*THE POPULAR SCIENCE MONTHLY*

cumulated (for the most part) by BrahÃ©. He took infinite pains, testing 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 overwhelming," 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:

While Kepler was laying the enduring foundations of the Copernican 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