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148 weight; but if so he would probably have said that it would fall ten times as far, or else that it would require ten times as long to fall the same distance. To actually try the experiment, to vary its conditions, so as to remove as many accidental causes of error as possible, to increase in some way the time of the fall so as to enable it to be measured with more accuracy, these ideas, put into practice by Galilei, were entirely foreign to the prevailing habits of scientific thought, and were indeed regarded by most of his colleagues as undesirable if not dangerous innovations. A few simple experiments were enough to prove the complete falsity of the current beliefs in this matter, and to establish that in general bodies of different weights fell nearly the same distance in the same time, the difference being not more than could reasonably be ascribed to the resistance offered by the air.

These and other results were embodied in a tract, which, like most of Galilei's earlier writings, was only circulated in manuscript, the substance of it being first printed in the great treatise on mechanics which he published towards the end of his life (§ 133).

These innovations, coupled with the slight respect that he was in the habit of paying to those who differed from him, evidently made Galilei far from popular with his colleagues at Pisa, and either on this account, or on account of domestic troubles consequent on the death of his father (1591), he resigned his professorship shortly before the expiration of his term of office, and returned to his mother's home at Florence.

117. After a few months spent at Florence he was appointed, by the influence of a Venetian friend, to a professorship of mathematics at Padua, which was then in the territory of the Venetian republic (1592). The appointment was in the first instance for a period of six years, and the salary much larger than at Pisa. During the first few years of Galilei's career at Padua his activity seems to have been very great and very varied; in addition to giving his regular lectures, to audiences which rapidly increased, he wrote tracts, for the most part not printed at the time, on astronomy, on mechanics, and on fortification, and invented a variety of scientific instruments.