XX 11 



THE PROGRESS OF 



of the heavens. His first discussions related to 

 astronomical refraction, and to the calculation of 

 eclipses. 



lie observed that the orbits of the planets arc 

 in planes passing through tho sun, and that of 

 consequence the lines of their nodes all intersect 

 in the centre of that luminary. The opposition 

 of the planets, or their places when they pass the 

 meridian at midnight, offer the most favourable 

 opportunities for observing them, both because 

 they are at that lime nearest the earth, and 

 because their places seen from thence is the same 

 as if they were seen from the sun. But the true 

 time of opposition had hitherto been mistaken 

 by astronomers, who held it to be at the moment 

 \\l\vn the apparent place of the planet was oppo- 

 site to the mean place of the sun. It ought to 

 have been when the apparent places of both 

 were opposed to each other. This correction 

 was made by Kepler, and though violently op- 

 posed by Tycho, was finally acquiesced in. 



Having undertaken to examine the orbit of 

 Mars, in which the irregularities are most con- 

 siderable, Kepler discovered by comparing 

 together seven oppositions of that planet, that 

 its orbit is elliptical ; that the sun is placed in 

 one of the foci ; and that there is no point round 

 which the angular motion is uniform. In the 

 pursuit of this inquiry he found that the same 

 thing is true of the earth's orbit round the sun. 

 It was reasonable to conclude by analogy, that 

 the orbits of all the other planets are elliptical, 

 having the sun in their common focus. 



The industry and patience of Kepler, in these 

 investigations, are almost incredible. Logarithms 

 did not yet exist, so that arithmetical calculations 

 were extremely laborious. The computation of 

 every opposition of Mars filled ten folio pages ; 

 and Kepler repeated each calculation ten times. 

 Seven oppositions thus calculated filled 700 folio 

 pages. In such calculations the introduction of 

 hypotheses was unavoidable. Kepler rejected 

 them whenever they appeared erroneous, with- 

 out hesitation, regretting merely the time which 

 they had uselessly cost him. He began with 

 hypotheses, and ended by rejecting every thing 

 hypothetical. 



Though the angular motion of the planets was 

 not found to be uniform, it was discovered that a 

 very simple law connected that motion with the 

 rectilinear distance from the sun, the former 

 being every where inversely as the square of the 

 latter. Hence it was easy to prove, that the area 

 described by the line drawn from the planet to 

 the sun increased at a uniform rate ; and, there- 

 fore, that any two such areas were proportioned 

 to the times in which they were described. 



This was the second of Kepler's three famous 

 laws ; the third was not less remarkable. He 



was of opinion that some simple relation must 

 exist between the periodical times of the planets 

 and their distances from the sun. After an in- 

 finite number of trials, he discovered, to his great 

 delight, that in any two planets the squares of 

 the times of the revolution are as the cubes of 

 their mean distances from the sun. 



It is humiliating to be obliged to state, that 

 these great discoveries were at first underrated 

 by astronomers, and that they even reproached 

 Kepler for making them ; because, in calculating 

 the place of a planet, they introduced a problem 

 too difficult to be resolved by elementary geo- 

 metry. 



While Kepler was thus perfecting the theory 

 of the planetary motions, Galileo had constructed 

 a telescope, and directed it to the moon. The 

 appearance of that luminary, under the telescope, 

 is now so well known, that we need not describe 

 it. The effect produced upon the mind of Galileo 

 may be easily conceived, He became satisfied of 

 the resemblance between the surface of the moon 

 and that of the earth. The telescope brought 

 into view multitudes of fixed stars, which cannot 

 be seen by the naked eye. In Jupiter he observed 

 a large disc, approaching in size to the moon. 

 Near it he saw, for the first time, three luminous 

 points in a straight line; two of them on one 

 side, and one on the other. By observing them, 

 however, night after night, he found these small 

 stars to be four in number, and to be moons or 

 satellites accompanying Jupiter, and revolving 

 round him as the moon does round the earth. 



In Saturn he saw one large disc, with two 

 smaller ones very near it, and diametrically op- 

 posite, and always seen in the same places. l!ut 

 more powerful telescopes were wanting before 

 these appearances could be interpreted. 



The horned figure of Venus, and the gibbosity 

 of Mars, added to the evidence of the Copernican 

 system, and verified the conjecture of its author, 

 who ventured to say, that if the sight were suf- 

 ficiently powerful, we should see Mercury and 

 Venus exhibiting phases similar to those of the 

 moon. 



These discoveries were probably the most 

 splendid that ever fell to the lot of any individual. 

 In a more enlightened age they would have 

 secured the gratitude and admiration of the 

 whole scientific world. But Galileo had raised a 

 host of enemies, by attempting to overturn the 

 Aristotelian doctrines, and the church itself was 

 roused to action, because it had staked its in- 

 fallibility in support of dogmas which the dis- 

 coveries and reasoning of Galileo had overturned. 

 Galileo was twice brought before the inquisition ; 

 and a council of seven cardinals pi-onounced the 

 following 1 sentence : " That to maintain the sun 

 to be immovable, and without local motion in 



