458 LECTURE XLVIII. 



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discovered that their orbits are ellipses, and demonstrated, chiefly from his 

 observations on the planet Mars, that the revolving radius, or the line 

 drawn from the sun to the planet, always describes equal areas in equal 

 times. By comparing the periods and the mean distances of the different 

 planets with each other, he found, after 17 years calculation, that the 

 squares of the times of revolution are always proportional to the cubes of 

 the mean distances from the sun.* 



Kepler died in 1630 : before his death he had the satisfaction of applying 

 his theory to the motions of the satellites of Jupiter, which, as well as the 

 phases of Venus, and the spots of the sun, had lately been discovered in 

 Italy by the telescopic observations of Galileo. This great man, celebrated 

 as well for his theory of projectiles, as for his zealous defence of the 

 Copernican system, was born at Pisa in 1564, and lived to the age of 78, 

 full of that enthusiasm which made him despise the threats of the Inquisi- 

 tion, and submit patiently to its persecutions. He died in 1642, the year 

 in which Newton was born. 



The invention of logarithms, by Baron Napier, requires to be noticed 

 for its importance to practical astronomy, and the laborious observations of 

 Hevelius deserve also to be mentioned with commendation. The dis- 

 coveries of the form of the ring of Saturn, and of one of his satellites, by 

 Huygens, and of four more, together with the belts and rotation of Jupiter, 

 by Dominic Cassini, were among the early improvements derived from 

 the introduction of the telescope. But, without dwelling on any of these 

 subjects, we hasten to the establishment of the system of gravitation, 

 which has immortalised the name of Newton, and done unrivalled honour 

 to the country that gave him birth. 



The mutual attraction of all matter seems to have been suspected by the 

 Epicureans, but Lucretius never speaks of it in such terms as are sufficient 

 to convey by any means a distinct idea of a reciprocal force. Gregory, in 

 the preface of his Astronomy, has endeavoured to prove that Pythagoras 

 must have been acquainted even with the law of the decrease of gravita- 

 tion ; and Lalande appears to assent to his arguments ; but they rest only 

 on the bare possibility that Pythagoras might have deduced an analogy 

 from the tension of cords, which we have no reason to suppose that he 

 even completely understood : and this merely because he fancifully 

 imagined, that there was a correspondence between the planets and the 

 strings of a lyre. But the nature of gravitation had long been in some 

 measure suspected ; Plutarch had asserted that the moon is retained by it 

 in her orbit, like a stone in a sling; and Bacon, Copernicus, Kepler, 

 Fermat, and Roberval were aware of its efficacy. Bacon, in his Novum 

 organum, calls the descent of heavy bodies the motion of " general con- 

 gregation," and attributes the tides to the attraction of the moon. Kepler 

 mentions also the perfect reciprocality of the action of gravitation, and 

 considers the lunar irregularities as produced by the attraction of the 

 sun. But our most ingenious countryman, Dr. Hooke, was still more 

 decided in attributing the revolutions of the planets to the combination of 

 a projectile motion with a centripetal force ; he expresses his sentiments 



* See Lect. IV. 



