distraction by terminating the mathematical tutor’s engagement.  But it was too late for the desired end to be attained.  Galileo had now made such progress that he was able to continue his geometrical studies by himself.  Presently he advanced to that famous 47th proposition which won his lively admiration, and on he went until he had mastered the six books of Euclid, which was a considerable achievement for those days.

The diligence and brilliance of the young student at Pisa did not, however, bring him much credit with the University authorities.  In those days the doctrines of Aristotle were regarded as the embodiment of all human wisdom in natural science as well as in everything else.  It was regarded as the duty of every student to learn Aristotle off by heart, and any disposition to doubt or even to question the doctrines of the venerated teacher was regarded as intolerable presumption.  But young Galileo had the audacity to think for himself about the laws of nature.  He would not take any assertion of fact on the authority of Aristotle when he had the means of questioning nature directly as to its truth or falsehood.  His teachers thus came to regard him as a somewhat misguided youth, though they could not but respect the unflagging industry with which he amassed all the knowledge he could acquire.

[Plate:  Galileo’s pendulum.]

We are so accustomed to the use of pendulums in our clocks that perhaps we do not often realise that the introduction of this method of regulating time-pieces was really a notable invention worthy the fame of the great astronomer to whom it was due.  It appears that sitting one day in the Cathedral of Pisa, Galileo’s attention became concentrated on the swinging of a chandelier which hung from the ceiling.  It struck him as a significant point, that whether the arc through which the pendulum oscillated was a long one or a short one, the time occupied in each vibration was sensibly the same.  This suggested to the thoughtful observer that a pendulum would afford the means by which a time-keeper might be controlled, and accordingly Galileo constructed for the first time a clock on this principle.  The immediate object sought in this apparatus was to provide a means of aiding physicians in counting the pulses of their patients.

The talents of Galileo having at length extorted due recognition from the authorities, he was appointed, at the age of twenty-five, Professor of Mathematics at the University of Pisa.  Then came the time when he felt himself strong enough to throw down the gauntlet to the adherents of the old philosophy.  As a necessary part of his doctrine on the movement of bodies Aristotle had asserted that the time occupied by a stone in falling depends upon its weight, so that the heavier the stone the less time would it require to fall from a certain height to the earth.  It might have been thought that a statement so easily