We do not trouble the reader with the fractions of a second, which indicate the quantity of the apparent increase of the radius from the end of June to the end of December, and its apparent decrease from the beginning of January to the end of June.
A glance at the above figures shows that the mean of the apparent diameters, all measured at the moment of the sun's passing the meridian, is about half a degree, or 30'; and that--which is sufficiently curious--720 of these mean suns, set one against another, would be required to fill up the contour of a great circle of the celestial sphere. Is it this fact which suggested the idea of dividing the circle into 720/2 = 360°?
Simultaneously with the discovery of the variations of the solar charioteer, it was ascertained that the moments of the sun's passage of the meridian--moments which measure the 365 different positions occupied by the sun in the 365 days of the year--are not separated by equal intervals, or that equal intervals of time do not correspond to the equal angular displacements,--in fine, that the maximum and minimum of the sun's angular velocity coincide with the maximum and minimum of its apparent diameter. Now, remember that the extreme points where the sun experiences its maximum and minimum angular displacement are named, according to Ptolemæus, the former the _perigee_, the latter the _apogee_; or, if we follow Copernicus, the former the _perihelion_, and the latter the _aphelion_.
The aggregate of these facts was known to the ancients; but the manner in which it was sought to explain them merits notice as a specimen of blind attachment to a preconceived system.
Ptolemæus, the organ of the dictatorial astronomy of antiquity, declares, _ex cathedrâ_, that "the inequalities of the sun's movements are only apparent; that they are simply the effects of the position and of the arrangements of the circles in which these movements are accomplished; and that, in this _apparent disorder of the phenomena_ (περί τὴν ὑπονουμένην τῶν φαινομένων ἀταξίαν), nothing really occurs contrary to their actual immobility (τῷ ὄντι πέφυκε συμβαίνειν οὐδὲν ἀλλότριον αὐτῶν τῆς ἀΐδιοτητος)."
Now, according to this dogmatic immutability, the straight lines, or radii, which proceed from the revolving star to the centre of the circle, would describe "equal angles in equal times." This is exactly the contrary of the result obtained, as we have seen, by careful observation.