Galileo

I N 1582, whilst Francis Bacon was studying law at Gray's Inn, and secretly cherishing his great scheme for inaugurating a new system of thought—a new philosophy of science—which should place the human mind 'on a level with things and nature', a young Italian student named Galileo Galilei was poring over his medical books in the University of Pisa. His father, Vincenzo Galilei, though in poor circumstances, was of noble descent, and proud of the title of philosopher, to which his learning gave him a just claim, though his talents were chiefly exercised in the direction of music, in the theory and practice of which art he excelled. Galileo was the eldest of a family of three sons and three daughters, and when his father cast about to find an opening for him in life it was as an apprentice in the woollen trade that he first designed to place him. But young Galileo soon showed so much promise in the convent school to which he had been sent, that the idea of a business career was abandoned, and in November, 1581, Galileo entered Pisa University as a student of medicine.

At the university Galileo was placed under the tuition of Cesalpino, the celebrated botanist, who held the chair of medicine and whose researches with regard to the structure and action of the heart entitles him to rank as one of the forerunners of Harvey, the discoverer of the circulation. Galileo soon showed the material of which he was made. He gave the professors little peace, for he refused to accept for fact any statement that could not be demonstrated, or the truth of which he could not ferret out by his own inquiry. A spirit of contradiction was his most noticeable characteristic in the eyes of his instructors; but they mistook for such his earnest love of truth—a love which never forsook him, and which in after years made him doubt and question his own conclusions quite as much as he had done those of his masters. He studied for himself Aristotle and Plato, and the rest of the 'ancients', instead of blindly accepting their axioms as established truths, and he persevered in this course, even at the risk of offending those who presumed to know.

It was not long before this spirit of inquiry let to a practical result. Seated one day in the Cathedral of Pisa, at dusk, he observed the verger lighting the great bronze lamp which was suspended from the roof. When the numerous wicks had been ignited the verger left the lamp swinging to and fro, and Galileo watched its movements, at first idly, and then with growing interest. For an idea connected with the swinging lamp had entered his mind and he wanted to verify its truth. He noticed that the swings, whatever their range, were executed in equal times; in other words, though the momentum of the lamp slackened, and the distance traversed in each oscillation grew less, the time occupied in swinging from one point to another was exactly, or very nearly, the same. This discovery (it is known as the isochronism of the pendulum) he proceeded to turn to practical use by constructing a pendulum of proper length for measuring the speed and regularity of the pulse. The apparatus was extremely simple, consisting of a light weight attached to a thread, which in turn was affixed to a graduated scale, but it served its purpose and it was probably the first instrument ever devised for precise observation of phenomena in a living organism. Fifty years later Galileo applied the principle of the pendulum to the construction of astronomical clocks.

Of mathematics Galileo was as yet quite ignorant, but in the summer of 1586 the Tuscan Grand-Ducal Court visited Pisa, and amongst the suite was Ostilio Ricci, a distinguished mathematician and a friend of Galileo's family. Chance made Galileo a listener to a lesson in Euclid which was being given by Ricci to the pages of the court. The student listened like one entranced; in a flash the light broke in upon his mind—here was the key which would unlock the secrets of nature, and enable him to penetrate those mysteries which he had pondered and puzzled over so long! Scarcely waiting for the end of the lesson, Galileo flung himself into Ricci's presence and begged him to teach him more. Ricci, pleased with the student's enthusiasm for his own subject, readily consented, and Galileo joyfully entered upon his new study.

In a short time he had mastered the whole of Euclid, and then passed on to Archimedes, concentrating his attention upon that portion of the great geometer's researches which deals with the lever and the specific gravity of floating bodies. As a result of his studies he constructed a balance for solving in a simpler and more exact manner the problem with King Hiero had set to Archimedes with respect to the crown of gold alloyed with silver. How Archimedes acquitted himself of his task may be briefly told as follows. Hiero had given to a goldsmith a certain weight of gold to be made into a crown. When the work was finished he suspected that the gold had been alloyed with some baser metal, and he applied to Archimedes in the hope that the latter would be enabled to detect the supposed imposture. The weight of the crown being correct, the problem was to measure its bulk; for silver being, weight for weight, of greater bulk than gold, any alloy of the former, in place of an equal weight of the latter, necessarily increase the bulk of the crown. To measure the bulk, however, was difficult without melting the crown into a regular figure. Archimedes on stepping into his bath one day observed that a quantity of water of the same bulk as his body must flow over before he could immerse himself, and this suggested a plan to his mind. He procured two masses of metal each of equal weight with the crown—one of gold and the other of silver—and having filled a vessel accurately with water he plunged into it the silver and marked the exact quantity of water that overflowed. He then treated the gold in the same manner, and observed that a less quantity of water overflowed than before. He next plunged the crown into the same vessel full of water, and observed that it displaced more of the fluid than the gold had done, and less than the silver, from which he inferred that the crown was neither pure gold nor pure silver, but a mixture of both.

Galileo's balance secured him the interest and patronage of the Marchese Guidobaldo of Pesaro, who was distinguished for his mathematical acquirements, and at whose instance Galileo in 1588 wrote an essay on the Centre of Gravity in Solids, which was the means of making his name known throughout Italy. The interest of the Marchese did not stop here, for in the following year he used his influence to obtain for Galileo the post of mathematical lecturer at the university. As for Galileo himself, the smallness of the salary was of less moment than the fact that the necessity of eking it out by private teaching restricted his leisure for independent research. For he had now some important work to carry out.

He had set himself no less formidable a task than that of disproving the teaching which passed under the name of Aristotle, of the falsity of which he had convinced himself by his inquiries. It was 'his first crusade against the decrepit philosophy of his time, in which Aristotle's conjectures had been petrified into a creed, while of the open mind and patient observation of the great master not a trace was left'.

Galileo's first trial of strength with the university professors was connected with his researches into the laws of motion as illustrated by falling bodies. It was an accepted axiom of Aristotle that the speed of falling bodies was regulated by their respective weights: this, a stone weighing two pounds would fall twice as quick as one weighing only a single pound, and so on. No one seems to have questioned the correctness of this rule, until Galileo gave it his denial. He declared that weight had nothing to do with the matter, and that it was the resistance of the air which determined the rate of speed of a body falling through it; if, therefore, two bodies of unequal weight could overcome the resistance to the same extent they would reach the ground at the same moment. As Galileo's statement was flouted by the body of professors, he determined to put it to a public test. So he invited the whole University to witness the experiment which he was about to perform from the Leaning Tower. On the morning of the day fixed Galileo, in the presence of the assembled University and townsfolk, mounted to the top of the tower, carrying with him two iron balls, one weighing one hundred pounds and the other weighing one pound. Balancing the balls carefully on the edge of the parapet, he rolled them over together; they were seen to fall evenly, and the next instant, with a loud clang, they struck the ground together. The old tradition was false, and modern science, in the person of the young discoverer, had vindicated her position.

In 1591 Galileo resigned his post and went to Florence.

In the following year, through the influence of his first patron, Guidobaldo, he was appointed professor of mathematics at Padua University, the appointment being for six years, and the salary 180 florins. The death of his father just before this event, made it necessary for Galileo to contribute towards the support of the family, so that once more he was compelled to resort to private teaching to increase his means. His fame as a lecturer spread rapidly; the lecture hall, which was capable of seating two thousand persons, was crowded with students, including many strangers from every part of Europe, who listened with delight to Galileo's brilliant descriptions of his discoveries and to his suggestions for researches in various branches of physical science.

On the completion of the first period of his engagement Galileo was re-elected for a further term of six years, with an increased salary of 320 florins; at this time his reputation extended to all the principal seats of learning in Europe, and his lectures were attended by members of the reigning royal families who visited Italy.

We now pass to Galileo's work in astronomy; and here it is necessary to say a few words regarding the opinions held at that time on the subject of the structure of the universe and the movement of the heavenly bodies. The system of astronomy then taught was that founded by (or to speak more correctly, ascribed to) Ptolemy, who flourished 130-160 A.D. In reality the system was founded upon the researches of still earlier philosophers, chief amongst whom is to be reckoned Hipparchus (about 150 B.C.), to whose observations and discoveries Ptolemy owed a great part of the 'immense reputation enjoyed by him through the times of Arabian and mediaeval astronomy'. It would take too long to describe the Ptolemaic system as it was accepted and taught under the sanction of the Church of Rome in Galileo's time; but so far as the system concerned the movements of the heavenly bodies and their relation to the earth, it may suffice to say that the belief was that the sun and the planets revolved in regular circles round the earth as a centre.

In conformity with the custom of the day Galileo taught the Ptolemaic system to his pupils; but he had for some time secretly become a convert to the views of Copernicus, and acute observer and deep reasoner in astronomical science, whose book, De Revolutionibus Orbium Cælestium, containing the results of his life-work, was published in 1543, the year of his death. Copernicus (who was himself a canon of the Church) in a dedicatory epistle to the Pope Paul III, had modestly disclaimed any intention of opposing his theories to the version of astronomy sanctioned by the Holy Office, and by this means had secured for his book the toleration, and even the approval, of the Church. He had never thrust his opinions forward, and it was only with great reluctance that he consented to their publication when on his deathbed. Yet the far-reaching importance and significance of the views thus modestly advanced by Copernicus were apparent to Galileo, and to others beside, though they were, for obvious reasons, not held openly or taught in the schools.

We will now consider, briefly, what these views implied. Copernicus, impressed by the complexity of the Ptolemaic system, sought to simplify it by an hypothesis to the effect that the sun, and not the earth was the centre of the universe, and that the earth and the planets revolved round the sun. He did not arrive at this momentous conclusion (it was indeed a discovery though he put it forward as a mere hypothesis) without numberless observations, undertaken with poor instruments and extending over many years, and he supported it by calculations worked out with marvellous patience and exactitude. To say that the views advanced by Copernicus were momentous, is to convey only a faint impression of their bearing upon the scientific thought and belief of the age. If the idea of the sun as the central point in the universe were to be accepted, it meant that the teaching with regard to the importance of the earth relatively to the other heavenly bodies would now have to be abandoned. Instead, the earth must be numbered in importance only with the planets (possibly to be exceeded in size by one or more of those bodies), whilst preconceived notions of the sun, planets, and stars being attendant luminaries of the earth would be no longer tenable. Moreover, though the idea of the solid earth revolving in and travelling through space has long been familiar to us, the advancement of such an idea in the state of knowledge which prevailed in the sixteenth century must have been so startling as to tax the credulity of all but the deepest thinkers of the time. Nor was the shock to religious thought and belief any less great; for if the idea of the earth as the one fixed and central figure in the universe were to be given up, what was man's place in the scheme of creation, or where lay his future hopes? Or, again, how were the doctrines of the Church to be maintained? So startling an innovation—so complete a revolution of current ideas and beliefs—could not have been tolerated by the Church had it been in opposition to the received doctrines. As it was, however, Copernicus's views were clothed in modest dress, and buried in a learned treatise such as few were likely to read and fewer still to understand; and 'so long as the new doctrine was confined to the learned the Church did not care to interfere with it'.

Among the astronomers of the day who welcomed the new system with enthusiasm was the German, Kepler, of whom it must be said that, in spite of poverty, ill-health, and misfortune—all of which pursued him relentlessly—he was destined by his discoveries to shed a lustre on the science to which he devoted his life. It is to Kepler's untiring energy and genius (aided, as he undoubtedly was, by his association with that prince of observers, Tycho Brahe, whose work he continued after Tycho's death) that we owe our knowledge of the laws governing the movements of the planets. To mention the chief of those laws—that the planets move in ellipses, instead of circles—is to indicate the point of discovery at which the new astronomy (as distinguished from the ancient order of circular motion) took its rise.

Galileo seems to have made the acquaintance of Kepler in 1597, when the latter sent him a copy of his work Mysterium Cosmographicum. In a letter acknowledging the gift, Galileo, after deploring the fact that the lovers of truth were so few in number, goes on: 'Many years ago I became a convert to the opinions of Copernicus, and by that theory have succeeded in fully explaining many phenomena, which on the contrary hypothesis are altogether inexplicable. I have drawn up many arguments and confutations of the opposite opinions, which, however, I have not hitherto dared to publish, for fear of sharing the fate of our master, Copernicus, who, although he has earned immortal fame with some, yet with very many (so great is the number of fools) has become an object of ridicule and scorn.'

One of the axioms of Aristotle was the 'incorruptibility of the heavens': the universe was incapable of either change or decay; it was finite and perfect; nothing could be added to it and nothing taken away from it. There were seven planets, corresponding to the number of days in the week, viz. Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn; the various constellations were known, and the number of stars contained in each was fixed and certain. The sudden appearance of a new star in the constellation Serpentarius, in the month of September, 1604, therefore naturally excited much interest amongst the astronomers. Kepler observed it, and Galileo made it the subject of a course of three lectures delivered to great audiences, to whom he took occasion to administer a rebuke for taking so deep an interest in a phenomenon of a temporary nature, whilst they showed indifference towards the permanent wonders that surrounded them. His attach upon the Aristotelians, whom he did not spare in wit or sarcasm, was bitterly resented, and a controversy arose in which Galileo was induced to throw aside his reserve and boldly declare himself an upholder and defender of the Copernican theory.

But Galileo was soon to weild against his challengers a weapon more powerful than argument, however forcible or well founded, more potent than satire, however pointed—a weapon which was destined in his hands to carry conviction to the minds of many doubters and to inflict defeat and dismay upon the enemies of truth. A dangerous weapon, too, when all is said; for it laid him who used it under the danger of the law which had no part or interest in the search for truth and no scruple in subjecting those who transgressed its doctrines to the penalties of imprisonment, torture, and death.

This 'weapon' was the Telescope—as yet unknown to science and in its beginnings a mere toy. In June, 1609, a rumour reached Venice and found its way to the ears of Galileo, that a Dutchman, named Johannes Lippershey, an optician of Middleburg, had in the previous year petitioned the States-General of the Low Countries for the exclusive rights in manufacture of 'an instrument for increasing the apparent size of remote objects'. This rumour set Galileo thinking, and the results of his cogitations may best be told in his own words. In a letter to his brother-in-law, Landucci, on August 29, 1609, he says: 'I write now because I have a piece of news for you, though whether you will be glad or sorry to hear it I cannot say, for I have now no hope of returning to my own country, though the occurrence which has destroyed that hope has had results both useful and honourable. You must know, then, that about two months ago there was a report spread here that in Flanders someone had presented to Count Maurice (of Nassau) a glass [occhiale, eye-glass; spectacles in the plural], manufactured in such a way as to make distant objects appear very near, so that a man at the distance of two miles could be clearly seen. This seemed to me so marvellous that I began to think about it; as it appeared to me to have a foundation in the science of perspective, I set about thinking how to make it, and at length I found out, and have succeeded so well that the one I have made is far superior to the utch telescope. It was reported to Venice that I had made one, and a week since I was commanded to show it to His Serenity and to all the members of the Senate, to their infinite amazement.' The letter goes on to relate how Galileo took his telescope to the Senate to present it to the Doge as a gift, that the present was accepted, and that he was told that the Senate would elect him to the professorship for life, with a yearly stipend of one thousand florins. The election was carried out at once, and without a single dissentient voice.

'But the greatest marvel of all' (writes Galileo in a letter to a friend, describing his discoveries) 'is the discovery I have made of four new planets; I have observed their proper motions in relation to themselves and to each other, and wherein they differ from all other motions of the stars. And these new planets move round another very great star, in the same way as Venus and Mercury, and peradventure the other known planets, mover round the Sun.' He is here referring to his great discovery of the four satellites of Jupiter on the nights of the 7th to the 12th of January, 1910.

The whole University flocked to hear Galileo's lectures on the new satellites of Jupiter. Some were convinced, some only pretended to be convinced, and some (though these latter were a small minority) declared that even if they were forced to look through the telescope and see the satellites, they would not believe them to be in the sky—'because the heavens were unchangeable.' The force of this argument is obvious; the satellites were not there before Galileo saw them.

The Senate had expressed their honourable sense of Galileo's services to astronomy by conferring upon him a life professorship with a salary of one thousand florins; but about the same time he had received an invitation from the reigning Grand Duke, Cosmo II (who had been one of Galileo's pupils) to come to Florence, and take up his abode at the Court. As the salary offered was equal to that fixed by the Senate, with the additional advantage of freedom from teaching, Galileo decided to accept the offer, and in July, 1610, he left Padua for Florence, where he was established as Philosopher and Mathematician Extraordinary at the Grand Ducal Court. We need not question the motives which induced Galileo to take this step; he had passed eighteen years of active work at Padua, and he ardently desired rest and leisure for carrying out the great ideas which he had formed in his mind. But in thus abruptly severing his connection with the University which had been the scene of his recent triumphs he acted in a manner that was hardly consistent with a sense of what was due to those who had honoured his genius. And as events showed, the step was a disastrous one, for 'from that time till his death he never knew peace'.

As yet, however, there were no signs of the coming trouble, and Galileo found ample opportunity for continuing his telescopic observations.

In 1611 he visited Rome for the first time, and was received with the respect and distinction which his talents and reputation had ensured for him. He took with him his best telescope and exhibited it in the Quirinal Garden to numbers of admiring friends and disciples, who were allowed to see the sun-spots, the mountains of the moon, and the other marvels connected with Galileo's discoveries. He discoursed freely on these subjects, and made no secret of his intention to devote the rest of his life to the establishment of the Copernican doctrine. Galileo's progress, in fact, had been marked by a fatal facility in the art of making enemies. His successes and discoveries provoked hostility, not so much by rason of the envy they aroused as by the use he made of them to enforce, in language the reverse of conciliatory, the truths which he upheld. Ultimately, on February 24, 1616, the Holy Office issued its decree, condemning the propositions of the sun's fixity and the earth's diurnal motion as heretical, and ordering that Galileo should be admonished by Cardinal Bellarmin not thenceforward to 'hold, teach, or defend' the condemned doctrine. The admonition was given, and Galileo promised obedience; for seven years he remained silent, living in studious retirement partly at his house in Florence and partly in his villa at Arcetri close to the town. Except for occasional attacks of illness (for he was now grown old and rheumatic) his life was one of quiet happiness, the happier by reason of his constant intercourse with his two daughters, who were nuns at the neighbouring convent of St. Matthew. One of these daughters, known as Sister Maria Celeste, was specially beloved by the old man for her gentle, affectionate disposition, as well as for her striking intellectual gifts.

In 1630 Galileo set himself to produce his famous Dialogues on the Two Systems. The manuscript was finished in 1630, but it was not until two years later (and after much difficulty) that leave was obtained to print it at Florence. The book spread rapidly though Europe, and was everywhere received with applause. Of the Dialogues  and the plan on which they are composed, Miss Agnes Clerke writes: 'It would be difficult to find in any language a book in which animation and elegance of style are so happily combined with strength and clearness of scientific exposition. Three interlocutors, named respectively Salviati, Sagredo, and Simplicio, take part in the four dialogues of which the work is composed. The first-named expounds the views of the author; the second is an eager and intelligent listener; the third represents a well-meaning but obtuse Peripatetic, whom the others treat at times with undisguised contempt. Salviati and Sagredo took their names from two of Galileo's early friends, the former a learned Florentine, the latter a distinguished Venetian gentleman; Simplicio ostensibly derived his name from the Sicilian commentator of Aristotle, but the choice was doubtless instigated by a sarcastic regard to the double meaning of the word. There were not wanting those who insinuated that Galileo intended to depict the Pope himself in the guise of the simpleton of the party; and the charge, though preposterous in itself, was supported by certain imprudences of expression, which Urban was not permitted to ignore.

The effects of the publication were instantaneous. The sale of the book was prohibited, and Galileo was summoned to Rome.

In vain his friends (including the Tuscan ambassador) interceded in his behalf, pleading his age, his ill-health, the season of the year, and the miseries of the quarantine existing on account of the plague. The Pope (Urban VIII, who as Cardinal Barbarini had been his friend), acting, it is believed, under extreme pressure, was inexorable. Worn out with fatigue and anxiety, Galileo arrived in Rome on February 14, and was lodged in the palace of the Tuscan ambassador.

In April he was removed to the Holy Office, where he was shown every consideration, and where his first examination took place. After a few days' confinement, however, his health broke down, and he was once more allowed to take up his quarters at the ambassador's house, leave being obtained for him to drive out in the public gardens in a half-closed carriage. His defence had in the meantime been prepared; but the difficulty of finding any plausible justification of his offence appeared insurmountable, and the artifice to which he resorted of trying to show that the decree of 1616 did not specifically enjoin him not to teach in any manner the condemned doctrine, was held to be an aggravation of his crime.

From February to June he was kept in a state of suspense as to his ultimate fate, but early in the morning of June 21 Galileo was conducted to the court, and the doors closed behind him. Exactly what happened during his examination is not known, for no outsider was present, and Galileo himself was bound by the laws of secrecy which guarded the proceedings of the Inquisition. It is, however, certain that Galileo was not subjected to the rack. The ordeal comprised five stages, of which the threat of the torture (twice uttered) formed the first and second; the entry of the torture chamber and the showing of the instruments, the third; while the fourth and fifth stages were the preparation for and actual subjection to the rack. But the last stage was never reached. Galileo gave way and promised to recant, and he was removed to a cell while the court drew up his special form of perjury.

On the 22nd he was clothed in the dress of a penitent and taken to the Convent of Minerva, where the Inquisition was assembled to pass judgement. The sentence was that he should adjure and curse the heresies which he had cherished; that he should be imprisoned during the pleasure of the Inquisition; and that he should recite once a week the seven Penitential Psalms. The judgement having been read, Galileo 'fell upon his knees before the assembled Cardinal; and laying his hands upon the Holy Evangelists, he invoked the Divine aid in abjuring and detesting, and vowing never again to teach the doctrine of the earth's motion, and of the sun's stability. He pledged himself that he would never more, either in words or in writing, propagate such heresies; and he swore that he would fulfil and observe the penances which had been inflicted upon him. At the conclusion of this ceremony, in which he recited his abjuration, word for word, and then signed it, he was conveyed, in conformity with his sentence, to the prison of the Inquisition.'

Broken both in spirit and in health, he was allowed, after a short imprisonment in Rome, to go to Siena, where he was lodged in the palace of the Archbishop Piccolomini. The Archbishop was one of Galileo's best friends, and though confined to the grounds of the palace no other restrictions were imosed upon him. He was cheered and consoled by a letter from Maria, telling him how greatly she rejoiced at his escape and how, to relieve him of a part of his burden, she had recited the Penitential Psalms for him every week.

After spending six months beneath the roof of his friend Galileo obtained permission to return to his villa at Arcetri under similar restrictions. But amidst the rejoicings at his return a cruel blow fell upon him; his beloved daughter, 'whose loving care had been his mainstay for years,' fell ill, and in six days passed away. Galileo was overwhelmed with grief, and for long remained in a state of melancholy from which nothing could rouse him. Then, as he slowly recovered, he became desirous of changing his residence from Arcetri to Florence. But the permission he sought was sternly refused; he must remain at Arcetri; he was to see no friends; and if he persisted in his requests he would be subjected to more stringent measures. For five years longer, therefore, he continued a semi-prisoner in his villa, and sought by diligent application to his studies to overcome the tedium of his confinement.

In 1636 he completed his Dialogues on the two Sciences of Mechanics and Motion. In this, which is considered to be his greatest work, he recapitulates the results of his early experiments and later mediations on the principles of mechanics. The Dialogues  were printed in Leyden in 1638, and 'excited admiration equal to and more lasting than that accorded to his astronomical treatises'. For astronomy he performed one more service—the discovery of the moon's libration (i.e., the periodical changes in the outlines of the moon's disc). Then his sight began to fail, and in a short time he became totally blind. This last calamity completed the sum of his misfortunes. 'Alas!' he writes to one at this time, 'your dear friend and servant has become totally and irreparably blind. These heavens, this universe, which by wonderful observation I had enlarged a thousand times beyond the belief of past ages, are henceforth shrunk into the narrow space which I myself occupy. So it pleases God; it shall, therefore, please me also.' 'The noblest eye,' said Gastelli, 'which nature ever made, is darkened.' Still, he was not to be turned aside from his work, and being allowed an amanuensis, he with the help of his pupils, Torricelli, and Viviani, completed several important papers of observations, amongst them one on the adaptation of the pendulum to measurement of time. Visitors were also allowed him, and amongst those who journeyed to Arcetri to pay their respects to the blind astronomer during these last years was John Milton, then a young man of twenty-nine, travelling in Italy. Galileo often complained that his head was too busy for his body; and in truth the body was to succumb before the active mind. At the end of 1641, whilst still full of plans for future work, he was attacked by fever, and after lingering for two months he died on January 8, 1642, in his 78th year.

His telescopic discoveries, though they make the strongest appeal to our imagination, do not comprise the best of even the most brilliant part of his work. Galileo's fame rests mainly on the fact that he was the first to demonstrate the true laws of Motion, and thus to lay the foundation of a Science of Mechanics. 'The problem of the heavens,' says Miss Clerke, 'is essentially a mechanical one; and without the mechanical conception of the dependence of motion upon force which Galileo familiarized to men's minds, that problem might have remained a sealed book even to the intelligence of Newton.' The firstfruits of the new system of investigation was his determination of the laws of falling bodies.

The best eulogium of Galileo, it has been said, consists in the fallacies which he exposed. And the secret of his power in combating and destroying the erroneous opinions which prevailed in his day regarding natural philosophy, was his reliance upon mathematical science. To quote his own words: 'Philosophy is written in the great book of the Universe which lies always open. But we must first understand the language and the character in which it is written. That language is mathematics. Its characters are triangles, circles, and other geometric figures, without which we cannot, humanly speaking, understand the words, and wander aimlessly through a dark labyrinth.'