235. If the Sun’s motion were equable in the Ecliptic, the whole difference between the equal time as shewn by a 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; ’tis 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.
Fig. IV.
237. As the real Sun moves unequably in the Ecliptic, let us suppose a fictitious Sun to move equably in it. Let ABCD be the Ecliptic or Orbit in which the real Sun moves, and the dotted Circle abcd 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 it’s 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 be noon by the Sun-dial sooner than by the Clock.
As the real Sun moves from A towards 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 equally moving fictitious Sun till the former comes to C, and the latter to c, when each has gone half round it’s respective orbit; and then being in conjunction, the Meridian EH revolving to EK 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; and therefore, the same Meridian will come to the fictitious Sun sooner than to the real: for whilst 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 it’s fictitious noon when it comes to k, but not it’s real noon 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 coming nearer to the real Sun, yet they are not in conjunction till the one comes to A and the other to a; and then it is noon by them both at the same moment.
And thus it appears, that the real noon by the Sun is always later than the fictitious noon by the clock whilst the Sun goes from C to A, sooner whilst 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, Perigee, and Apsides, what.
Fig. IV.
238. The point A is called the Sun’s Apogee, because 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: and a right line, as AEC, drawn through the Earth’s center, from one of these points to the other, is called the line of the Apsides.