ERA OF COPERNICUS, TYCHO BRAHE, KEPPLER, AND GALILEO. 27 



tigation, and left him the legacy of his own observations at his decease. JOHN KEPPLER, 

 born at Wiel, in the duchy of Wirtemberg, in 1571, was educated for the church, and 

 entered upon an ecclesiastical office, but withdrew from the science of theology to that of 

 mathematics and astronomy, and occupied the chair of the latter at Gratz in 1 594. His 

 native lively imagination and fiery impetuosity led him to plunge headlong, at first, into 

 the regions of speculation ; but Tycho's advice, " to lay a solid foundation for his views 

 by actual observation, and then, by ascending from these, to strive to reach the causes of 

 things," advice expressing the principle of inductive philosophy, drew him away from 

 pursuing the vain phantoms of fancy to conform his mind to the results of calculation and 

 experience. His first reward was the discovery of the elliptical orbits of the planets. 

 The Copernican system had respected the ancient reverence for the circle as the only 

 path proper for celestial bodies to describe. An opposition of Mars, whose path is one of 

 the most eccentric in the planetary system, led Keppler to study his motions, and among 

 the papers of Tycho, then deceased, he found a large number of observations upon this 

 and the other planets. He began his researches with his mind fully possessed with the 

 idea of circular motion, but he found it utterly impossible, by any conceivable arrange- 

 ment of cycle and epicycle, to represent the known motions of Mars. The discovery 

 came at length that the planet's path was an ellipse, the sun occupying one of the foci, 

 the two points around which the oval is formed, instead of being in the centre. Circum- 

 stances forbid us estimating aright the labour involved in this discovery, the difficulties 

 that arose in its progress, and the mental conflict they occasioned ; but Keppler describes 

 his battles, defeats, and conquests in the following racy manner : " While in this way 

 I triumph over the motions of Mars, and form for him, as one completely conquered, the 

 prison of tables, and the chains of the equations of the eccentric, intelligence is brought 

 me from different places that the victory is all vain, and the war as fierce as ever ; for 

 the captive enemy has broken through all the bonds of the equations, and the dungeons 

 of the tables . . . And the fugitive would have effected his junction with the rebels, and 

 driven me to despair, had I not suddenly brought up a new reserve of physical consider- 

 ations, the first having been beaten and scattered." Well might he think, as he tells 

 us, of Galatea in the eclogue of Virgil, who, after inviting approach, the nearer she was 

 approached was the more petulant in her sportive attempts to escape. The demonstration, 

 however, of the orbit of Mars being an ellipse was finally complete, and Keppler ultimately 

 established the fact, that all the planets describe ellipses the FIRST of his great Laws. 



His next discovery was no less remarkable. While the scheme of Copernicus retained 

 the ancient idea of the heavenly bodies describing circles, it held also the notion of their 

 velocities being uniform. But the mass of facts accumulated by Tycho proved that the 

 motions of Mars were not uniform that the planets move with different velocities in 

 different parts of their orbits ; and the inquiring mind of Keppler directed itself to ascer- 

 tain the rule which regulated their rate of motion a bold attempt, but crowned with 

 complete success. Let the ellipse represent the orbit of a planet, and s the sun in one of 

 the foci. A straight line drawn from the planet at a to the focus, called the radius vector, 

 and another line drawn from the planet at b, bound a certain extent of area, and the 

 7 c , planet periodically passes from a to b in a certain amount of 



time proportioned to the area. For the sake of illustration, the 

 time may be rated at a month. If we now draw straight lines 

 from the planet at c, d, e, f t and g, other areas will be bounded, 

 which we may suppose equal to the former, and to each other. 

 The planet will then pass from a to b, from b to c, from c to d> 

 and so on, in equal times or in a month. But, obviously, while the areas described by 

 the radius vector are equal, the actual orbital path of the planet is unequal, and it must 



