While Galileo was studying medicine in Pisa, boarding with a relative, the court of Tuscany came to the city for a few months. Among the suite was Ostilio Ricci, a distinguished mathematician, and Governor of the Pages of the Grand Ducal Court. He was a friend of the Galilei family, and was pleased to see the bright young son, Galileo. When he taught Euclid, the medical student would stand shyly at the schoolroom door, and listen with intense interest. Soon he began to study mathematics secretly; then begged Ricci to teach him, who gladly consented, till the father forbade it, seeing that Euclid interfered with medicine. Meantime, the youth of nineteen, kneeling at prayers in the Pisa Cathedral, had dreamily watched a bronze lamp swinging from an arch. The oscillations were at first considerable, but as they grew less and less, Galileo observed that they were all performed in the same time, measuring the time by feeling his pulse. The idea occurred to him that an instrument could be constructed which should mark the rate and variation of the pulse. He began to experiment, and soon invented the pulselogia, which the physicians hailed with great delight. The pendulum was not applied to clocks till a half-century later, but its invention attracted the attention of all scholars. After four years' residence at Pisa, Vincenzo Galilei appealed to the reigning Grand Duke, Ferdinand de Medici, to grant to his son one of the forty free places founded for poor students, but the request was denied, and Galileo, unable to pay for his doctor's degree, was obliged to leave the university without it. Already he had learned bitter lessons of privation and disappointment, but youth has a brave heart, and looks ever toward the sunlight. He went back to his home in Florence to study the works of Archimedes, whom he called his "master," to write his first essay on his Hydrostatic Balance, and to earn the reputation of a bold inquirer in geometrical and mechanical speculations. The father had now given up all hope of a fortune coming through medicine! Henceforward, the genius which was to shed lustre on his own name, otherwise buried in obscurity, was to have its own bent, and work out its own destiny. If we are in earnest, a door opens sooner or later; but our own hands usually open it. At twenty-four a door opened to Galileo. Marquis Guidubaldo, a celebrated mathematician, appreciating what the young scientist had done, began a correspondence with him, and a valuable friendship resulted. The marquis asked him to study the position of the centre of gravity in solid bodies. Galileo applied himself to it, and wrote a valuable essay, which waited fifty years for publication. Perhaps no person can be really great who has not learned patience, and Galileo had many lessons in this virtue before he died.