296

THE SUN'S VISUAL ANGLE.

sun is greater in winter than in summer-that we are nearer the sun in the cold season, than in the hot!

On more closely examining a result apparently so paradoxical, man discovered that the angle which subtracts the sun, as seen from the earth,-the visual angle which gives the sun's apparent diameter,—varies necessarily throughout the year. Thus, the semi-diameter, or radius, which on the 24th of June equals 15′ 45′′, will, a month later, have increased one second (15'46"); on the 2d of August will equal 15′ 47′′; on the 2d September, 15' 53", and so on. We put the exact measurements before the reader in a tabulated form :

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

MAXIMUM AND MINIMUM.

297

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 = 360°?

2

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

298

ASTRONOMICAL INFALLIBILITY.

of the circles in which these movements are accomplished ; and that, in this apparent disorder of the phenomena (gi ὑπονουμένην τῶν φαινομένων ἀταξίαν), nothing really occurs contrary to their actual immobility (τῷ ὄντι πέφυκε συμβαίνειν οὐδὲν ἀλλότριον αὐτῶν τῆς ἀΐδιότητος).”

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."*

Examine Fig. 67. Here A B G D represent the ecliptic. E its centre, and A E G its diameter; Z HT K is the epicycle, in which the planet moves uniformly around the * Ptolemæus, "Syntaxis Mathematicalis,” iii. 3.

ITS THEORY OF EPICYCLES.

299

centre A, while the epicycle uniformly traverses the circle A B G D. Now, suppose that the star has arrived at H; it would appear to an observer at E to be more advanced by the uniform movement of all the arc A H; if it be at K, it would appear, on the contrary, to be less advanced by all the arc A K. At Z the star would appear more distant, and at T, nearer than if it were at A.

FIG. 67.-The Circle and the
Epicycle.

To explain the other phenomena, such as the stations and retrocessions of the planets, recourse was again had to the epicycles or deferred eccentric circles. By multiplying these it was possible to account for all the angular inequalities in the movements of a planet. It is of importance to note this point, in order to show how very dangerous it is to trust absolutely to mathematics in our search after the truth; that science which, by the certainty of its demonstrations, nourishes our intellectual pride, and may, therefore, occasionally lull the mind into a false security. The theory of epicycles, from a mathematical point of view, was irreproachable, and it sufficiently accounted for the facts which threatened to overthrow the dogma of circular orbits and uniform planetary move

ment.

But by degrees, as observations grew more accurate and

300

KEPLER'S GOOD WORK.

comprehensive, these and other theories, however fine in appearance,-teres atque rotundus,-gradually disappeared, if fundamentally erroneous. By the invention of micrometers, we were enabled to measure more exactly than had formerly been possible the variations of diameter or the modifications of distance, and afterwards to compare them with the changes of velocity. From this comparison it results that the latter are not greater than is compatible with the alterations of distance indicated by the variations of diameter; in a word, that the hypothesis of epicycles is decidedly insufficient to account for all the inequalities detected by careful investigation.

Kepler was the first to break the charm which had held captive the mind of astronomers, including even Copernicus and Tycho Brahé. Ptolemæus had considered the mean positions of the stars to be real. Kepler, strong in his researches, declared that they were but a factitious mode of calculation by which the true positions might be ascertained; that the mean movement is simply an artifice representing the star's place, if no inequality existed; in fine, that we must take the movements as they are in nature,-the true movements, given by observation,-and not the mean movements, deduced from an erroneous hypothesis.

This declaration of principles met, at the time, with the hostility of all astronomers of any reputation, but it has become the starting-point of the discovery of the laws on which the whole edifice of astronomy reposes. Had Kepler,