Chapter 16

Fig. 57.—The differential method of parallax.

130. Entirely new ground is broken in theDialoguewhen Galilei’s discoveries of the laws of motion of bodies are applied to the problem of the earth’s motion. His great discovery, which threw an entirely new light on the mechanics of the solar system, was substantially the law afterwards given by Newton as the first of his three laws of motion, in the form:Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force applied to it to change that state.Putting aside for the present any discussion offorce, a conception first made really definite by Newton, and only imperfectly grasped by Galilei, we may interpret this law as meaning that a body has no more inherent tendency to diminish its motion or to stop than it has to increase its motion or to start, and that any alteration in either the speed or the direction of a body’s motion is to be explained by the action on it of some other body, or at any rate bysome other assignable cause. Thus a stone thrown along a road comes to rest on account of the friction between it and the ground, a ball thrown up into the air ascends more and more slowly and then falls to the ground on account of that attraction of the earth on it which we call its weight. As it is impossible to entirely isolate a body from all others, we cannot experimentally realise the state of things in which a body goes on moving indefinitely in the same direction and at the same rate; it may, however, be shewn that the more we remove a body from the influence of others, the less alteration is there in its motion. The law is therefore, like most scientific laws, an abstraction referring to a state of things to which we may approximate in nature. Galilei introduces the idea in the Dialogue by means of a ball on a smooth inclined plane. If the ball is projected upwards, its motion is gradually retarded; if downwards, it is continually accelerated. This is true if the plane is fairly smooth—like a well-planed plank—and the inclination of the plane not very small. If we imagine the experiment performed on an ideal plane, which is supposedperfectlysmooth, we should expect the same results to follow, however small the inclination of the plane. Consequently, if the plane were quite level, so that there is no distinction between up and down, we should expect the motion to be neither retarded nor accelerated, but to continue without alteration. Other more familiar examples are also given of the tendency of a body, when once in motion, to continue in motion, as in the case of a rider whose horse suddenly stops, or of bodies in the cabin of a moving ship which have no tendency to lose the motion imparted to them by the ship, so that,e.g., a body falls down to all appearances exactly as if the rest of the cabin were at rest, and therefore, in reality, while falling retains the forward motion which it shares with the ship and its contents. Salviati states also that—contrary to general belief—a stone dropped from the masthead of a ship in motion falls at the foot of the mast, not behind it, but there is no reference to the experiment having been actually performed.

This mechanical principle being once established, it becomes easy to deal with several common objections tothe supposed motion of the earth. The case of a stone dropped from the top of a tower, which if the earth be in reality moving rapidly from west to east might be expected to fall to the west in its descent, is easily shewn to be exactly parallel to the case of a stone dropped from the masthead of a ship in motion. The motion towards the east, which the stone when resting on the tower shares with the tower and the earth, is not destroyed in its descent, and it is therefore entirely in accordance with the Coppernican theory that the stone should fall as it does at the foot of the tower.76Similarly, the fact that the clouds, the atmosphere in general, birds flying in it, and loose objects on the surface of the earth, shew no tendency to be left behind as the earth moves rapidly eastward, but are apparently unaffected by the motion of the earth, is shewn to be exactly parallel to the fact that the flies in a ship’s cabin and the loose objects there are in no way affected by the uniform onward motion of the ship (though the irregular motions of pitching and rolling do affect them). The stock objection that a cannon-ball shot westward should, on the Coppernican hypothesis, carry farther than one shot eastward under like conditions, is met in the same way; but it is further pointed out that, owing to the imperfection of gunnery practice, the experiment could not really be tried accurately enough to yield any decisive result.

The most unsatisfactory part of theDialogueis the fourth day’s discussion, on the tides, of which Galilei suggests with great confidence an explanation based merely on the motion of the earth, while rejecting with scorn the suggestion of Kepler and others—correct as far as it went—that they were caused by some influence emanating from the moon. It is hardly to be wondered at that the rudimentary mechanical and mathematical knowledge at Galilei’s command should not have enabled him to dealcorrectly with a problem of which the vastly more powerful resources of modern science can only give an imperfect solution (cf. chapterXI.,§ 248, and chapterXIII.,§ 292).

131. The book as a whole was in effect, though not in form, a powerful—indeed unanswerable—plea for Coppernicanism. Galilei tried to safeguard his position, partly by the use of dialogue, and partly by the very remarkable introduction, which was not only read and approved by the licensing authorities, but was in all probability in part the composition of the Roman censor and of the Pope. It reads to us like a piece of elaborate and thinly veiled irony, and it throws a curious light on the intelligence or on the seriousness of the Pope and the censor, that they should have thus approved it:—

“Judicious reader, there was published some years since inRomea salutiferous Edict, that, for the obviating of the dangerous Scandals of the present Age, imposed a reasonable Silence upon the Pythagorean Opinion of the Mobility of the Earth. There want not such as unadvisedly affirm, that the Decree was not the production of a sober Scrutiny, but of an informed passion; and one may hear some mutter that Consultors altogether ignorant of Astronomical observations ought not to clipp the wings of speculative wits with rash prohibitions. My zeale cannot keep silence when I hear these inconsiderate complaints. I thought fit, as being thoroughly acquainted with that prudent Determination, to appear openly upon the Theatre of the World as a Witness of the naked Truth. I was at that time inRome, and had not only the audiences, but applauds of the most Eminent Prelates of that Court; nor was that Decree published without Previous Notice given me thereof. Therefore it is my resolution in the present case to give Foreign Nations to see, that this point is as well understood inItaly, and particularly inRome, as Transalpine Diligence can imagine it to be: and collecting together all the proper speculations that concerne theCopernican Systemeto let them know, that the notice of all preceded the Censure of theRoman Court; and that there proceed from this Climate not only Doctrines for the health of the Soul, but also ingenious Discoveries for the recreating of the Mind.... I hope that by these considerations the world will know, that if other Nations have Navigated more than we, we have not studied less than they; and that our returning to assert the Earth’s stability, and to take the contrary only for a MathematicalCapriccio, proceeds not from inadvertency of what others have thought thereof, but (had one no other inducements), from these reasons that Piety, Religion, the Knowledge of the Divine Omnipotency, and a consciousness of the incapacity of man’s understanding dictate unto us.”77

132. Naturally Galilei’s many enemies were not long in penetrating these thin disguises, and the immense success of the book only intensified the opposition which it excited; the Pope appears to have been persuaded that Simplicio—the butt of the whole dialogue—was intended for himself, a supposed insult which bitterly wounded his vanity; and it was soon evident that the publication of the book could not be allowed to pass without notice. In June 1632 a special commission was appointed to inquire into the matter—an unusual procedure, probably meant as a mark of consideration for Galilei—and two months later the further issue of copies of the book was prohibited, and in September a papal mandate was issued requiring Galilei to appear personally before the Inquisition. He was evidently frightened by the summons, and tried to avoid compliance through the good offices of the Tuscan court and by pleading his age and infirmities, but after considerable delay, at the end of which the Pope issued instructions to bring him if necessary by force and in chains, he had to submit, and set off for Rome early in 1633. Here he was treated with unusual consideration, for whereas in general even the most eminent offenders under trial by the Inquisition were confined in its prisons, he was allowed to live with his friend Niccolini, the Tuscan ambassador, throughout the trial, with the exception of a period of about three weeks, which he spent within the buildings of the Inquisition, in comfortable rooms belonging to one of the officials, with permission to correspond with his friends, to take exercise in the garden, and other privileges. At his first hearing before the Inquisition, his reply to the charge of having violated the decree of 1616 (§ 126) was that he had not understood that the decree or the admonition given to him forbade the teaching of the Coppernican theory as a mere “hypothesis,” and that his book had not upheld the doctrine in any other way. Between his first and second hearing the Commission, which had beenexamining his book, reported that it did distinctly defend and maintain the obnoxious doctrines, and Galilei, having been meanwhile privately advised by the Commissary-General of the Inquisition to adopt a more submissive attitude, admitted at the next hearing that on reading his book again he recognised that parts of it gave the arguments for Coppernicanism more strongly than he had at first thought. The pitiable state to which he had been reduced was shewn by the offer which he now made to write a continuation to the Dialogue which should as far as possible refute his own Coppernican arguments. At the final hearing on June 21st he was examined under threat of torture,78and on the next day he was brought up for sentence. He was convicted “of believing and holding the doctrines—false and contrary to the Holy and Divine Scriptures—that the sun is the centre of the world, and that it does not move from east to west, and that the earth does move and is not the centre of the world; also that an opinion can be held and supported as probable after it has been declared and decreed contrary to the Holy Scriptures.” In punishment, he was required to “abjure, curse, and detest the aforesaid errors,” the abjuration being at once read by him on his knees; and was further condemned to the “formal prison of the Holy Office” during the pleasure of his judges, and required to repeat the seven penitential psalms once a week for three years. On the following day the Pope changed the sentence of imprisonment into confinement at a country-house near Rome belonging to the Grand Duke, and Galilei moved there on June 24th.79On petitioning to be allowed to return to Florence, he was at first allowed to go as far as Siena, and at the end of the year was permitted to retire to his country-house at Arcetri near Florence, on condition of not leaving it for the future without permission, while his intercourse with scientific and other friends was jealously watched.

GALILEI.[To face p. 171.

[To face p. 171.

The story of the trial reflects little credit either on Galilei or on his persecutors. For the latter, it may be urged that they acted with unusual leniency considering the customs of the time; and it is probable that many of those who were concerned in the trial were anxious to do as little injury to Galilei as possible, but were practically forced by the party personally hostile to him to take some notice of the obvious violation of the decree of 1616. It is easy to condemn Galilei for cowardice, but it must be borne in mind, on the one hand, that he was at the time nearly seventy, and much shaken in health, and, on the other, that the Roman Inquisition, if not as cruel as the Spanish, was a very real power in the early 17th century; during Galilei’s lifetime (1600) Giordano Bruno had been burnt alive at Rome for writings which, in addition to containing religious and political heresies, supported the Coppernican astronomy and opposed the traditional Aristotelian philosophy. Moreover, it would be unfair to regard his submission as due merely to considerations of personal safety, for—apart from the question whether his beloved science would have gained anything by his death or permanent imprisonment—there can be no doubt that Galilei was a perfectly sincere member of his Church, and although he did his best to convince individual officers of the Church of the correctness of his views, and to minimise the condemnation of them passed in 1616, yet he was probably prepared, when he found that the condemnation was seriously meant by the Pope, the Holy Office, and others, to believe that in some senses at least his views must be wrong, although, as a matter of observation and pure reason, he was unable to see how or why. In fact, like many other excellent people, he kept watertight compartments in his mind, respect for the Church being in one and scientific investigation in another.

Copies of the sentence on Galilei and of his abjuration were at once circulated in Italy and in Roman Catholic circles elsewhere, and a decree of the Congregation of the Index was also issued adding theDialogueto the three Coppernican books condemned in 1616, and to Kepler’sEpitomeof the Coppernican Astronomy (chapterVII.,§ 145), which had been put on theIndexshortly afterwards. Itmay be of interest to note that these five books still remained in the edition of theIndex of Prohibited Bookswhich was issued in 1819 (with appendices dated as late as 1821), but disappeared from the next edition, that of 1835.

133. The rest of Galilei’s life may be described very briefly. With the exception of a few months, during which he was allowed to be at Florence for the sake of medical treatment, he remained continuously at Arcetri, evidently pretty closely watched by the agents of the Holy Office, much restricted in his intercourse with his friends, and prevented from carrying on his studies in the directions which he liked best. He was moreover very infirm, and he was afflicted by domestic troubles, especially by the death in 1634 of his favourite child, a nun in a neighbouring convent. But his spirit was not broken, and he went on with several important pieces of work, which he had begun earlier in his career. He carried a little further the study of his beloved Medicean Planets and of the method of finding longitude based on their movements (§ 127), and negotiated on the subject with the Dutch government. He made also a further discovery relating to the moon, of sufficient importance to deserve a few words of explanation.

Fig. 58.—The daily libration of the moon.

It had long been well known that as the moon describes her monthly path round the earth we see the same markings substantially in the same positions on the disc, so that substantially the same face of the moon is turned towards the earth. It occurred to Galilei to inquire whether this was accurately the case, or whether, on the contrary, some change in the moon’s disc could be observed. He saw that if, as seemed likely, the line joining the centres of the earth and moon always passed through the same point on the moon’s surface, nevertheless certain alterations in an observer’s position on the earth would enable him to see different portions of the moon’s surface from time to time. The simplest of these alterations is due to the daily motion of the earth. Let us suppose for simplicity that the observer is on the earth’s equator, and that the moon is at the time in the celestial equator. Let the larger circle in fig. 58 represent the earth’s equator, and the smaller circle the section of the moon by the plane of the equator. Then in about 12 hours the earth’s rotation carries theobserver fromA, where he sees the moon rising, toB, where he sees it setting. When he is atC, on the line joining the centres of the earth and moon, the pointOappears to be in the centre of the moon’s disc, and the portioncOc′is visible,cRc′invisible. But when the observer is atA, the pointP, on the right ofO, appears in the centre, and the portionaPa′is visible, so thatc′ a′is now visible anda cinvisible. In the same way, when the observer is atB, he can see the portionc b, whileb′ c′is invisible andQappears to be in the centre of the disc. Thus in the course of the day the portionaOb′(dotted in the figure) is constantly visible andbRa′(also dotted) constantly invisible, whilea c banda′ c′ b′alternately come into view and disappear. In other words, when the moon is rising we see a little more of the side which is the then uppermost, and when she is setting we see a little more of the other side which is uppermost in this position. A similar explanation applies when the observer is not on the earth’s equator, but the geometry is slightly more complicated. In the same way, as the moon passes from south to north of the equator and back as she revolves round the earth, we see alternately more and less of the northern and southern half of the moon. This set of changes—the simplest of several somewhat similar ones which are now known aslibrationsof the moon—being thus thought of as likely to occur, Galilei set to work to test their existence by observing certain markings of the moon usually visible near the edge, and at once detected alterations in their distance from the edge, which were in general accordance with his theoretical anticipations. A more precise inquiry was however interrupted by failing sight, culminating (at the end of 1636) in total blindness.

But the most important work of these years was the completion of the great book, in which he summed up and completed his discoveries in mechanics,Mathematical Discourses and Demonstrations concerning Two New Sciences, relating to Mechanics and to Local Motion. It was written in the form of a dialogue between the same three speakers who figured in the Dialogue on the Systems, but is distinctly inferior in literary merit to the earlier work. We have here no concern with a large part of the book, which deals with the conditions under whichbodies are kept, at rest by forces applied to them (statics), and certain problems relating to the resistance of bodies to fracture and to bending, though in both of these subjects Galilei broke new ground. More important astronomically—and probably intrinsically also—is what he calls the science of local motion,80which deals with the motion of bodies. He builds up on the basis of his early experiments (§ 116) a theory of falling bodies, in which occurs for the first time the important idea ofuniformly accelerated motion, oruniform acceleration,i.e.motion in which the moving body receives in every equal interval of time an equal increase of velocity. He shews that the motion of a falling body is—except in so far as it is disturbed by the air—of this nature, and that, as already stated, the motion is the same for all bodies, although his numerical estimate is not at all accurate.81From this fundamental law he works out a number of mathematical deductions, connecting the space fallen through, the velocity, and the time elapsed, both for the case of a body falling freely and for one falling down an inclined plane. He gives also a correct elementary theory of projectiles, in the course of which he enunciates more completely than before the law of inertia already referred to (§ 130), although Galilei’s form is still much less general than Newton’s:—

Conceive a body projected or thrown along a horizontal plane, all impediments being removed. Now it is clear by what we have said before at length that its motion will be uniform and perpetual along the said plane, if the plane extend indefinitely.

In connection with projectiles, Galilei also appears to realise that a body may be conceived as having motions in two different directions simultaneously, and that each may be treated as independent of the other, so that, for example, if a bullet is shot horizontally out of a gun, its downward motion, due to its weight, is unaffectedby its horizontal motion, and consequently it reaches the ground at the same time as a bullet simply allowed to drop; but Galilei gives no general statement of this principle, which was afterwards embodied by Newton in his Second Law of Motion.

The treatise on theTwo New Scienceswas finished in 1636, and, since no book of Galilei’s could be printed in Italy, it was published after some little delay at Leyden in 1638. In the same year his eyesight, which he had to some extent recovered after his first attack of blindness, failed completely, and four years later (January 8th, 1642) the end came.

134. Galilei’s chief scientific discoveries have already been noticed. The telescopic discoveries, on which much of his popular reputation rests, have probably attracted more than their fair share of attention; many of them were made almost simultaneously by others, and the rest, being almost inevitable results of the invention of the telescope, could not have been delayed long. But the skilful use which Galilei made of them as arguments for the Coppernican system, the no less important support which his dynamical discoveries gave to the same cause, the lucidity and dialectic brilliance with which he marshalled the arguments in favour of his views and demolished those of his opponents, together with the sensational incidents of his persecution, formed conjointly a contribution to the Coppernican controversy which was in effect decisive. Astronomical textbooks still continued to give side by side accounts of the Ptolemaic and of the Coppernican systems, and the authors, at any rate if they were good Roman Catholics, usually expressed, in some more or less perfunctory way, their adherence to the former, but there was no real life left in the traditional astronomy; new advances in astronomical theory were all on Coppernican lines, and in the extensive scientific correspondence of Newton and his contemporaries the truth of the Coppernican system scarcely ever appears as a subject for discussion.

Galilei’s dynamical discoveries, which are only in part of astronomical importance, are in many respects his most remarkable contribution to science. For whereas inastronomy he was building on foundations laid by previous generations, in dynamics it was no question of improving or developing an existing science, but of creating a new one. From his predecessors he inherited nothing but erroneous traditions and obscure ideas; and when these had been discarded, he had to arrive at clear fundamental notions, to devise experiments and make observations, to interpret his experimental results, and to follow out the mathematical consequences of the simple laws first arrived at. The positive results obtained may not appear numerous, if viewed from the standpoint of our modern knowledge, but they sufficed to constitute a secure basis for the superstructure which later investigators added.

It is customary to associate with our countryman Francis Bacon (1561-1627) the reform in methods of scientific discovery which took place during the seventeenth century, and to which much of the rapid progress in the natural sciences made since that time must be attributed. The value of Bacon’s theory of scientific discovery is very differently estimated by different critics, but there can be no question of the singular ill-success which attended his attempts to apply it in particular cases, and it may fairly be questioned whether the scientific methods constantly referred to incidentally by Galilei, and brilliantly exemplified by his practice, do not really contain a large part of what is valuable in the Baconian philosophy of science, while at the same time avoiding some of its errors. Reference has already been made on several occasions to Galilei’s protests against the current method of dealing with scientific questions by the interpretation of passages in Aristotle, Ptolemy, or other writers; and to his constant insistence on the necessity of appealing directly to actual observation of facts. But while thus agreeing with Bacon in these essential points, he differed from him in the recognition of the importance, both of deducing new results from established ones by mathematical or other processes of exact reasoning, and of using such deductions, when compared with fresh experimental results, as a means of verifying hypotheses provisionally adopted. This method of proof, which lies at the base of nearly all important scientific discovery, can hardly be described better than byGalilei’s own statement of it, as applied to a particular case:—

“Let us therefore take this at present as aPostulatum, the truth whereof we shall afterwards find established, when we shall see other conclusions built upon thisHypothesis, to answer and most exactly to agree with Experience.”82

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