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146 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.

115. Before very long it became evident that Galilei had no special taste for medicine, a study selected for him chiefly as leading to a reasonably lucrative professional career, and that his real bent was for mathematics and its applications to experimental science. He had received little or no formal teaching in mathematics before his second year at the University, in the course of which he happened to overhear a lesson on Euclid's geometry, given at the Grand Duke's court, and was so fascinated that he continued to attend the course, at first surreptitiously, afterwards openly; his interest in the subject was thereby so much stimulated, and his aptitude for it was so marked, that he obtained his father's consent to abandon medicine in favour of mathematics.

In 1585, however, poverty compelled him to quit the University without completing the regular course and obtaining a degree, and the next four years were spent