[Sidenote: 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. [Sidenote: PLATE VI.] 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. [Sidenote: Apogee, Perigee, and Apsides, what. Fig. IV.]