Popular Science Monthly/Volume 66/January 1905/Galileo I

by Edward Singleton Holden

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GALILEO.

By Dr. EDWARD S. HOLDEN,

U. S. MILITARY ACADEMY, WEST POINT, N. Y.

I.

When the position of a heavenly body changes with such extreme slowness as to leave astronomers undecided as to the change even, and still more as to the direction of the change, it is their custom to compare two observations made at a great interval of time. If the doubt still exists, they affirm with certainty that the position they have measured is invariable, or nearly so, since it is subject to no regular and persistent alteration. Such a method applied to the history of the human mind leads to grave melancholy and discouragement. Men have been ignorant and blind at every epoch. Always we find the same ignorance, the same rash illusions, the same obstinate prejudices.

Toujours mêmes acteurs et même comédie.

Three centuries before our era, a philosopher, Cleanthes, demanded that Aristarchus should be brought to justice for his blasphemies in declaring the earth in motion, and the sun to be the fixed centre of the universe. Two thousand years later, the human understanding had not progressed. The desire of Cleanthes was realized, and Galileo was accused of blasphemy and impiety, in his turn. A tribunal dreaded by all condemned his writings, constrained him to denials disavowed by his conscience, and, judging him unworthy of a freedom that he had abused, deprived him of a part of it, and thought it an indulgence to have left him any liberty whatever.

But history is not to be judged in this way. Events in themselves are of small moment; the impression that events produce is the only revelation of the public consciousness. Never before has its generous aversion for intolerance burst forth so strongly as for the sufferings of Galileo. The story of his misfortunes, exaggerated like a pious legend, has confirmed the triumph of the truths for which he suffered, at the same time avenging him. The scandal of his condemnation will forever vex the pride of those who still wish to put down reason by force; and the just severity of opinion will preserve the unwelcome remembrance as an eternal reproach. But it is necessary to be frank: this great lesson did not cause any deep sorrows. The long life of Galileo, taken all in all, is one of the most peaceful and most enviable that the history of science records.

The foregoing paragraphs translated freely from the life of Galileo by M. Bertrand, perpetual secretary of the Paris Academy of Sciences, expresses so precisely the point of view of this article that I have quoted them in order to have, from the outset, the support of his great authority. And to them may be added the following extracts from the ‘History of the Inductive Sciences’ of Dr. Whewell, master of Trinity College, Cambridge. The words in brackets are my own.

The heliocentric doctrine has for a century been making its way into the minds of thoughtful men on the general ground of its simplicity and symmetry. Galileo appears to have thought that now, when these original recommendations of the system had been reenforced by his own discoveries and reasonings, it ought to be universally acknowledged as a truth and a reality. And when arguments against the fixity of the sun and the motion of the earth were adduced from scripture, he could not be satisfied without maintaining his favorite opinion to be conformable to scripture as well as to philosophy; and he was very eager in his attempts to obtain from authority a declaration to this effect. The ecclesiastical authorities were naturally averse to express themselves in favor of a novel opinion, startling to the common mind, and contrary to the most obvious meaning of the words of the Bible; and when they were compelled to pronounce, they decided against Galileo and his doctrines. He was accused before the Inquisition in 1615;. . . the result was a declaration of the Inquisition that the doctrine of the earth's motion [was] contrary to the sacred scripture. Galileo was prohibited from defending and teaching this doctrine in any manner, and promised obedience to this injunction [as will be shown later].

But in 1632 he published his Dialogues and in these he defended the heliocentric system by all the strongest arguments which its admirers used. Not only so, but he introduced into this dialogue a character under the name of Simplicius [supposed by contemporaries to have been intended to represent the Pope then reigning, which idea was fully accepted by the Pope himself, especially as the Pope's own words were attributed to Simplicius,] in whose mouth was put the defense of all the ancient dogmas and who was represented as defeated at all points of the discussion; and he prefixed to the dialogue a notice To the Discreet Reader, in which, in a view of transparent irony he assigned his reasons for the publication. . . . The result of this was that Galileo was condemned for his infraction of the injunction laid upon him in 1616; his dialogue was prohibited; he himself was commanded to abjure on his knees the doctrine he had taught; and this abjuration he performed.

. . . The general acceptance of the Copernican system was no longer a matter of doubt. Several persons in the highest positions including the Pope himself [not the Pope] looked upon the doctrine with favorable eyes; and had shown their interest in Galileo and his discoveries. They had tried to prevent his involving himself in trouble by [through] discussing the question on scriptural grounds. It is probable that his knowledge of those favorable dispositions towards himself and his opinions led him to suppose that the slightest color of professed submission to the church in his belief, would enable his arguments in favor of the system to pass unvisited; the notice [To the Discreet Reader] in which the irony is quite transparent and the sarcasm glaringly obvious, was deemed too flimsy a veil for the purpose of decency, and, indeed, must have aggravated the offence.

The foregoing extracts from the writings of authoritative historians of science place the chief events of Galileo's long life in what seems to be the true light. There is little doubt as to the events themselves—except in a single particular, which will be considered in what follows. Much controversy has raged over their interpretation. They must be considered in two regards: First, in respect of Galileo's private and personal experience; second, in respect of the lesson which that experience has taught to the world in general. The remark of Bertrand that has just been quoted is profoundly significant: events in themselves are small affairs; it is their effect on the public consciousness that remains and is permanent. Galileo's private life was essentially peaceful, as a whole even ‘enviable.’ To the world in general he is, on the other hand, the protomartyr. His trials have opened new roads for human thought, given liberty to science and philosophy, and were the occasion of a final delimitation of the provinces of the church and of philosophy. The modern attitude of mind may be said to take its date from him. It is in this that his greatest service to mankind consists. The astonishing discoveries that we owe to his genius are small matters in comparison.

In what follows the events of his life will be recited. Where there is doubt it will be pointed out. There is no space to discuss controverted points at length. Volumes have already been written on the history of his trial by the Inquisition; on the documents, genuine or fabricated, of this process; on the question whether or no he was put to the torture.^[1] To these volumes reference must be made, once for all, for the original documents and for a discussion of their authenticity. The object of the present chapter is, first, to tell the story of his life, second, and most important, to exhibit its effect upon his own and succeeding centuries. It will conduce to clearness if his private and personal life be separated in thought from his services to mankind in general; if the story of his experience be discriminated from the legend.

The popular legend in its crudest form declared that Galileo, a martyr of science, languished in the dungeons of the Inquisition; defended his doctrines boldly; was tortured; and under bodily torture recanted and abjured; saying, however, at the last, E pur si muove before he was again removed to his prison, where his eyes were blinded. If the legend had not taken on this crude shape it would, perhaps, have been less efficacious in the century immediately following his death. As it stands it is almost entirely devoid of truth. The real history is hardly less distressing, but the facts are utterly different.

Galileo was born at Pisa on February 18, 1564, of the noble family of the Bonajuti which since 1343 had been known as the Galilei. In 1445 a representative of the family was Gonfalonier of Florence, and no less than fifteen of its members had served in the Signoria. The father of Galileo, Vincenzio, was skilled in mathematics and especially in music, on which he wrote several treatises. He was poor and wished his brilliant son to adopt the lucrative profession of medicine. Galileo's early inclinations seem to have been to become a painter. The boy was educated at the monastery of Vallombrosa, where he learned Latin, some Greek, a little logic. He was an excellent pupil, but as his eyes were affected his father removed him and, at the age of seventeen (1581), sent him to study medicine at Pisa. He was already a clever musician, witty, eloquent, with a strong talent for painting, and had laid the foundations of a literary style which Italians estimate highly. In his later years Galileo knew the poems of Ariosto by heart. His general health was not good, but he was amiable, gay, versatile, fond of society and also very fond of a country life and of his vineyards and groves. He was considerate and liberal to his family, devoted to his children.^[2] His friends loved him ardently, and his enemies were equally constant in their dislike. The characteristics of his maturer life were in evidence throughout his youth also. His powers of observation were extraordinarily quick. He was a philosopher, also, from the first, and very expert in all mechanical matters.

Before the high altar of the cathedral at Pisa hangs a lamp,—a masterpiece of Maestro Possenti. Watching its swingings to and fro one day Galileo, then a student, observed that although the amplitude of the swings diminished the time of oscillation remained the same (1583). From this chance observation resulted the law: The time of oscillation of a pendulum is independent of the amplitude of its swings. If this be true (and it is true when the amplitudes are small), the pendulum can be used to measure, with precision, intervals of time. A hundred of its swings will always require the same time whenever the arc of swinging is not large. The first application of this discovery was the invention of a pendulum suited to measure pulse-beats. Towards the end of his life Galileo endeavored to construct a pendulum clock. He was engaged in this research at the time of his death, aided by his son Vincenzio, who carried on the work. A short pendulum beats more quickly than a long one. The law of the relation of length to period was also discovered by Galileo. It is: The lengths of pendulums are proportional to the squares of the times of oscillation. A pendulum beating seconds is four times as long as one beating half-seconds, therefore. These laws are the basis of horology. They were first fully utilized in the construction of clocks by Huyghens.

A lesson in geometry overheard by Galileo while a pupil excited his deepest interest. Euclid soon became his master and, from this day, his attention to medicine slackened, much to his father's regret. The salaries of mathematical professors were extremely small in those days, while the rewards of successful physicians were very much greater. Owing to his father's poverty, Galileo was withdrawn from the university in 1586, and returned to Florence. It is recorded that at the university he was known as a brilliant, though disputatious, pupil, and was nicknamed 'The Wrangler.' At Florence he lectured before the academy on the situation and dimensions of the Inferno of Dante—a question partly philosophical, partly scientific. It was at this time that he studied the works of Archimedes and wrote a little treatise on the hydrostatic balance. In 1587 he went to Rome and made the acquaintance of Clavius and other scientific men.

In 1588 he had the great good fortune to meet a generous patron, the Marchese Guidobaldo del Monte, and, in the same year, wrote at his request a treatise on the center of gravity of solid bodies. By his influence Galileo was appointed to be lecturer on mathematics in the University of Pisa (1589). His salary was only sixty scudi annually (about $65), and he was obliged to eke it out by giving private lessons. The salary of the professor of medicine was 2,000 scudi. During the years 1589 to 1591 he made those experiments on falling bodies which are the basis of the science of mechanics.

From the time of Archimedes (287-212 B. C.) till that of Leonardo da Vinci and Galileo there had been no progress in theoretical mechanics. Archimedes discovered the theory of the lever: 'Give me where I may stand and (with the lever) I will move the world.' His knowledge of practical mechanics was, no doubt, derived from his famous works of military engineering. All the great buildings of antiquity had been built by processes not unfamiliar to him. All the great basilicas of Europe and all the Gothic cathedrals with their nice system of balanced thrusts had also been erected before the time of Leonardo. The practical processes of engineering were highly developed, therefore, but as yet no one had formulated a theory. That Leonardo comprehended its fundamentals is abundantly shown by his note-books recently published. Every military engineer who had watched the flight of a projectile was aware that the received notions of mechanics would not explain its motions. No theory of the impact of such projectiles had even been proposed. A whole science was to be created. The doctrine of mechanical equilibrium is statics—and this science was founded by Archimedes. The doctrine of mechanical motion is dynamics—and nothing was done in this science till the time of Galileo. The theories of the lever, of the inclined plane and of the screw were familiar to Leonardo.^[3]

The ideas of Aristotle as to motion and rest were not physical, but metaphysical. An example will illustrate his mode of reasoning which satisfied the scientific world for something like two thousand years. When a stone is thrown from the hand why does it continue to move for a time, and why does it eventually come to rest? Where is the cause of motion—in the hand?—or in the stone? If in the hand, how can the stone continue to move after it has left the hand? If in the stone, why does it ever come to rest? Aristotle's answer is that ‘a motion is communicated to the air, the successive parts of which urge the stone onward; each portion of the air continues to act for some little time after it has been acted upon, and the motion ceases when it comes to a particle which can not act after it has been acted upon.’ The confusion of this explanation is complete.

The mechanical ideas of Aristotle and of his successors, as to falling bodies, are expressed in these words: ‘That body, is heavier than another which, in an equal bulk, moves downward quicker.’ Transforming the phrase, we may say, that if two bodies, A and B, are of equal bulk but of different weights, then the heavier body will fall the quicker; or, again, if A weighs ten pounds and B one pound, A will fall faster than B. The Aristotelians of Galileo's time further maintained that A would fall exactly ten times faster than B. Galileo's experiments proved that they fell in precisely the same time. Sixteen hundred years earlier Lucretius had come near to the same truth: “For whenever bodies fall through water and thin air they must quicken their descents in proportion to their weights, because the body of water and subtle nature of air can not retard everything to an equal degree; on the other hand, empty void can not offer resistance to anything in any direction at any time, but must continually give way; and for this reason all things must be moved and borne along with equal velocity, though of unequal weights, through the unresisting void.”

While Kepler was determining the empirical laws according to which the planets move in their orbits, Galileo was laying the foundations of the science of mechanics by which, eventually, Newton was to explain why they so move. The foundations of mechanics rest on experiments made by Galileo, at Pisa, on the laws of falling bodies. It was the opinion of the time that heavy bodies fell faster than light ones, and it was a matter of common observation that a square foot of wood reached the ground before a square foot of paper released at the same time. The fact was explained by Galileo as due to the resistance of the air. In a vacuum they would fall at the same time. By crumpling the paper into a solid ball, it could be made to fall as rapidly as a ball of wood or iron. Experiments of this nature led Galileo to the discovery of the first law of motion, to wit: The velocity of falling bodies varies directly as the time.

At the beginning of the fall the velocity is zero; at the end of the first second, it is a certain quantity which experiment shows to be the same for all bodies. Let us call this velocity $g$. Galileo's experiments showed that at the end of the second second the terminal velocity was $2g$, at the end of the third, $3g$ and so on. The algebraic expression of the first law is, then,

The second law of motion refers to the relation of the spaces through which the body falls in different intervals of time; it is: The spaces through which a body falls vary as the squares of the times. All bodies obey this law, also, no matter of what materials they are made up.

At the beginning of the fall the time ($t$) is zero, and the velocity ($v$) is also zero. At the end of the first second, $t=I$ and $v=g$ (by I.). The velocity has increased from 0 to $g$ and its average value is therefore $0+g/2={\tfrac {1}{2}}g$. The space traversed at the end of the first second is (by II.) ${\tfrac {1}{2}}g$; at the end of the second second, $2g$; at the end of the third second, ${\tfrac {9}{2}}g$, and so on. The two laws are not independent but are separated for convenience. They are sometimes united into one, and the law of inertia (also known to Galileo) added in this form: Every body preserves its state of rest or of uniform motion in a right line unless it is compelled to change that state by forces impressed thereon.^[4]

It is this latter law that changed the whole face of science. It was supposed by the ancients and by Copernicus that the normal condition of all bodies was rest; that if they were moving it was because some force was perpetually impelling them. On the earth a pendulum stops because of the resistance of the air and the friction at its supports. Remove the air and annul the friction and it will swing forever until some impressed force stops it, so Galileo announced. Kepler was incessantly trying to conceive how a planet could continue to move in its orbit, and was forced to conclude that some inherent energy, perhaps an angel, perpetually acted to keep it moving. Galileo's law announces that if it is once set in motion it will continue to move until some impressed and extraneous force causes it to stop. Motion is as ‘natural’ as rest, therefore. It happens that on the earth there is no body moving under the action of no force. Falling bodies, projectiles, and the like, are perpetually attracted by the earth's mass, continually retarded by the resistance of the air. It required abstract philosophical reasoning to determine how such bodies would move were the impressed forces removed, and it is this reasoning that is Galileo's chief title to enduring fame. In this respect he changed the whole thought of the world. His telescopic discoveries might have been made by others. There was no man in Italy besides himself who could have founded the new science of mechanics.

Newton added two laws of motion which read: The alternation of motion is ever proportional to the moving force impressed and is made in the right line in which that force acts. To every action there is always opposed an equal reaction; or the mutual actions of two bodies upon each other are always equal, and in opposite directions. His law of universal gravitation is: Every particle of matter in the universe attracts every other particle with a force directly as the masses of the two particles, and inversely as the squares of the distance that separates them. With these laws as bases of calculation the question may be answered: What orbit will a planet describe about the sun? The answer is, a conic section, an ellipse for example. Again: What will be the law of the motion of each planet in its ellipse? The answer is: Its radius-vector will sweep over equal areas in equal times. Again: In a system of such planets, how will their orbits be related? The answer is: The squares of their periodic times will be proportional to the cubes of their mean distances from the sun. From the single law of gravitation the three laws of Kepler (as above) necessarily follow. Kepler's laws were empirical and were not complete until Newton's discoveries. This brief note explains the logical outcome of Kepler's and of Galileo's researches.

The new laws of motion were expounded to the students of Pisa with fire and eloquence. The theories of Aristotle and of his followers were treated with scorn and contempt. In his zeal for the truth Galileo branded the scientific errors of his colleagues almost as if they had been moral faults. His asperity laid the foundation of enmities that followed him throughout the whole of his life and led to his ruin. It is as true of Galileo as of Roger Bacon that his character was his fate.

How the strictures of Galileo were received by the exasperated Aristotelians may be imagined. If his experiments were to be believed, the words of Aristotle were false. If the philosophy of Aristotle were false in one part it might be false in all. The experiments must therefore be denied, and their author discredited. It is recorded that the experiments were, in fact, denied. The facts of experience were met with argument. Galileo's retorts were bitter and brilliant, his sarcasms searching and unsparing. Before the end of his three years' engagement as professor had expired, he had involved himself in a hopeless wrangle with his colleagues and with Aristotelians throughout Italy. An imbroglio with John of Medici put him out of favor at court also at this very time. The nephew of the reigning Duke of Florence had invented a machine for dredging the harbor of Leghorn, and the plans were submitted to Galileo, who declared the apparatus to be useless, as indeed it was. He made no friends by this candor and gave another weapon to his enemies which they were not slow to use. The students in the university were incited against him and he was publicly hissed at lectures, so that he felt it advisable to resign his professorship (1591).

He returned to Florence discredited and out of favor. His father died in July of this year, leaving his family in distress for money. Galileo's friend and patron, the Marquis del Monte, warmly recommended him to his friends in Venice, and as a result he was appointed to be professor of mathematics at the University of Padua, for a term of six years, this time at a salary of 72 zecchini, about $90. He remained titular professor for a period of eighteen years, until 1610, his appointment being three times renewed and his emoluments increased to $500. In December, 1592, he entered upon his duties. His lessons embraced a wide range of subjects: astronomy, gnomonics, fortification, mechanics and the like. His lectures were thronged with students. The halls were not spacious enough to hold them all and at times he taught in the open air.

In 1597 he invented his proportional compasses of which he was very proud. His manuscript description of them was plagiarized by one Balthasar Capra, and Galileo's scathing review of the work excited general notice for its bitter satire. He was already recognized as an adversary to be feared.

It has lately been demonstrated that we owe the invention of the thermometer to Galileo. His first instrument appears to have been a crude air thermometer devised in 1595. It was soon (1611) applied by physicians to the diagnosis of fevers and about 1641 to regular meteorological observations of temperature. The scales were arbitrary. The idea was developed by his pupils in various ways. The ‘Florentine’ thermometers used by the Accademia del Cimento (1657-1667) had straight sealed tubes connected with bulbs filled with spirits of wine. The highest summer heat corresponded to 80°, the lowest winter cold to 20°. So late as 1741 Florentine thermometers were in common use throughout Europe. It was not till 1694 that the freezing and boiling points of water were proposed as standard. Fahrenheit's thermometer date from 1709, Réaumer's from 1730, Celsius's (the centigrade) from 1742-3.

In 1604 a new star suddenly appeared in the heavens. It was discovered in October and quickly grew to be brighter than Jupiter. By the end of March, 1605, it had diminished to the brightness of a star of the third magnitude and in about a year it had vanished from sight. Its career was like that of the new star of 1572—Tycho's star. Galileo delivered three lectures on the new star to crowded audiences. He enforced upon the Aristotelians the conclusion that the heavens were not incorruptible, as they maintained. Here was a glaring proof of it. The star had no parallax. Hence it was far beyond our atmosphere. It was no ‘meteor,’ as they also maintained. These just conclusions were advanced with rasping criticisms of the old philosophy and the breach with his colleagues was widened still further.

In 1597 Kepler sent his Prodromus to Galileo, who writes to thank him for it, saying:

I count myself happy, in the search after truth, to have so great an ally as your self. . . . I have been for many years an adherent of the Copernican system. . . . I have collected many arguments for the purpose of refuting (the commonly accepted hypothesis), but I do not venture to the light of publicity 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.

It is to be noticed that Galileo (like Copernicus himself) dreaded the ridicule of fools. It is probable that neither of them feared the discipline of the church, or even considered it likely to be exerted.

The revolution in men's ideas to be worked by the Copernican system was not understood in the sixteenth century. It was regarded as a scientific hypothesis—an absurd one, contrary to scripture, Tycho Brahe had said. Its theological import was appreciated first by Lutherans and afterwards in Italy. Pope Paul III., to whom Copernicus dedicated his book in 1543, received it ‘with pleasure.’ A second edition was printed in 1566 without exciting the slightest adverse remark. It was not until the time of Galileo that men began to see that the accepted order of heaven and earth was inverted by the new doctrine. The earth was no longer the center of the universe. The planets were not made for man, who was dethroned not only in science, but in philosophy and theology as well. It remained for more modern times to appreciate that as it was by man himself that man was so dethroned, a new glory had been added to his crown.

All men find it painful to face novel ideas, and it is but natural to seek and find sufficient reasons for avoiding painful thoughts. When they are once familiar, new pleasures are discovered; and not until then do they begin to gain acceptance. Kepler ‘shuddered’ at the very idea of an infinite universe. Even he had not completely shaken off the Ptolemaic conception of a limited world. The authority of the Roman Church had been in theory literally universal, and Copernicus limited its world to one small planet, not so large as Jupiter as Galileo showed a few years later. The new doctrine disgraced the dignity of the earth among the planets. The authorities of a universal church could not but feel that their own dignities were attacked by the same blow. Arguments against the scientific truth were forthcoming from every chair of philosophy in Italy, and every theologian could successfully defend the literal sense of Holy Writ against such subtile and wire-drawn interpretations as were subsequently advanced by Foscarini and Galileo. I imagine the state of mind of their more intelligent contemporaries to have been one of interested bewilderment. The less intelligent were repelled and offended. The mass of pious christians was outraged and indignant. The Pope (Urban VIII.) and most of the cardinals sincerely believed that incalculable injury would result to the church from the promulgation of an opinion flatly contradicting the literal words of scripture. It was not until the discoveries of the telescope came to confirm the hypothesis of Copernicus that all these questions were pressed home for decision.

(To be continued.)

1. Among these the reader may wish to consult Martin, ‘Galilée, etc.,’ 1868; Wohlwill, ‘Der Inquisitions Process des Galileo Galilei, etc.,’ 1870; L'Epinois, ‘Galilée, son procès, etc.,’ 1867; Gebler, ‘Galileo Galilei, etc.’ (English edition), 1879; Galileo, ‘Opere, edizione nazionale,’ 1890-8.
2. Galileo was never married. He formed an illicit connection with a Venetian woman, Marina Gamba, by whom he had three children, two daughters and a son. His daughters took the veil in a convent at Arcetri. His son married and left descendants. The mother of his children subsequently married one Bartolucci, with whom Galileo was in friendly relations after the marriage. In 1627 Pope Urban VIII. granted a pension to Galileo's son who did not accept it, owing to religious observances necessitated by the grant. The pension was transferred to a nephew and finally it was increased and bestowed upon Galileo himself with the condition that he should adopt the tonsure. This pension was drawn by Galileo till his death.
3. Leonardo's investigations in mechanics were not published during his lifetime, but a correct theory of the lever was known to him as early as 1499.
4. The statement of the law is Newton's. It is implicit in Galileo's laws of falling bodies and must have been understood by Leonardo da Vinci. Kepler, perhaps, anticipated Galileo in its discovery. It is a necessary part of Huyghens's theory of central forces, but it was not clearly enunciated until the day of Newton.