113. To the generation which succeeded Tycho belonged two of the best known of all astronomers, Galilei and Kepler. Although they were nearly contemporaries, Galilei having been born seven years earlier than Kepler, and surviving him by twelve years, their methods of work and their contributions to astronomy were so different in character, and their influence on one another so slight, that it is convenient to make some departure from strict chronological order, and to devote this chapter exclusively to Galilei, leaving Kepler to the next. _Galileo Galilei_ was born in 1564, at Pisa, at that time in the Grand Duchy of Tuscany, on the day of Michel Angelo’s death and in the year of Shakespeare’s birth. His father, Vincenzo, was an impoverished member of a good Florentine family, and was distinguished by his skill in music and mathematics. Galileo’s talents shewed themselves early, and although it was originally intended that he should earn his living by trade, Vincenzo was wise enough to see that his son’s ability and tastes rendered him much more fit for a professional career, and accordingly he sent him in 1581 to study medicine at the University of Pisa. Here his unusual gifts soon made him conspicuous, and he became noted in particular for his unwillingness to accept without question the dogmatic statements of his teachers, which were based not on direct evidence, but on the authority of the great writers of the past. This valuable characteristic, which marked him throughout his life, coupled with his skill in argument, earned for him the dislike of some of his professors, and from his fellow-students the nickname of The Wrangler. 114. In 1582 his keen observation led to his first scientific discovery. Happening one day in the Cathedral of Pisa to be looking at the swinging of a lamp which was hanging from the roof, he noticed that as the motion gradually died away and the extent of each oscillation became less, the time occupied by each oscillation remained sensibly the same, a result which he verified more precisely by comparison with the beating of his pulse. Further thought and trial shewed him that this property was not peculiar to cathedral lamps, but that any weight hung by a string (or any other form of pendulum) swung to and fro in a time which depended only on the length of the string and other characteristics of the pendulum itself, and not to any appreciable extent on the way in which it was set in motion or on the extent of each oscillation. He devised accordingly an instrument the oscillations of which could be used while they lasted as a measure of time, and which was in practice found very useful by doctors for measuring the rate of a patient’s pulse.