326 THE POPULAR SCIENCE MONTHLY 



cumulated (for the most part) by Brahe. He took infinite pains, test- 

 ing by actual calculation every hypothesis or rule that he could think 

 of. For example, he tried circular orbits with constant velocities for 

 the planets and the sun at the center. Finding that this did not fit 

 the facts, he placed the sun a little off center and tried again, but the 

 theory did not yet fit the observed facts. " After incredible labor, 

 through innumerable wrong guesses, and six years of almost incessant 

 calculation " the truth began to dawn upon him, until he was able to 

 enunciate three laws which have since gone by his name. The first of 

 these to yield itself to his zeal was the so-called second law which gives 

 the rule governing the velocity of the planet in its orbit. 



Law II., The radius vector sweeps out equal areas in equal times. 

 Having determined, as he believed, the law of speed, he next inquired 

 into the exact shape of the orbit. Here " however, the geometrical and 

 mathematical difficulties of calculation threatened to become over- 

 whelming," and as the days dragged into months he had every reason 

 to become disheartened. By day he worked, by night he dreamed of 

 his problem, and it is said that the hint which led to its solution came 

 to him as he slept and awoke him. Arising at once, he lighted his lamp 

 and set to work anew at his calculations. Step by step he progressed, 

 and finally, in a paroxysm of delight, he proved what is now known as 

 Kepler's first law. 



Law I., The planets move in ellipses with the sun at one focus. 

 To these two laws Kepler nine years later in 1618 added a third. 



Law III., The square of the time of revolution of each planet is 

 proportional to the cube of its mean distance from the sun. 



In these three statements Kepler brought order out of chaos and 

 reduced to system a heterogeneous mass of observations and records. 

 When we remember that these laws of Kepler's furnished Newton not 

 only a point of departure, but also gave him a criterion by which to test 

 his results, we begin to see that without Kepler, Newton might not 

 have been possible. Lodge says of him: 



A man of keen imagination, indomitable perseverance and uncompromising 

 love of truth, Kepler overcame ill-health, poverty and misfortune, and placed 

 himself in the very highest rank of scientific men. His laws so extraordinarily 

 discovered introduced order and simplicity into what else would have been a 

 chaos of detailed observations; and they served as a secure basis for the 

 splendid erection made on them by Newton. 



While Kepler was laying the enduring foundations of the Coperni- 

 can theory, Galileo (1564-1642), was carrying on an open propaganda 

 in Italy. In 1609 he perfected the telescope, and with it, night by 

 night, questioned the heavens. The mountains on the moon, the 

 satellites of Jupiter, sun-spots, the strange appearance of Saturn due 

 to its rings, the changing phases of Venus, were discoveries rapidly 



