Johann Kepler (1571-1630) had been called, as the astronomer's assistant, to the Bohemian capital in 1600 and in a few months fell heir to Tycho's data in reference to 777 stars, which he made the basis of the Rudolphine tables of 1627. Kepler's genius was complementary to that of his predecessor. He was gifted with an imagination to turn observations to account. His astronomy did not rest in mere description, but sought the physical explanation. He had the artist's feeling for the beauty and harmony, which he divined before he demonstrated, in the number relations of the planetary movements. After special studies of Mars based on Tycho's data, he set forth in 1609 (_Astronomia Nova_) (1) that every planet moves in an ellipse of which the sun occupies one focus, and (2) that the area swept by the radius vector from the planet to the sun is proportional to the time. Luckily for the success of his investigation the planet on which he had concentrated his attention is the one of all the planets then known, the orbit of which most widely differs from a circle. In a later work (_Harmonica Mundi_, 1619) the title of which, the _Harmonics of the Universe_, proclaimed his inclination to Pythagorean views, he demonstrated (3) that the square of the periodic time of any planet is proportional to the cube of its mean distance from the sun. Kepler's studies were facilitated by the invention, in 1614 by John Napier, of logarithms, which have been said, by abridging tedious calculations, to double the life of an astronomer. About the same time Kepler in purchasing some wine was struck by the rough-and-ready method used by the merchant to determine the capacity of the wine-vessels. He applied himself for a few days to the problems of mensuration involved, and in 1615 published his treatise (_Stereometria Doliorum_) on the cubical contents of casks (or wine-jars), a source of inspiration to all later writers on the accurate determination of the volume of solids. He helped other scientists and was himself richly helped. As early as 1610 there had been presented to him a means of precision of the first importance to the progress of astronomy, namely, a Galilean telescope.