened: but when she moves to B, it is evident that only a part of her enlightened hemisphere will be towards the Earth, and so seen by us; wherefore, the Moon will appear somewhat defective of light on that side which is from the Sun, and is hence, said to be gibbous, from (gibbus, bunched out) her light part being bunched out or convex. The Moon having moved to C, only half of her enlightened hemisphere will be towards the Earth, for which reason she will appear with a half-orb, or as we then say, as a half-moon; but, when she has come to D, a very little portion of her enlightened hemisphere will be towards the Earth, and therefore she will appear to us to be horned, the horns bending from the Sun, Westward. When the Moon is at F, none of her enlightened hemisphere will be towards the Earth, and therefore she is invisible to us, wherefore we then say the Moon changes, or it is New Moon, because she will appear anew in G; at G she is again horned, her light part being towards the Sun, whilst her horns bend from him, and so Eastward. After this, the Moon will appear at 37 Ritè Latonæ puerum canentes, Volvere menses. Hor. Carm. IV. vi. 40. H with a half-orb again (as at C), and at I gibbous again (as at B), and so, she will proceed to A, where it will be again full moon 38. 42. It must be observed, that, whether increasing or decreasing, the illuminated part of the Moon is always towards the Sun: and therefore whenever the horns and hollow part of the Moon appear Eastward or on the left hand as we look at her, then she is increasing; but whenever the horns and hollow part appear Westward or on the right hand as we look at her, then she is decreasing, or on the wane. 43. When the Moon is horned, that is a little before and after the New Moon, besides her bright horns she has a faint light which renders all the rest of her dise visible. This faint light is supposed to be caused by the reflection of the Sun's rays cast back upon her from the Earth; for it will be evident by referring to the dotted line X Y in fig. 6, the Earth's position at such times is precisely that, in which such a reflection would be thrown upon the Moon: whereas the Moon has no sooner moved beyond the limits of such a reflection (which limits are shown near enough by the line O R), than the faint light ceases. 44. What has been observed concerning the Sun takes place also with the Moon, namely, that in one part of her orbit she appears to be smaller and to move slower, whilst in the other she appears to be larger and to move swifter: this is likewise caused by the Earth's being in one of the foci of the Moon's elliptical orbit. For, in fig. 5, suppose S to represent the Earth, and A P the Moon's orbit; then A will represent the Moon's Apogee (άπò from, and yй the Earth) or greatest distance from the Earth, when she will appear less, and P her Perigee (repì near, and yŋ) or least distance from the Earth, when she will consequently appear greater: and, necause she is longer in traversing the greater segment of her orbit than the less, therefore she will appear to move slower in the former and quicker in the latter. 45. ECLIPSES OF THE SUN AND MOON. The Earth and Moon are both opacous bodies, which receive their light from the Sun. So, whenever the Moon passes between the Earth and the Sun, in such a manner as to hinder the rays of the latter from falling on the Earth, then will the Sun be eclipsed to the inhabitants of the Earth: and, whenever the Moon passes behind the Earth so as to hinder the rays of the Sun from falling on the Moon, then will the Moon be eclipsed to the inhabitants of the Earth. An eclipse of the Sun can only happen at the Change of the Moon, when the Moon is between the Sun and the Earth; and an Eclipse of the Moon can only happen at the Full of the Moon, when the Earth is between the Sun and Moon. This will be evident by referring to the positions of the Sun, Moon, and Earth during the full and change, as exhibited in fig. 6 of Plate II. 46. The orbit of the Moon crosses the Ecliptic so as to make an angle of five degrees' inclination, and these points of intersection are called the Nodes of the Moon, being distinguished from each other as the ascending and descending: the ascending node is where the Moon ascends Northward above the ecliptic, and the descending node, where she descends Southward below the ecliptic; they are both marked in Plate II. fig. 7. Now, these Nodes being the only two points where the Moon crosses the Ecliptic, hence, there can be no Eclipse of the Sun but when 38 there the neighbouring Moon (So call that opposite fair star) her aid And in her pale dominion checks the night. Milton, Par. Lost, Book IIL 742. she changes in, or near, one of the Nodes, because, then only she comes so between the Earth and Sun, as to intercept the rays of the latter from the Earth: and in like manner, there can be no Eclipse of the Moon but when she is full in, or near, one of the Nodes, because, then only the Earth comes so between her and the Sun, as to hinder the rays of the latter from falling on her. This is the reason why there is not an Eclipse of the Sun at every change of the Moon, and an Eclipse of the Moon at every full of the Moon. 47. The Shadows cast by the Earth and Moon are of a conical figure (as may be seen in fig. 7), growing narrower and narrower the farther they go from the Earth and Moon, until at last they end in a point, and so cease. This is owing to the Earth and Moon being smaller bodies than the Sun: were they the same size as the Sun, it is evident that the shadows must be cylindrical (as in fig. 8), and were they larger than the Sun, the shadows would be like inverted cones (as in fig.9). And hence, in consequence of the Earth being much bigger than the Moon, the cone of its shadow is great enough to intercept the Sun's rays from the whole of the Moon's surface at one time: whilst, on the other hand, the Moon being smaller than the Earth, can intercept the Sun's rays only from a small part of the Earth at one time. [Herein too, the much greater distance of the orbit of Mars becomes evident; for, though the Earth may be directly between the Sun and Mars, yet is the latter not eclipsed, as it must necessarily be, did the shade of the Earth reach to its orbit.] The Shadows of the Earth and Moon being thus of a conical figure, it is obvious, that an Eclipse of the Sun or Moon will be greatest or longest, when the Moon is in her Perigee, or nearest the Earth; for then she has to traverse a thicker part of the Earth's shadow, than when eclipsed in her Apogee or greatest distance from the Earth. This may be seen in fig. 7, where P P denotes the breadth of the Earth's shadow traversed by the Moon in her Perigee, and A A so much of it, as is traversed by her when in her Apogee. And in like manner, if the Sun be eclipsed when the Moon is in her Perigee, it meets with a thicker part of the Moon's shade, than it does when she is in her Apogee; as may be also seen in fig. 7, by supposing T to be the Moon, P P her shadow traversed by the Earth when she is in her Perigee, and AA her shadow traversed by the Earth when she is in her Apogee. 48. But the Greatness and Duration of an Eclipse, arise principally from the Moon's being then more, or less distant, from a Node. An Eclipse of the Moon is either Total, that is, when the whole of her is eclipsed, or Partial, when only a part of her is eclipsed: and, as some partial eclipses are of longer duration than others, so, some total eclipses are likewise of longer duration than others. Now, those Total Eclipses, which are of the longest duration, happen when the Moon is exactly in a Node; they are called Central Eclipses, from the centre of the Moon passing through the centre of the Earth's shadow. This is illustrated in fig. 10 of Plate II., where the shaded circle represents the Earth's shadow, O M the Moon's orbit, and EC the Ecliptic: whence it is evident, that the Moon crossing the Earth's shadow in a diametrical direction, makes the longest possible stay, she ever can make, in it; this stay is about four hours long, the breadth of the Earth's shade being about three diameters of the Moon. A Total, but not Central, Eclipse is represented in fig. 11, where the Moon meets the Earth's shadow at a small distance from a Node, and so crosses only a Chord (or portion) of the Earth's shadow, and not its diameter; whence likewise, it is evident, that this chord will be greater or smaller, according as the Moon is nearer to, or farther from, a Node, and that the duration of every Total Eclipse will necessarily depend on the length of this chord. Hence also it follows, that some Eclipses are more Partial than others, according as the Moon is at a greater, or less distance from a Node; and that the longer a Partial Eclipse is, so much more of the Moon passes through the shadow of the Earth. A Partial Eclipse is reprepresented in fig. 12, where it will be seen, that the Node is at some distance from the centre of the Earth's shadow, and that, consequently, the 39 Quale per incertam Lunam sub luce maliguà Virg. Æn. VI. 270. |