“Dans la Science nous sommes tous disciples de GalilÉe.”—Trouessart.

“Bacon pointed out at a distance the road to true philosophy: Galileo both pointed it out to others, and made himself considerable advances in it.”—David Hume.

113. To the generation which succeeded Tycho belonged two of the best known of all astronomers, Galilei and Kepler. Although they were nearly contemporaries, Galilei having been born seven years earlier than Kepler, and surviving him by twelve years, their methods of work and their contributions to astronomy were so different in character, and their influence on one another so slight, that it is convenient to make some departure from strict chronological order, and to devote this chapter exclusively to Galilei, leaving Kepler to the next.

Galileo Galilei was born in 1564, at Pisa, at that time in the Grand Duchy of Tuscany, on the day of Michel Angelo’s death and in the year of Shakespeare’s birth. His father, Vincenzo, was an impoverished member of a good Florentine family, and was distinguished by his skill in music and mathematics. Galileo’s talents shewed themselves early, and although it was originally intended that he should earn his living by trade, Vincenzo was wise enough to see that his son’s ability and tastes rendered him much more fit for a professional career, and accordingly he sent him in 1581 to study medicine at the University of Pisa. Here his unusual gifts soon made him conspicuous, and he became noted in particular for his unwillingness to accept without question the dogmatic statements of his teachers, which were based not on direct evidence, but on the authority of the great writers of the past. This valuable characteristic, which marked him throughout his life, coupled with his skill in argument, earned for him the dislike of some of his professors, and from his fellow-students the nickname of The Wrangler.114. In 1582 his keen observation led to his first scientific discovery. Happening one day in the Cathedral of Pisa to be looking at the swinging of a lamp which was hanging from the roof, he noticed that as the motion gradually died away and the extent of each oscillation became less, the time occupied by each oscillation remained sensibly the same, a result which he verified more precisely by comparison with the beating of his pulse. Further thought and trial shewed him that this property was not peculiar to cathedral lamps, but that any weight hung by a string (or any other form of pendulum) swung to and fro in a time which depended only on the length of the string and other characteristics of the pendulum itself, and not to any appreciable extent on the way in which it was set in motion or on the extent of each oscillation. He devised accordingly an instrument the oscillations of which could be used while they lasted as a measure of time, and which was in practice found very useful by doctors for measuring the rate of a patient’s pulse.115. Before very long it became evident that Galilei had no special taste for medicine, a study selected for him chiefly as leading to a reasonably lucrative professional career, and that his real bent was for mathematics and its applications to experimental science. He had received little or no formal teaching in mathematics before his second year at the University, in the course of which he happened to overhear a lesson on Euclid’s geometry, given at the Grand Duke’s court, and was so fascinated that he continued to attend the course, at first surreptitiously, afterwards openly; his interest in the subject was thereby so much stimulated, and his aptitude for it was so marked, that he obtained his father’s consent to abandon medicine in favour of mathematics.

In 1585, however, poverty compelled him to quit the University without completing the regular course and obtaining a degree, and the next four years were spent chiefly at home, where he continued to read and to think on scientific subjects. In the year 1586 he wrote his first known scientific essay,66 which was circulated in manuscript, and only printed during the present century.116. In 1589 he was appointed for three years to a professorship of mathematics (including astronomy) at Pisa. A miserable stipend, equivalent to about five shillings a week, was attached to the post, but this he was to some extent able to supplement by taking private pupils.

In his new position Galilei had scope for his remarkable power of exposition, but far from being content with giving lectures on traditional lines he also carried out a series of scientific investigations, important both in themselves and on account of the novelty in the method of investigation employed.

It will be convenient to discuss more fully at the end of this chapter Galilei’s contributions to mechanics and to scientific method, and merely to refer here briefly to his first experiments on falling bodies, which were made at this time. Some were performed by dropping various bodies from the top of the leaning tower of Pisa, and others by rolling balls down grooves arranged at different inclinations. It is difficult to us nowadays, when scientific experiments are so common, to realise the novelty and importance at the end of the 16th century of such simple experiments. The mediaeval tradition of carrying out scientific investigation largely by the interpretation of texts in Aristotle, Galen, or other great writers of the past, and by the deduction of results from general principles which were to be found in these writers without any fresh appeal to observation, still prevailed almost undisturbed at Pisa, as elsewhere. It was in particular commonly asserted, on the authority of Aristotle, that, the cause of the fall of a heavy body being its weight, a heavier body must fall faster than a lighter one and in proportion to its greater weight. It may perhaps be doubted whether any one before Galilei’s time had clear enough ideas on the subject to be able to give a definite answer to such a question as how much farther a ten-pound weight would fall in a second than a one-pound weight; but if so he would probably have said that it would fall ten times as far, or else that it would require ten times as long to fall the same distance. To actually try the experiment, to vary its conditions, so as to remove as many accidental causes of error as possible, to increase in some way the time of the fall so as to enable it to be measured with more accuracy, these ideas, put into practice by Galilei, were entirely foreign to the prevailing habits of scientific thought, and were indeed regarded by most of his colleagues as undesirable if not dangerous innovations. A few simple experiments were enough to prove the complete falsity of the current beliefs in this matter, and to establish that in general bodies of different weights fell nearly the same distance in the same time, the difference being not more than could reasonably be ascribed to the resistance offered by the air.

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

These innovations, coupled with the slight respect that he was in the habit of paying to those who differed from him, evidently made Galilei far from popular with his colleagues at Pisa, and either on this account, or on account of domestic troubles consequent on the death of his father (1591), he resigned his professorship shortly before the expiration of his term of office, and returned to his mother’s home at Florence.117. After a few months spent at Florence he was appointed, by the influence of a Venetian friend, to a professorship of mathematics at Padua, which was then in the territory of the Venetian republic (1592). The appointment was in the first instance for a period of six years, and the salary much larger than at Pisa. During the first few years of Galilei’s career at Padua his activity seems to have been very great and very varied; in addition to giving his regular lectures, to audiences which rapidly increased, he wrote tracts, for the most part not printed at the time, on astronomy, on mechanics, and on fortification, and invented a variety of scientific instruments.

No record exists of the exact time at which he first adopted the astronomical views of Coppernicus, but he himself stated that in 1597 he had adopted them some years before, and had collected arguments in their support.

In the following year his professorship was renewed for six years with an increased stipend, a renewal which was subsequently made for six years more, and finally for life, the stipend being increased on each occasion.

Galilei’s first contribution to astronomical discovery was made in 1604, when a star appeared suddenly in the constellation Serpentarius, and was shewn by him to be at any rate more distant than the planets, a result confirming Tycho’s conclusions (chapter V., §100) that changes take place in the celestial regions even beyond the planets, and are by no means confined—as was commonly believed—to the earth and its immediate surroundings.118. By this time Galilei had become famous throughout Italy, not only as a brilliant lecturer, but also as a learned and original man of science. The discoveries which first gave him a European reputation were, however, the series of telescopic observations made in 1609 and the following years.

Roger Bacon (chapter III., §67) had claimed to have devised a combination of lenses enabling distant objects to be seen as if they were near; a similar invention was probably made by our countryman Leonard Digges (who died about 1571), and was described also by the Italian Porta in 1558. If such an instrument was actually made by any one of the three, which is not certain, the discovery at any rate attracted no attention and was again lost. The effective discovery of the telescope was made in Holland in 1608 by Hans Lippersheim (?-1619), a spectacle-maker of Middleburg, and almost simultaneously by two other Dutchmen, but whether independently or not it is impossible to say. Early in the following year the report of the invention reached Galilei, who, though without any detailed information as to the structure of the instrument, succeeded after a few trials in arranging two lenses—one convex and one concave—in a tube in such a way as to enlarge the apparent size of an object looked at; his first instrument made objects appear three times nearer, consequently three times greater (in breadth and height), and he was soon able to make telescopes which in the same way magnified thirty-fold.

That the new instrument might be applied to celestial as well as to terrestrial objects was a fairly obvious idea, which was acted on almost at once by the English mathematician Thomas Harriot (1560-1621), by Simon Marius (1570-1624) in Germany, and by Galilei. That the credit of first using the telescope for astronomical purposes is almost invariably attributed to Galilei, though his first observations were in all probability slightly later in date than those of Harriot and Marius, is to a great extent justified by the persistent way in which he examined object after object, whenever there seemed any reasonable prospect of results following, by the energy and acuteness with which he followed up each clue, by the independence of mind with which he interpreted his observations, and above all by the insight with which he realised their astronomical importance.119. His first series of telescopic discoveries were published early in 1610 in a little book called Sidereus Nuncius, or The Sidereal Messenger. His first observations at once threw a flood of light on the nature of our nearest celestial neighbour, the moon. It was commonly believed that the moon, like the other celestial bodies, was perfectly smooth and spherical, and the cause of the familiar dark markings on the surface was quite unknown.67

Galilei discovered at once a number of smaller markings, both bright and dark (fig. 53), and recognised many of the latter as shadows of lunar mountains cast by the sun; and further identified bright spots seen near the boundary of the illuminated and dark portions of the moon as mountain-tops just catching the light of the rising or setting sun, while the surrounding lunar area was still in darkness. Moreover, with characteristic ingenuity and love of precision, he calculated from observations of this nature the height of some of the more conspicuous lunar mountains, the largest being estimated by him to be about four miles high, a result agreeing closely with modern estimates of the greatest height on the moon. The large dark spots he explained (erroneously) as possibly caused by water, though he evidently had less confidence in the correctness of the explanation than some of his immediate scientific successors, by whom the name of seas was given to these spots (chapter VIII., §153). He noticed also the absence of clouds. Apart however from details, the really significant results of his observations were that the moon was in many important respects similar to the earth, that the traditional belief in its perfectly spherical form had to be abandoned, and that so far the received doctrine of the sharp distinction to be drawn between things celestial and things terrestrial was shewn to be without justification; the importance of this in connection with the Coppernican view that the earth, instead of being unique, was one of six planets revolving round the sun, needs no comment.

One of Galilei’s numerous scientific opponents68 attempted to explain away the apparent contradiction between the old theory and the new observations by the ingenious suggestion that the apparent valleys in the moon were in reality filled with some invisible crystalline material, so that the moon was in fact perfectly spherical. To this Galilei replied that the idea was so excellent that he wished to extend its application, and accordingly maintained that the moon had on it mountains of this same invisible substance, at least ten times as high as any which he had observed.120. The telescope revealed also the existence of an immense number of stars too faint to be seen by the unaided eye; Galilei saw, for example, 36 stars in the Pleiades, which to an ordinary eye consist of six only. Portions of the Milky Way and various nebulous patches of light were also discovered to consist of multitudes of faint stars clustered together; in the cluster PrÆsepe (in the Crab), for example, he counted 40 stars.121. By far the most striking discovery announced in the Sidereal Messenger was that of the bodies now known as the moons or satellites of Jupiter. On January 7th, 1610, Galilei turned his telescope on to Jupiter, and noticed three faint stars which caught his attention on account of their closeness to the planet and their arrangement nearly in a straight line with it. He looked again next night, and noticed that they had changed their positions relatively to Jupiter, but that the change did not seem to be such as could result from Jupiter’s own motion, if the new bodies were fixed stars. Two nights later he was able to confirm this conclusion, and to infer that the new bodies were not fixed stars, but moving bodies which accompanied Jupiter in his movements. A fourth body was noticed on January 13th, and the motions of all four were soon recognised by Galilei as being motions of revolution round Jupiter as a centre. With characteristic thoroughness he watched the motions of the new bodies night after night, and by the date of the publication of his book had already estimated with very fair accuracy their periods of revolution round Jupiter, which ranged between about 42 hours and 17 days; and he continued to watch their motions for years.

The new bodies were at first called by their discoverer Medicean planets, in honour of his patron Cosmo de Medici, the Grand Duke of Tuscany; but it was evident that bodies revolving round a planet, as the planets themselves revolved round the sun, formed a new class of bodies distinct from the known planets, and the name of satellite, suggested by Kepler as applicable to the new bodies as well as to the moon, has been generally accepted.

The discovery of Jupiter’s satellites shewed the falsity of the old doctrine that the earth was the only centre of motion; it tended, moreover, seriously to discredit the infallibility of Aristotle and Ptolemy, who had clearly no knowledge of the existence of such bodies; and again those who had difficulty in believing that Venus and Mercury could revolve round an apparently moving body, the sun, could not but have their doubts shaken when shewn the new satellites evidently performing a motion of just this character; and—most important consequence of all—the very real mechanical difficulty involved in the Coppernican conception of the moon revolving round the moving earth and not dropping behind was at any rate shewn not to be insuperable, as Jupiter’s satellites succeeded in performing a precisely similar feat.

The same reasons which rendered Galilei’s telescopic discoveries of scientific importance made them also objectionable to the supporters of the old views, and they were accordingly attacked in a number of pamphlets, some of which are still extant and possess a certain amount of interest. One Martin Horky, for example, a young German who had studied under Kepler, published a pamphlet in which, after proving to his own satisfaction that the satellites of Jupiter did not exist, he discussed at some length what they were, what they were like, and why they existed. Another writer gravely argued that because the human body had seven openings in it—the eyes, ears, nostrils, and mouth—therefore by analogy there must be seven planets (the sun and moon being included) and no more. However, confirmation by other observers was soon obtained and the pendulum even began to swing in the opposite direction, a number of new satellites of Jupiter being announced by various observers. None of these, however, turned out to be genuine, and Galilei’s four remained the only known satellites of Jupiter till a few years ago (chapter XIII., §295).122. The reputation acquired by Galilei by the publication of the Messenger enabled him to bring to a satisfactory issue negotiations which he had for some time been carrying on with the Tuscan court. Though he had been well treated by the Venetians, he had begun to feel the burden of regular teaching somewhat irksome, and was anxious to devote more time to research and to writing. A republic could hardly be expected to provide him with such a sinecure as he wanted, and he accordingly accepted in the summer of 1610 an appointment as professor at Pisa, and also as “First Philosopher and Mathematician” to the Grand Duke of Tuscany, with a handsome salary and no definite duties attached to either office.123. Shortly before leaving Padua he turned his telescope on to Saturn, and observed that the planet appeared to consist of three parts, as shewn in the first drawing of fig. 67 (chapter VIII., §154). On subsequent occasions, however, he failed to see more than the central body, and the appearances of Saturn continued to present perplexing variations, till the mystery was solved by Huygens in 1655 (chapter VIII., §154).

The first discovery made at Florence (October 1610) was that Venus, which to the naked eye appears to vary very much in brilliancy but not in shape, was in reality at times crescent-shaped like the new moon and passed through phases similar to some of those of the moon. This shewed that Venus was, like the moon, a dark body in itself, deriving its light from the sun; so that its similarity to the earth was thereby made more evident.

124. The discovery of dark spots on the sun completed this series of telescopic discoveries. According to his own statement Galilei first saw them towards the end of 1610,69 but apparently paid no particular attention to them at the time; and, although he shewed them as a matter of curiosity to various friends, he made no formal announcement of the discovery till May 1612, by which time the same discovery had been made independently by Harriot (§118) in England, by John Fabricius (1587-? 1615) in Holland, and by the Jesuit Christopher Scheiner (1575-1650) in Germany, and had been published by Fabricius (June 1611). As a matter of fact dark spots had been seen with the naked eye long before, but had been generally supposed to be caused by the passage of Mercury in front of the sun. The presence on the sun of such blemishes as black spots, the “mutability” involved in their changes in form and position, and their formation and subsequent disappearance, were all distasteful to the supporters of the old views, according to which celestial bodies were perfect and unchangeable. The fact, noticed by all the early observers, that the spots appeared to move across the face of the sun from the eastern to the western side (i.e. roughly from left to right, as seen at midday by an observer in our latitudes), gave at first sight countenance to the view, championed by Scheiner among others, that the spots might really be small planets revolving round the sun, and appearing as dark objects whenever they passed between the sun and the observer. In three letters to his friend Welser, a merchant prince of Augsburg, written in 1612 and published in the following year,70 Galilei, while giving a full account of his observations, gave a crushing refutation of this view; proved that the spots must be on or close to the surface of the sun, and that the motions observed were exactly such as would result if the spots were attached to the sun, and it revolved on an axis in a period of about a month; and further, while disclaiming any wish to speak confidently, called attention to several of their points of resemblance to clouds.

One of his arguments against Scheiner’s views is so simple and at the same time so convincing, that it may be worth while to reproduce it as an illustration of Galilei’s method, though the controversy itself is quite dead.

Galilei noticed, namely, that while a spot took about fourteen days to cross from one side of the sun to the other, and this time was the same whether the spot passed through the centre of the sun’s disc, or along a shorter path at some distance from it, its rate of motion was by no means uniform, but that the spot’s motion always appeared much slower when near the edge of the sun than when near the centre. This he recognised as an effect of foreshortening, which would result if, and only if, the spot were near the sun.

If, for example, in the figure, the circle represent a section of the sun by a plane through the observer at O, and A, B, C, D, E be points taken at equal distances along the surface of the sun, so as to represent the positions of an object on the sun at equal intervals of time, on the assumption that the sun revolves uniformly, then the apparent motion from A to B, as seen by the observer at O, is measured by the angle A O B, and is obviously much less than that from D to E, measured by the angle D O E, and consequently an object attached to the sun must appear to move more slowly from A to B, i.e. near the sun’s edge, than from D to E, near the centre. On the other hand, if the spot be a body revolving round the sun at some distance from it, e.g. along the dotted circle c d e, then if c, d, e be taken at equal distances from one another, the apparent motion from c to d, measured again by the angle c O d, is only very slightly less than that from d to e, measured by the angle d O e. Moreover, it required only a simple calculation, performed by Galilei in several cases, to express these results in a numerical shape, and so to infer from the actual observations that the spots could not be more than a very moderate distance from the sun. The only escape from this conclusion was by the assumption that the spots, if they were bodies revolving round the sun, moved irregularly, in such a way as always to be moving fastest when they happened to be between the centre of the sun and the earth, whatever the earth’s position might be at the time, a procedure for which, on the one hand, no sort of reason could be given, and which, on the other, was entirely out of harmony with the uniformity to which mediÆval astronomy clung so firmly.

The rotation of the sun about an axis, thus established, might evidently have been used as an argument in support of the view that the earth also had such a motion, but, as far as I am aware, neither Galilei nor any contemporary noticed the analogy. Among other facts relating to the spots observed by Galilei were the greater darkness of the central parts, some of his drawings (see fig. 55) shewing, like most modern drawings, a fairly well-marked line of division between the central part (or umbra) and the less dark fringe (or penumbra) surrounding it; he noticed also that spots frequently appeared in groups, that the members of a group changed their positions relatively to one another, that individual spots changed their size and shape considerably during their lifetime, and that spots were usually most plentiful in two regions on each side of the sun’s equator, corresponding roughly to the tropics on our own globe, and were never seen far beyond these limits.

Similar observations were made by other telescopists, and to Scheiner belongs the credit of fixing, with considerably more accuracy than Galilei, the position of the sun’s axis and equator and the time of its rotation.125. The controversy with Scheiner as to the nature of spots unfortunately developed into a personal quarrel as to their respective claims to the discovery of spots, a controversy which made Scheiner his bitter enemy, and probably contributed not a little to the hostility with which Galilei was henceforward regarded by the Jesuits. Galilei’s uncompromising championship of the new scientific ideas, the slight respect which he shewed for established and traditional authority, and the biting sarcasms with which he was in the habit of greeting his opponents, had won for him a large number of enemies in scientific and philosophic circles, particularly among the large party who spoke in the name of Aristotle, although, as Galilei was never tired of reminding them, their methods of thought and their conclusions would in all probability have been rejected by the great Greek philosopher if he had been alive.

It was probably in part owing to his consciousness of a growing hostility to his views, both in scientific and in ecclesiastical circles, that Galilei paid a short visit to Rome in 1611, when he met with a most honourable reception and was treated with great friendliness by several cardinals and other persons in high places.

Unfortunately he soon began to be drawn into a controversy as to the relative validity in scientific matters of observation and reasoning on the one hand, and of the authority of the Church and the Bible on the other, a controversy which began to take shape about this time and which, though its battle-field has shifted from science to science, has lasted almost without interruption till modern times.

In 1611 was published a tract maintaining Jupiter’s satellites to be unscriptural. In 1612 Galilei consulted Cardinal Conti as to the astronomical teaching of the Bible, and obtained from him the opinion that the Bible appeared to discountenance both the Aristotelian doctrine of the immutability of the heavens and the Coppernican doctrine of the motion of the earth. A tract of Galilei’s on floating bodies, published in 1612, roused fresh opposition, but on the other hand Cardinal Barberini (who afterwards, as Urban VIII., took a leading part in his persecution) specially thanked him for a presentation copy of the book on sun-spots, in which Galilei, for the first time, clearly proclaimed in public his adherence to the Coppernican system. In the same year (1613) his friend and follower, Father Castelli, was appointed professor of mathematics at Pisa, with special instructions not to lecture on the motion of the earth. Within a few months Castelli was drawn into a discussion on the relations of the Bible to astronomy, at the house of the Grand Duchess, and quoted Galilei in support of his views; this caused Galilei to express his opinions at some length in a letter to Castelli, which was circulated in manuscript at the court. To this a Dominican preacher, Caccini, replied a few months afterwards by a violent sermon on the text, “Ye Galileans, why stand ye gazing up into heaven?”71 and in 1615 Galilei was secretly denounced to the Inquisition on the strength of the letter to Castelli and other evidence. In the same year he expanded the letter to Castelli into a more elaborate treatise, in the form of a Letter to the Grand Duchess Christine, which was circulated in manuscript, but not printed till 1636. The discussion of the bearing of particular passages of the Bible (e.g. the account of the miracle of Joshua) on the Ptolemaic and Coppernican systems has now lost most of its interest; it may, however, be worth noticing that on the more general question Galilei quotes with approval the saying of Cardinal Baronius, “That the intention of the Holy Ghost is to teach us not how the heavens go, but how to go to heaven,”72 and the following passage gives a good idea of the general tenor of his argument:—

“Methinks, that in the Discussion of Natural Problemes we ought not to begin at the authority of places of Scripture; but at Sensible Experiments and Necessary Demonstrations. For ... Nature being inexorable and immutable, and never passing the bounds of the Laws assigned her, as one that nothing careth, whether her abstruse reasons and methods of operating be or be not exposed to the capacity of men; I conceive that that concerning Natural Effects, which either sensible experience sets before our eyes, or Necessary Demonstrations do prove unto us, ought not, upon any account, to be called into question, much less condemned upon the testimony of Texts of Scripture, which may under their words, couch senses seemingly contrary thereto.”73

126. Meanwhile his enemies had become so active that Galilei thought it well to go to Rome at the end of 1615 to defend his cause. Early in the next year a body of theologians known as the Qualifiers of the Holy Office (Inquisition), who had been instructed to examine certain Coppernican doctrines, reported:—

“That the doctrine that the sun was the centre of the world and immoveable was false and absurd, formally heretical and contrary to Scripture, whereas the doctrine that the earth was not the centre of the world but moved, and has further a daily motion, was philosophically false and absurd and theologically at least erroneous.”

In consequence of this report it was decided to censure Galilei, and the Pope accordingly instructed Cardinal Bellarmine “to summon Galilei and admonish him to abandon the said opinion,” which the Cardinal did.74 Immediately afterwards a decree was issued condemning the opinions in question and placing on the well-known Index of Prohibited Books three books containing Coppernican views, of which the De Revolutionibus of Coppernicus and another were only suspended “until they should be corrected,” while the third was altogether prohibited. The necessary corrections to the De Revolutionibus were officially published in 1620, and consisted only of a few alterations which tended to make the essential principles; of the book appear as mere mathematical hypotheses, convenient for calculation. Galilei seems to have been on the whole well satisfied with the issue of the inquiry, as far as he was personally concerned, and after obtaining from Cardinal Bellarmine a certificate that he had neither abjured his opinions nor done penance for them, stayed on in Rome for some months to shew that he was in good repute there.127. During the next few years Galilei, who was now more than fifty, suffered a good deal from ill-health and was comparatively inactive. He carried on, however, a correspondence with the Spanish court on a method of ascertaining the longitude at sea by means of Jupiter’s satellites. The essential problem in finding the longitude is to obtain the time as given by the sun at the required place and also that at some place the longitude of which is known. If, for example, midday at Rome occurs an hour earlier than in London, the sun takes an hour to travel from the meridian of Rome to that of London, and the longitude of Rome is 15° east of that of London. At sea it is easy to ascertain the local time, e.g. by observing when the sun is highest in the sky, but the great difficulty, felt in Galilei’s time and long afterwards (chapter X., §§197, 226), was that of ascertaining the time at some standard place. Clocks were then, and long afterwards, not to be relied upon to keep time accurately during a long ocean voyage, and some astronomical means of determining the time was accordingly wanted. Galilei’s idea was that if the movements of Jupiter’s satellites, and in particular the eclipses which constantly occurred when a satellite passed into Jupiter’s shadow, could be predicted, then a table could be prepared giving the times, according to some standard place, say Rome, at which the eclipses would occur, and a sailor by observing the local time of an eclipse and comparing it with the time given in the table could ascertain by how much his longitude differed from that of Rome. It is, however, doubtful whether the movements of Jupiter’s satellites could at that time be predicted accurately enough to make the method practically useful, and in any case the negotiations came to nothing.

In 1618 three comets appeared, and Galilei was soon drawn into a controversy on the subject with a Jesuit of the name of Grassi. The controversy was marked by the personal bitterness which was customary, and soon developed so as to include larger questions of philosophy and astronomy. Galilei’s final contribution to it was published in 1623 under the title Il Saggiatore (The Assayer), which dealt incidentally with the Coppernican theory, though only in the indirect way which the edict of 1616 rendered necessary. In a characteristic passage, for example, Galilei says:—

“Since the motion attributed to the earth, which I, as a pious and Catholic person, consider most false, and not to exist, accommodates itself so well to explain so many and such different phenomena, I shall not feel sure ... that, false as it is, it may not just as deludingly correspond with the phenomena of comets”;

and again, in speaking of the rival systems of Coppernicus and Tycho, he says:—

“Then as to the Copernican hypothesis, if by the good fortune of us Catholics we had not been freed from error and our blindness illuminated by the Highest Wisdom, I do not believe that such grace and good fortune could have been obtained by means of the reasons and observations given by Tycho.”

Although in scientific importance the Saggiatore ranks far below many others of Galilei’s writings, it had a great reputation as a piece of brilliant controversial writing, and notwithstanding its thinly veiled Coppernicanism, the new Pope, Urban VIII., to whom it was dedicated, was so much pleased with it that he had it read aloud to him at meals. The book must, however, have strengthened the hands of Galilei’s enemies, and it was probably with a view to counteracting their influence that he went to Rome next year, to pay his respects to Urban and congratulate him on his recent elevation. The visit was in almost every way a success; Urban granted to him several friendly interviews, promised a pension for his son, gave him several presents, and finally dismissed him with a letter of special recommendation to the new Grand Duke of Tuscany, who had shewn some signs of being less friendly to Galilei than his father. On the other hand, however, the Pope refused to listen to Galilei’s request that the decree of 1616 should be withdrawn.128. Galilei now set seriously to work on the great astronomical treatise, the Dialogue on the Two Chief Systems of the World, the Ptolemaic and Coppernican, which he had had in mind as long ago as 1610, and in which he proposed to embody most of his astronomical work and to collect all the available evidence bearing on the Coppernican controversy. The form of a dialogue was chosen, partly for literary reasons, and still more because it enabled him to present the Coppernican case as strongly as he wished through the mouths of some of the speakers, without necessarily identifying his own opinions with theirs. The manuscript was almost completed in 1629, and in the following year Galilei went to Rome to obtain the necessary licence for printing it. The censor had some alterations made and then gave the desired permission for printing at Rome, on condition that the book was submitted to him again before being finally printed off. Soon after Galilei’s return to Florence the plague broke out, and quarantine difficulties rendered it almost necessary that the book should be printed at Florence instead of at Rome. This required a fresh licence, and the difficulty experienced in obtaining it shewed that the Roman censor was getting more and more doubtful about the book. Ultimately, however, the introduction and conclusion having been sent to Rome for approval and probably to some extent rewritten there, and the whole work having been approved by the Florentine censor, the book was printed and the first copies were ready early in 1632, bearing both the Roman and the Florentine imprimatur.129. The Dialogue extends over four successive days, and is carried on by three speakers, of whom Salviati is a Coppernican and Simplicio an Aristotelian philosopher, while Sagredo is avowedly neutral, but on almost every occasion either agrees with Salviati at once or is easily convinced by him, and frequently joins in casting ridicule upon the arguments of the unfortunate Simplicio. Though many of the arguments have now lost their immediate interest, and the book is unduly long, it is still very readable, and the specimens of scholastic reasoning put into the mouth of Simplicio and the refutation of them by the other speakers strike the modern reader as excellent fooling.

Many of the arguments used had been published by Galilei in earlier books, but gain impressiveness and cogency by being collected and systematically arranged. The Aristotelian dogma of the immutability of the celestial bodies is once more belaboured, and shewn to be not only inconsistent with observations of the moon, the sun, comets, and new stars, but to be in reality incapable of being stated in a form free from obscurity and self-contradiction. The evidence in favour of the earth’s motion derived from the existence of Jupiter’s satellites and from the undoubted phases of Venus, from the suspected phases of Mercury and from the variations in the apparent size of Mars, are once more insisted on. The greater simplicity of the Coppernican explanation of the daily motion of the celestial sphere and of the motion of the planets is forcibly urged and illustrated in detail. It is pointed out that on the Coppernican hypothesis all motions of revolution or rotation take place in the same direction (from west to east), whereas the Ptolemaic hypothesis requires some to be in one direction, some in another. Moreover the apparent daily motion of the stars, which appears simple enough if the stars are regarded as rigidly attached to a material sphere, is shewn in a quite different aspect if, as even Simplicio admits, no such sphere exists, and each star moves in some sense independently. A star near the pole must then be supposed to move far more slowly than one near the equator, since it describes a much smaller circle in the same time; and further—an argument very characteristic of Galilei’s ingenuity in drawing conclusions from known facts—owing to the precession of the equinoxes (chapter II., §42, and IV., §84) and the consequent change of the position of the pole among the stars, some of those stars which in Ptolemy’s time were describing very small circles, and therefore moving slowly, must now be describing large ones at a greater speed, and vice versa. An extremely complicated adjustment of motions becomes therefore necessary to account for observations which Coppernicus explained adequately by the rotation of the earth and a simple displacement of its axis of rotation.

Salviati deals also with the standing difficulty that the annual motion of the earth ought to cause a corresponding apparent motion of the stars, and that if the stars be assumed so far off that this motion is imperceptible, then some of the stars themselves must be at least as large as the earth’s orbit round the sun. Salviati points out that the apparent or angular magnitudes of the fixed stars, avowedly difficult to determine, are in reality almost entirely illusory, being due in great part to an optical effect known as irradiation, in virtue of which a bright object always tends to appear enlarged;75 and that there is in consequence no reason to suppose the stars nearly as large as they might otherwise be thought to be. It is suggested also that the most promising way of detecting the annual motion of stars resulting from the motion of the earth would be by observing the relative displacement of two stars close together in the sky (and therefore nearly in the same direction), of which one might be presumed from its greater brightness to be nearer than the other. It is, for example, evident that if, in the figure, E, E' represent two positions of the earth in its path round the sun, and A, B two stars at different distances, but nearly in the same direction, then to the observer at E the star A appears to the left of B, whereas six months afterwards, when the observer is at E', A appears to the right of B. Such a motion of one star with respect to another close to it would be much more easily observed than an alteration of the same amount in the distance of the star from some standard point such as the pole. Salviati points out that accurate observations of this kind had not been made, and that the telescope might be of assistance for the purpose. This method, known as the double-star or differential method of parallax, was in fact the first to lead—two centuries later—to a successful detection of the motion in question (chapter XIII., §278).

130. Entirely new ground is broken in the Dialogue when 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 of force, 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 by some 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 supposed perfectly smooth, 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 to the 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.76 Similarly, 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 the Dialogue is 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 deal correctly with a problem of which the vastly more powerful resources of modern science can only give an imperfect solution (cf. chapter XI., §248, and chapter XIII., §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 in Rome a 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 in Rome, 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 in Italy, and particularly in Rome, as Transalpine Diligence can imagine it to be: and collecting together all the proper speculations that concerne the Copernican Systeme to let them know, that the notice of all preceded the Censure of the Roman 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 Mathematical Capriccio, 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 been examining 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,78 and 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.79 On 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.

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 the Dialogue to the three Coppernican books condemned in 1616, and to Kepler’s Epitome of the Coppernican Astronomy (chapter VII., §145), which had been put on the Index shortly afterwards. It may be of interest to note that these five books still remained in the edition of the Index of Prohibited Books which 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.

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 the observer from A, where he sees the moon rising, to B, where he sees it setting. When he is at C, on the line joining the centres of the earth and moon, the point O appears to be in the centre of the moon’s disc, and the portion c O c' is visible, c R c' invisible. But when the observer is at A, the point P, on the right of O, appears in the centre, and the portion a P a' is visible, so that c' a' is now visible and a c invisible. In the same way, when the observer is at B, he can see the portion c b, while b' c' is invisible and Q appears to be in the centre of the disc. Thus in the course of the day the portion a O b' (dotted in the figure) is constantly visible and b R a' (also dotted) constantly invisible, while a c b and a' 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 as librations of 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 which bodies 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,80 which 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 of uniformly accelerated motion, or uniform 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.81 From 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 unaffected by 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 the Two New Sciences was 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 in astronomy 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 by Galilei’s own statement of it, as applied to a particular case:—

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