_Kepler found his master’s tables sufficiently accurate in his efforts to discover some recognizable motion of the planet Mars which would account for its apparent positions. In the course of this work he corrected some of the Ptolemaic ideas which Copernicus had not completely abandoned. The latter retained the epicycle motion of the planets within their larger revolutions in cycles. In comparing this theory with his tables, Kepler found that it would not satisfactorily account for the positions of Mars; and he was therefore led to the long studies and mathematical computations which finally resulted in his discovery of the orbit of Mars, and to the establishment of the first two of his three famous laws: “1. the planet describes an ellipse, the sun being in one focus; 2. the straight line joining the planet to the sun sweeps out equal areas in equal intervals of time.” (Sedgwick and Tyler, pp. 211-213). He published these laws in 1609 in his “Commentaries on the Motions of Mars.”_ _In 1611, when his patron, Emperor Rudolph, was compelled to abdicate, Kepler was left penniless, but he moved to Linz where he was appointed to a professorship. In 1619 he published his “Harmony of the World,” which contained his third law: “The squares of the times of revolution of any two planets (including the earth) about the sun are proportional to the cubes of their mean distances from the sun.” (Sedgwick and Tyler, p. 213). This was the triumph about which he wrote in the year of its discovery, 1618: “What I prophesied twenty-two years ago, as soon as I found the heavenly orbits were of the same number as the five (regular) solids, what I fully believed long before I had seen Ptolemy’s Harmonies, what I promised my friends in the name of this book, which I christened before I was sixteen years old, I urged as an end to be sought, that for which I joined Tycho Brahe, for which I settled at Prague, for which I have spent most of my life at astronomical calculations--at last I have brought to light, and seen to be true beyond my fondest hopes. It is not eighteen months since I saw the first ray of light, three months since the unclouded sun-glorious sight! burst upon me. Let nothing confine me: I will indulge my sacred ecstasy. I will triumph over mankind by the honest confession that I have stolen the golden vases of the Egyptians to raise a tabernacle for my God far away from the lands of Egypt. If you forgive me, I rejoice; if you are angry, I cannot help it. The book is written; the die is cast. Let it be read now or by posterity, I care not which. It may well wait a century for a reader, as God had waited six thousand years for an observer.” Kepler died at Ratisbon, November 15, 1630._ ON THE PRINCIPLES OF ASTRONOMY[5]