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6 some importance to the medical profession. Instruments of various patterns which he constructed for this purpose were welcomed with delight by leading doctors, and used under the name of Pulsilogia. All the patterns were founded on the original idea of a pendulum bob, swinging, as is now well known, more quickly as the supporting string was shortened, by drawing it through a hole or winding it round a wheel; so that the length of the string gave a measure of the rapidity of the pulse-beats when the swings were made to coincide with one or more beats. The use of the pendulum for regulating clocks was still in the far future, and it is doubtful whether Galileo ever really made this application, though before his death he seems to have had it in mind.

He was now nearly nineteen, and had still been kept away from mathematics. Some months before his entry into the University his family had returned from Pisa to Florence, and among their friends in that city was a capable mathematician named Ricci, attached to the Tuscan Court as tutor to the grand ducal pages. During Galileo's second year at the University the Court was in residence at Pisa, and Galileo naturally renewed his acquaintance with Ricci. Going to call on him one day he happened to find him lecturing on Euclid to his pupils, and stayed outside an open door to listen without announcing his presence. He was so fascinated by the new ideas, for which his brain must have been pining unawares, that he began to make a practice of secretly listening to Ricci until he plucked up courage to speak to him openly on the subject. After this it was plain enough sailing for a time, for Ricci gladly afforded all assistance in his power. But the inevitable neglect of medical studies, as well as the failure of every application for a free scholarship, convinced Galileo's father that he was not likely to get an adequate return for the crippling