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Galileo was born in the year 1564, so we may picture Galileo as a schoolboy in Italy while Queen Elizabeth and Mary Queen of Scots were reigning in England and Scotland.
 So soon as Galileo had completed his elementary education, he was sent to a monastery to receive a thorough literary education at the hands of the monks. He came very near accepting holy orders himself, but his father had other plans for him. His first intention had been to apprentice Galileo to the wool-merchant business, so that he might be of financial assistance to the family. But as Galileo showed exceptional talents, his father decided that the youth should go to the University and study Medicine.
It is in his student days that we see the first signs of Galileo's independence of thought. He had the audacity to question some of the time-honoured doctrines of the ancient philosopher Aristotle. It is difficult for us to realise fully the courage that was required to take such an unusual step. To do so we must keep in mind that in these days a man did not attempt to prove any theory by argument or experiment; it was deemed sufficient if he could give chapter and verse in Aristotle. Galileo's questioning spirit earned for him the title of "The Wrangler," and it goes without saying that this title carried with it no such honour as it did until recently in one of the great English Universities. It is interesting to note that the modern title has been derived from the fact that in the early days of these examinations for mathematical degrees there was a public disputation to test the powers of the candidate, and the successful student was named "The Wrangler."
By the time Galileo had reached the age of twenty years he was an excellent Latin and Greek scholar, and an accomplished artist and musician; still, with all these accomplishments he was very unpopular because of his  questioning spirit. There is no doubt that the lad acquired this spirit of independent thought from his father. There occurs this passage in one of his father's books: "It appears to me that they who in proof of any assertion rely simply on the weight of authority, without adducing any argument in support of it, act very absurdly."
One of the most interesting incidents in Galileo's student days was the far-reaching discovery which he made while sitting in the Cathedral at Pisa. It came about in a very simple way. His attention happened to be attracted by the swinging motion of a large hanging lamp, which the verger had set in motion in the act of lighting it. The lamp had probably been pulled to one side and then let go, for it continued to swing to and fro for quite a long time. Of course, its to-and-fro travel would become shorter and shorter until finally it would come to rest. It was a very common, everyday occurrence to which most people would pay no attention. But this young student noticed that the lamp seemed to take just as long to make one of its shorter swings as it had done to make a longer swing. Indeed, he had been impressed, from his first notice of it, with the apparent rhythmic regularity of the motion. There were, of course, no watches in these days, but the medical student, by feeling the regular beat of his own pulse, was able to determine that his surmise was correct.
Galileo saw that the pendulum provided a regular measure of time. In his day there were some very rough and ready timekeepers, but it does not seem to have occurred to him that his pendulum would be of any service in that direction, although he did make the sup-  gestion half a century later. What appealed to him was the usefulness of such a good timekeeper in enabling a physician to check the pulses of his patients. And so Galileo invented what he called a "pulsilogia." It was simply a length of cord with a weight, so arranged that he could alter the length of the cord conveniently.
The physician could adjust the length of cord so that the pendulum would count out the normal rate of a man's pulse, say about seventy beats per minute. Then it was an easy matter to alter the length of the cord to bring the pendulum into time with the patient's pulse, and it would be apparent whether it was too rapid or too slow. Any irregularity in the beat could be detected also. The axle, which wound up or unwound the cord, carried an indicator which pointed to figures marked on a dial, and in this way the physician could see at a glance the rate of the patient's heart-beats. The physicians were delighted with this invention of the medical student and the pulsilogia soon came into general use.
While Galileo was studying medicine he became interested in Mathematics. His father was well versed in this subject, but at that time the Science was looked down upon by the Italians as a thing of very little value, and Galileo's father purposely kept the subject away from his son, as it did not seem to be a necessary subject for his profession.
There is an interesting story told of how Galileo was attracted at first to Mathematics. A friend of his father was tutor to the pages of the Grand Duke's Court, and while the Court of Tuscany was stationed at Pisa, Galileo went to see this friend of the family. It is said that on one occasion, as Galileo reached the half-opened door of  the room in which this great mathematician taught, he overheard some problem of Euclid being explained. Galileo listened to the exposition of this subject, which, although it was "as old as the hills," was entirely new to him. It is said that he not only remained in hiding during this lecture, but that he returned each day to hear more of this fascinating subject. Whether this tradition is well founded on fact or not, it is true that Galileo became so fascinated with Mathematics that he neglected his medical studies, and applied to Ricci, this friend of his father, for more instruction. The great mathematician was delighted with the boy's aptitude for the subject, but when Galileo's father found that the medical studies were being neglected, he asked his friend Ricci to discontinue the lessons. But Galileo was quite able to continue the study on his own account. Indeed, he made such rapid progress that his father could not do otherwise than acknowledge that the youth was a born mathematician. And so it was agreed that his medical studies could be abandoned.
I think this concession says a good deal for the father's unselfishness. He had hoped that as a physician Galileo would be of financial assistance to the family. On the other hand, mathematicians were so poorly paid that the professor in Pisa University earned less in a day than any ordinary tradesman of to-day earns in a single hour. Indeed, the salary of the Professor of Mathematics was almost the same as any office boy gets in his first year of business.
With all his great intellect, which had been made evident already by the production of many brilliant essays, Galileo had a very hard fight to gain the vacant  Chair of Mathematics in Pisa, with its lordly salary of thirteen pounds per annum. The disregard in which Mathematics was held in Italy is emphasised when we compare this salary with that obtained by professors of other subjects in the same University; these were counted in hundreds of pounds.
But how would Galileo be received at the University, where he had been nicknamed "The Wrangler"? The professors were all hostile to him, with the exception of the professor of physiology, who had been appointed since Galileo's student days.
We know that as a student Galileo had been bold enough to argue against some of the theories of the great Aristotle. Now as a professor he was still bolder, offering to disprove one of Aristotle's "truths" by actual experiment. The great Philosopher had said that the time taken by an object to fall was dependent upon the weight of the object. A ten-pound weight would fall in one-tenth the time of a one-pound weight. Galileo had argued the matter and had come to a different conclusion. If two single pound weights each travel at the same rate and fall side by side, will they travel twice as fast if they are merely tied together? His argument was longer than this simple statement, but it was on lines such as these.
So sure was Galileo of his many arguments that he invited the professors and students to accompany him to the great leaning tower, from the top of which he could conveniently let two different weights try an honest race. Galileo mounted the great tower with his weights, which some writers state to have been a one-hundred-pound shot and a one-pound shot, but Galileo was no Samson to  carry a hundredweight up to the top of an eight-story building. It is more probable that some of the older writers, who mention a ten-pound and a one-pound shot, are correct. If one weight should travel even in one-tenth of the time of the other, the difference in their times of reaching the ground from such a height would be quite apparent.
I wonder how these assembled Aristotelians felt as Galileo climbed the tower to perform this experimental test. Probably every one of them was prepared to have a good laugh at the expense of the youthful professor who had so far forgotten himself as to dare to question the truths of the greatest of all philosophers; an authority of nearly two thousand years' standing. Possibly some of the older men would be feeling glad to have an opportunity of putting an end to what they considered to be very near to blasphemy.
Picture this crowd of learned professors and students, all positive what would happen. The heavy weight would come flying down, leaving the smaller weight to follow at a respectful and ever-increasing distance. That was bound to happen because the great Aristotle had declared it to be so, long, long ago. But the thoughts passing through the mind of Galileo would be different. He knew what would happen because his reason told him. No doubt there would be a referee at the top of the tower to see a fair start made. The race began and the suspense was broken by the simultaneous thud of the two weights upon the ground. It is difficult to realise what must have been the feelings of the assembled crowd. Some writers say,."Yet the Aristotelians, who with their own eyes saw the unequal weights strike the ground at the same in-  stant, ascribed the effect to some unknown cause, and preferred the decision of their master to that of Nature herself." I doubt if they all did really disbelieve their own eyes. Secretly they must have felt that their master's logic had received a shock. Doubtless they would try all they could to invent reasons why in this particular case the two weights did happen to fall together. Had they honestly disbelieved their own eyes, they would surely have set about making other experiments to support their views. But it is very difficult to give up ideas that have persisted for centuries. Besides, if they should acknowledge frankly even to themselves that Galileo was right, how many more of Aristotle's great doctrines might be false also? Their best plan seemed to be to try and silence this upstart. And so poor Galileo was hissed at his public lectures. The people would feel that they could take this step with safety, for it was well known that Galileo had got into the Grand Duke's bad books.
The Grand Duke had asked Galileo to tell him what he thought of an invention which one of His Royal Highness's sons had made. The Prince had made a model of a large hydraulic machine with which he declared he could dredge the harbour of Leghorn. Galileo reported that the invention was useless, and this decision was proved to be correct when an actual machine was tried. But the Prince was very angry with Galileo, and every one seemed so much against him that the young professor felt compelled to resign his Chair.
Through the good influence of a friend he obtained the Chair of Mathematics at Padua University, at a salary of thirty-two pounds, or two and a half times as much as he had at Pisa. But Galileo needed all this and more, for  by this time his father had died, and the responsibilities of the family rested upon him as the eldest son. He did not improve matters by promising dowries—which were the necessary accompaniments of marriage in those days—for his two sisters.
It is unnecessary to go into all the detail of Galileo's financial troubles. It is of more interest to find that he augmented his small salary by giving private lessons, keeping student boarders, and by becoming what we should now describe as a consulting engineer. Then he opened a workshop in his house for the manufacture of his mathematical instruments. He employed a workman, who came to reside in his house, bringing with him his wife and child. Galileo had to maintain them and pay a small salary over and above.
Our chief thoughts of Galileo centre round the very prominent support he gave to the theory of Copernicus that the Earth goes round the Sun. Italy still held to the theory of Ptolemy in which the Earth was the immovable centre of the Universe. In his lectures Galileo still taught this older theory, but in a letter to Kepler he writes: "Many years ago I became a convert to the opinions of Copernicus." Then he goes on to explain that he prefers to keep silent on the subject, "so great is the number of fools."
Galileo's fame as a mathematician had spread, and many foreign princes and other students came to Padua to be present at his lectures. Among these was an English student, Harvey, who afterwards became famous on account of his discovery of the circulation of the blood.
But if Galileo was so prudent as to refrain from teaching  the Copernican theory, how did he ever get into trouble with the Church of Rome? The first step that took him towards a public announcement was his invention of the telescope, and that in turn came about in the following fashion.
An apprentice to a Dutch spectacle-maker had fitted up a curious toy in this optician's shop. The toy consisted of two spectacle lenses so arranged that the weather-cock on a distant church could be seen much nearer and upside down. News of this scientific toy reached Galileo, who seems to have perceived at once that such an arrangement might be of use in spying out the distant heavenly bodies. Although Galileo did not foresee the tremendous advance which this invention would bring about, he is said to have sat up all night thinking out the matter and constructing the first real telescope. But it is the inventor more than the invention that interests us at present.
Galileo tells us that when he showed his invention in Venice, even old men climbed the highest church towers to see ships through his spy-glass. These ships seen approaching the harbour could not be seen with the unaided vision for two hours later.
When Galileo took the instrument to Padua University, he found the Senate so interested in it that he presented the telescope to them. They appreciated this gift so much that they not only raised Galileo's salary to two hundred and twenty pounds, but appointed him professor for the whole of his lifetime. Perhaps it should be remarked that Galileo's salary was not sprung from thirty-two pounds to two hundred and twenty; it had been increased several times, and at the time of his presentation  of the telescope it had reached one hundred and fifteen pounds.
In the following chapter we shall see how Galileo's telescope set him on that stormy road which led him to the Inquisition.