Plate VI. The se 234. Having explained one cause of the difference of time shewn by a well-regulated clock and a cond part true sun-dial, and considered the Sun, not the Earth, equation as moving in the ecliptic, we now proceed to exof time. plain the other cause of this difference, namely, the of the inequality of the Sun's apparent motion, 205, which is slowest in summer, when the Sun is farthest from the Earth, and swiftest in winter when he is nearest to it. But the Earth's motion on its axis. is equable all the year round, and is performed from west to east; which is the way that the Sun appears to change his place in the ecliptic. 235. If the Sun's motion were equable in the ecliptic, the whole difference between the equal time as shewn by the clock, and the unequal time as shewn by the Sun, would arise from the obliquity of the ecliptic. But the Sun's motion sometimes exceeds a degree in 24 hours, though generally it is less; and when his motion is slowest, any particular meridian will revolve sooner to him than when his motion is quickest; for it will overtake him in less time when he advances a less space than when he moves through a larger. 236. Now, if there were two suns moving in the plane of the ecliptic, so as to go round it in a year; the one describing an equal arc every 24 hours, and the other describing sometimes a less arc in 24 hours, and at other times a larger; gaining at one time of the year what it lost at the opposite; it is evident that either of these suns would come sooner or later to the meridian than the other, as it happened to be behind or before the other: and when they were both in conjunction, they would come to the meridian at the same moment. 237. As the real Sun moves unequably in the ecliptic, let us suppose a fictitious sun to move Fig. IV. equably in a circle coincident with the plane of the ecliptic. Let ABCD be the ecliptic or orbit in which the real Sun moves, and the dotted circle a, b, c, d, the imaginary orbit of the fictitious sun; each going round in a year according to the order of letters, or from west to east. Let HIKL be the Earth turning round its axis the same way every 24 hours; and suppose both suns to start from A and a, in a right line with the plane of the meridian EH, at the same moment: the real Sun at A, being then at his greatest distance from the Earth, at which time his motion is slowest; and the fictitious sun at a, whose motion is always equable, because his distance from the Earth is supposed to be always the same. In the time that the meridian revolves from H to H again, according to the order of the letters HIKL, the real Sun has moved from A to F; and the fictitious, with a quicker motion, from a to f, through a larger arc; therefore, the meridian EH will revolve sooner from H to h under the real Sun at F, than from H to k under the fictitious sun at f; and consequently it will then be noon by the sundial sooner than by the clock. As the real Sun moves from A toward C, the swiftness of his motion increases all the way to C, where it is at the quickest. But notwithstanding this, the fictitious sun gains so much upon the real, soon after his departing from A, that the increasing velocity of the real Sun does not bring him up with the equably-moving fictitious sun till the former comes to C, and the latter to c, when each has gone half round its respective orbit; and then, being in conjunction, the meridian E H revolving to E K comes to both Suns at the same time, and therefore it is noon by them both at the same moment. But the increased velocity of the real Sun, now being at the quickest, carries him before the fictitious one; and, therefore, the same meridian will come to the fictitious sun sooner than to the real : for while the fictitious sun moves from c to g, the real Sun moves through a greater arc from C to G: consequently the point K has its noon by the clock Ꮓ VI. PLATE when it comes to k, but not its noon by the Sun till it comes to l. And although the velocity of the real Sun diminishes all the way from C to A, and the fictitious sun by an equable motion is still com. ing nearer to the real Sun, yet they are not in con. junction till the one comes to A, and the other to a; and then it is noon by them both at the same mo and ap sides, what. ment. Thus it appears, that the solar noon is always later than noon by the clock while the Sun goes from C to A; sooner, while he goes from A to C, and at these two points, the Sun and clock being equal, it is noon by them both at the same moment. Apogee, 238. The point A is called the Sun's apogee, be perigee, cause when he is there, he is at his greatest distance from the Earth; the point C, his perigee, because when in it he is at his least distance from the Earth: Fig. IV. and a right line, as AEC, drawn through the Earth's centre, from one of these points to the other, is called the line of the apsides. maly, what. 239. The distance that the Sun has gone in any time from his apogee (not the distance he has to go Mean ano- to it, though ever so little) is called his mean anomaly, and is reckoned in signs and degrees, allow. ing 30 degrees to a sign. Thus, when the Sun has gone 174 degrees from his apogee at 4, he is said to be 5 signs 24 degrees from it, which is his mean anomaly; and when he has gone 355 degrees from his apogee, he is said to be 11 signs 25 degrees from it, although he be but 5 degrees short of A, in coming round to it again. 240. From what was said above, it appears, that when the Sun's anomaly is less than 6 signs, that is, when he is any where between A and C, in the half ABC of his orbit, the solar noon precedes the clock-noon; but when his anomaly is more than 6 signs, that is, when he is any where between C and A, in the half CDA of his orbit, the clock-noon precedes the solar. When his anomaly is 0 signs, O degrees, that is, when he is in his apogee at A; or 6 signs, 0 degrees, which is when he is in his perigee at C; he comes to the meridian at the moment that the fictitious sun does, and then it is noon by them both at the same instant. 241. The following table shews the variation, or equation of time depending on the Sun's anomaly, and arising from his unequal motion in the ecliptic; as the former table, 229, shews the variation depending on the Sun's place, and resulting from the obliquity of the ecliptic: this is to be understood the same way as the other, namely, that when the signs are at the head of the table, the degrees are at the left hand; but when the signs are at the foot of the table, the respective degrees are at the right hand; and in both cases the equation is in the angle of meeting. When both the above-mentioned equations are either faster or slower, their sum is the absolute equation of time; but when the one is faster, and the other slower, it is their difference. Thus suppose the equation depending on the Sun's place be 6 minutes 41 seconds too slow, and the equation depending on the Sun's anomaly, 4 minutes 20 seconds too slow, their sum is eleven minutes one se cond too slow. But if the one had been 6 minutes 41 seconds too fast, and the other 4 minutes 20 seconds too slow, their difference would have been 2 minutes 21 seconds too fast, because the greater quantity is too fast. |