The book in which this law was published ("On Celestial Harmonies") was dedicated to James of England. In 1620 had to intervene to protect his mother from being tortured for witchcraft. Accepted a professorship at Linz. Published the Rudolphine tables in 1627, embodying Tycho's observations and his own theory. Made a last effort to overcome his poverty by getting the arrears of his salary paid at Prague, but was unsuccessful, and, contracting brain fever on the journey, died in November, 1630, aged 59. 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. _Seven planets of the Ptolemaic system--_ Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn. _Six planets of the Copernican system--_ Mercury, Venus, Earth, Mars, Jupiter, Saturn. _The five regular solids, in appropriate order--_ Octahedron, Icosahedron, Dodecahedron, Tetrahedron, Cube. _Table illustrating Kepler's third law._ +---------+---------------+-----------+---------------+----------------+ | | Mean distance | Length | Cube of the | Square of the | | Planet. | from Sun. | of Year. | Distance. | Time. | | | D | T | D^3 | T^2 | +---------+---------------+-----------+---------------+----------------+ | Mercury | ·3871 | ·24084 | ·05801 | ·05801 | | Venus | ·7233 | ·61519 | ·37845 | ·37846 | | Earth | 1·0000 | 1·0000 | 1·0000 | 1·0000 | | Mars | 1·5237 | 1·8808 | 3·5375 | 3·5375 | | Jupiter | 5·2028 | 11·862 | 140·83 | 140·70 | | Saturn | 9·5388 | 29·457 | 867·92 | 867·70 | +---------+---------------+-----------+---------------+----------------+ The length of the earth's year is 365·256 days; its mean distance from the sun, taken above as unity, is 92,000,000 miles. LECTURE III KEPLER AND THE LAWS OF PLANETARY MOTION It is difficult to imagine a stronger contrast between two men engaged in the same branch of science than exists between Tycho Brahé, the subject of last lecture, and Kepler, our subject on the present occasion. The one, rich, noble, vigorous, passionate, strong in mechanical ingenuity and experimental skill, but not above the average in theoretical and mathematical power. The other, poor, sickly, devoid of experimental gifts, and unfitted by nature for accurate observation, but strong almost beyond competition in speculative subtlety and innate mathematical perception.