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In the year 1343 one Tommaso Bonajuti, being elected to the Council of Twelve in Florence, changed his family name to Galilei. His grandson, Galileo Galilei, a century later, was a celebrated physician, professor of medicine at the University of Florence, and became chief magistrate of the Republic. This Galileo's brother had a great-grandson Vincenzio, the father of the great Galileo, whose life forms the subject of this volume. We shall consistently drop the surname in our references to him, following a custom of the Italians in speaking of their great men; such as Dante, Raphael, and Michelangelo.

Vincenzio Galilei was a skilful and accomplished musician, with a good knowledge of classics and mathematics, but want of means and the expense of a growing family had sent him into commercial life, and induced him to choose for his eldest son's future career the business of a cloth-dealer, as something of fairly good standing and also lucrative.

This son Galileo was born in Pisa on February 15, 1564, the year that saw the birth of Shakespeare, and his education began in a day-school there with some assistance from his father at times when business did not take him away from Pisa. Vincenzio's help with lessons seems to have been confined to Greek and Latin to the exclusion of mathematics. It may sound odd to modern ears, but there is no doubt of the fact that in those days the objection to the study of mathematics was that it did not pay, as we shall be reminded later on.

At thirteen Galileo was sent to the monastery of Vallombrosa, near Florence, for the conventional classical education, but he only stayed about two years, and was then hurriedly removed by his father, who found him in danger of yielding to the attractions of monastic life, and thus abandoning the career projected for him. The boy showed no special aptitude for business, but had a natural leaning towards mechanics, and like Newton at a later date, made toy machines at an early age. He had inherited a full share of his father's musical ability, and besides theoretical knowledge he learnt to play on various instruments, even surpassing his father's skilful performance on the lute. He showed, moreover, considerable facility in other arts, poetry, and especially drawing and painting, and though his inability to choose an artistic career restricted him almost entirely to criticism, his opinion was greatly valued by several painters of repute. Vincenzio could not be blind to the unsuitability of commercial pursuits for a youth of such accomplishments, and may have regretted what had seemed the necessity in his own case. He therefore abandoned the idea of the cloth trade, and cast about for a paying profession. His own experience taught him that neither mathematics nor music could be regarded as satisfactory from this point of view, and besides, Galileo had so far learnt nothing of mathematics. The choice, possibly influenced by the career of the boy's distinguished namesake, fell on the medical profession, and in his eighteenth year Galileo was sent to the University of Pisa to study under the celebrated physician Andrea Cesalpini, in addition to the usual course in philosophy.

Now Vincenzio himself, as shown in his writings on musical theory, had a rooted objection to taking things on trust, so it is not surprising that Galileo found himself continually at issue with his teachers in philosophy, and thus early struck the keynote of his stormy career. What passed for philosophy in those days had degenerated almost entirely into blind repetition of the statements and doctrines of ancient philosophers, and particularly of Aristotle. But Aristotle and the Greek philosophers generally were not accustomed to put their highly speculative theories to the test of actual experiment, however easy and obvious such experiment might be. They contented themselves with discussions as to what ought to happen according to their preconceived notions of physical laws, rarely attempting to see what does actually happen. Galileo's mind worked in a very different way, and refused to bind or blind itself in such a manner, so he promptly questioned what appeared to be doubtful statements and did not hesitate to contradict if he felt he had a clear case against them. He soon gained such notoriety in this way that he was nicknamed the Wrangler by his fellow-students, and heartily disliked by the professors, who were not only sticklers for tradition, but probably found it less troublesome to rely on memory than on intelligence.

In what we should call his Freshman's term Galileo made his first notable discovery. In the Cathedral of Pisa he noticed a lamp swinging suspended from the roof, and remarked that as the swings died away they did not seem to get slower or quicker. He tested this by counting his pulse-beats, having no other means at hand for measuring time, and found the time of swing to be practically constant. He at once saw that the rule would work both ways, and that a swinging weight would provide a check on the regularity of the pulse, a matter of 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 expense of his son's university career, which he decided to curtail; so that Galileo gave up any idea of the medical profession and left Pisa without completing his full course.

We thus find Galileo back in Florence at the age of twenty-one, determined to devote himself entirely to mathematics and physics, with the aid of Ricci whenever the Court was in residence at Florence. Meeting with the works of Archimedes he conceived a profound admiration for that philosopher, and was dissatisfied with the vague accounts generally given of the solution of the celebrated problem always associated with the word "Eureka". This, it will be remembered, consisted in the detection of the presence of inferior metal in the Crown of Hiero, tyrant of Syracuse, without any injury to the crown, the weight of the crown being equal to that of the gold provided by Hiero. Archimedes found that the crown displaced more water than an equal weight of pure gold did, and calculated the extent of the goldsmith's fraud. Galileo set himself to consider how this calculation must have been performed, and constructed his Hydrostatic Balance for this purpose. This instrument, called "la Bilancetta," had some resemblance to a steelyard. Galileo also devoted himself to the determination of the centre of gravity in solids of different forms, and this work with the pulsilogia and bilancetta attracted the attention of the Marquis del Monte, who, being himself a competent mathematician, formed a just estimate of the young man's capabilities, and strongly recommended him to the Grand Duke of Tuscany, but without any immediate success.

The necessity of an income of some kind in default of medical fees, compelled Galileo to obtain pupils in mathematics and mechanics, and naturally he applied for every vacant mathematical professorship to be found. After failing to secure such an appointment at Bologna (1587), Padua (1588), Pisa (1588), and Florence (1588)—though the Pisa appointment was in the gift of the Grand Duke—he was on the point of going to the East in 1589 to "seek his fortune" in the company of a friend, when the Pisa professorship again fell vacant, and he secured the post with a salary of about five shillings a week. We cannot wonder at Vincenzio's poor opinion of mathematics as a means of livelihood, especially as the professor of medicine received more than thirty times as much. The position, however, was worth much more than its meagre official salary, as it naturally brought Galileo more pupils and probably raised his fees.