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. But this difficulty no more embarrassed the great pontiff of astronomy than a conscientious scruple would perplex the author of a theological dogma. Listen to him:-- "The true cause of these apparent irregularities is explained by two very simple hypotheses. Either the one or the other would account for the phenomena. In fact, if we suppose the movement to occur in a circle described around the centre of the world, and in the plane of the ecliptic, so that the point whence we are looking corresponds with this centre, we must admit either that the planets make their movements equal in non-concentric circles, or that, if these circles are concentric, it is not simply in these circles that they move, but in others, called _epicycles_, carried through the concentric."[73]