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Rh 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.