Tycho accepted the apology thus heartily rendered, and the temporary breach was permanently healed.

In 1601, Kepler was appointed "Imperial mathematician," to assist Tycho in his calculations.

The Emperor Rudolph did a good piece of work in thus maintaining these two eminent men, but it is quite clear that it was as astrologers that he valued them; and all he cared for in the planetary motions was limited to their supposed effect on his own and his kingdom's destiny. He seems to have been politically a weak and superstitious prince, who was letting his kingdom get into hopeless confusion, and entangling himself in all manner of political complications. While Bohemia suffered, however, the world has benefited at his hands; and the tables upon which Tycho was now engaged are well called the Rudolphine tables.

These tables of planetary motion Tycho had always regarded as the main work of his life; but he died before they were finished, and on his death-bed he intrusted the completion of them to Kepler, who loyally undertook their charge.

The Imperial funds were by this time, however, so taxed by wars and other difficulties that the tables could only be proceeded with very slowly, a staff of calculators being out of the question. In fact, Kepler could not get even his own salary paid: he got orders, and promises, and drafts on estates for it; but when the time came for them to be honoured they were worthless, and he had no power to enforce his claims.

So everything but brooding had to be abandoned as too expensive, and he proceeded to study optics. He gave a very accurate explanation of the action of the human eye, and made many hypotheses, some of them shrewd and close to the mark, concerning the law of refraction of light in dense media: but though several minor points of interest turned up, nothing of the first magnitude came out of this long research.

The true law of refraction was discovered some years after by a Dutch professor, Willebrod Snell.

We must now devote a little time to the main work of Kepler's life. All the time he had been at Prague he had been making a severe study of the motion of the planet Mars, analyzing minutely Tycho's books of observations, in order to find out, if possible, the true theory of his motion. Aristotle had taught that circular motion was the only perfect and natural motion, and that the heavenly bodies therefore necessarily moved in circles.

So firmly had this idea become rooted in men's minds, that no one ever seems to have contemplated the possibility of its being false or meaningless.

When Hipparchus and others found that, as a matter of fact, the planets did not revolve in simple circles, they did not try other curves, as we should at once do now, but they tried combinations of circles, as we saw in Lecture I. The small circle carried by a bigger one was called an Epicycle. The carrying circle was called the Deferent. If for any reason the earth had to be placed out of the centre, the main planetary orbit was called an Excentric, and so on.

But although the planetary paths might be roughly represented by a combination of circles, their speeds could not, on the hypothesis of uniform motion in each circle round the earth as a fixed body. Hence was introduced the idea of an Equant, i.e. an arbitrary point, not the earth, about which the speed might be uniform. Copernicus, by making the sun the centre, had been able to simplify a good deal of this, and to abolish the equant.

But now that Kepler had the accurate observations of Tycho to refer to, he found immense difficulty in obtaining the true positions of the planets for long together on any such theory.

He specially attacked the motion of the planet Mars, because that was sufficiently rapid in its changes for a considerable collection of data to have accumulated with respect to it. He tried all manner of circular orbits for the earth and for Mars, placing them in all sorts of aspects with respect to the sun. The problem to be solved was to choose such an orbit and such a law of speed, for both the earth and Mars, that a line joining them, produced out to the stars, should always mark correctly the apparent position of Mars as seen from the earth. He had to arrange the size of the orbits that suited best, then the positions of their centres, both being supposed excentric with respect to the sun; but he could not get any such arrangement to work with uniform motion about the sun. So he reintroduced the equant, and thus had another variable at his disposal—in fact, two, for he had an equant for the earth and another for Mars, getting a pattern of the kind suggested in Fig. 29.

The equants might divide the line in any arbitrary ratio. All sorts of combinations had to be tried, the relative positions of the earth and Mars to be worked out for each, and compared with Tycho's recorded observations. It was easy to get them to agree for a short time, but sooner or later a discrepancy showed itself.



I need not say that all these attempts and gropings, thus briefly summarized, entailed enormous labour, and required not only great pertinacity, but a most singularly constituted mind, that could thus continue groping in the dark without a possible ray of theory to illuminate its search. Grope he did, however, with unexampled diligence.

At length he hit upon a point that seemed nearly right. He thought he had found the truth; but no, before long the position of the planet, as calculated, and as recorded by Tycho, differed by eight minutes of arc, or about one-eighth of a degree. Could the observation be wrong by this small amount? No, he had known Tycho, and knew that he was never wrong eight minutes in an observation.

So he set out the whole weary way again, and said that with those eight minutes he would yet find out the law of the universe. He proceeded to see if by making the planet librate, or the plane of its orbit tilt up and down, anything could be done. He was rewarded by finding that at any rate the plane of the orbit did not tilt up and down: it was fixed, and this was a simplification on Copernicus's theory. It is not an absolute fixture, but the changes are very small (see Laplace, page 266).



At last he thought of giving up the idea of uniform circular motion, and of trying varying circular motion, say inversely as its distance from the sun. To simplify calculation, he divided the orbit into triangles, and tried if making the triangles equal would do. A great piece of luck, they did beautifully: the rate of description of areas (not arcs) is uniform. Over this discovery he greatly rejoices. He feels as though he had been carrying on a war against the planet and had triumphed; but his gratulation was premature. Before long fresh little errors appeared, and grew in importance. Thus he announces it himself:—

"While thus triumphing over Mars, and preparing for him, as for one already vanquished, tabular prisons and equated excentric fetters, it is buzzed here and there that the victory is vain, and that the war is raging anew as violently as before. For the enemy left at home a despised captive has burst all the chains of the equations, and broken forth from the prisons of the tables."

Still, a part of the truth had been gained, and was not to be abandoned any more. The law of speed was fixed: that which is now known as his second law. But what about the shape of the orbit—Was it after all possible that Aristotle, and every philosopher since Aristotle, had been wrong? that circular motion was not the perfect and natural motion, but that planets might move in some other closed curve?

Suppose he tried an oval. Well, there are a great variety of ovals, and several were tried: with the result that they could be made to answer better than a circle, but still were not right.

Now, however, the geometrical and mathematical difficulties of calculation, which before had been tedious and oppressive, threatened to become overwhelming; and it is with a rising sense of despondency that Kepler sees his six years' unremitting labour leading deeper and deeper into complication.

One most disheartening circumstance appeared, viz. that when he made the circuit oval his law of equable description of areas broke down. That seemed to require the circular orbit, and yet no circular orbit was quite accurate.

While thinking and pondering for weeks and months over this new dilemma and complication of difficulties, till his brain reeled, an accidental ray of light broke upon him in a way not now intelligible, or barely intelligible. Half the extreme breadth intercepted between the circle and oval was 429/100,000 of the radius, and he remembered that the "optical inequality" of Mars was also about 429/100,000. This coincidence, in his own words, woke him out of sleep; and for some reason or other impelled him instantly to try making the planet oscillate in the diameter of its epicycle instead of revolve round it—a singular idea, but Copernicus had had a similar one to explain the motions of Mercury.



Away he started through his calculations again. A long course of work night and day was rewarded by finding that he was now able to hit off the motions better than before; but what a singularly complicated motion it was. Could it be expressed no more simply? Yes, the curve so described by the planet is a comparatively simple one: it is a special kind of oval—the ellipse. Strange that he had not thought of it before. It was a famous curve, for the Greek geometers had studied it as one of the sections of a cone, but it was not so well known in Kepler's time. The fact that the planets move in it has raised it to the first importance, and it is familiar enough to us now. But did it satisfy the law of speed? Could the rate of description of areas be uniform with it? Well, he tried the ellipse, and to his inexpressible delight he found that it did satisfy the condition of equable description of areas, if the sun was in one focus. So, moving the planet in a selected ellipse, with the sun in one focus, at a speed given by the equable area description, its position agreed with Tycho's observations within the limits of the error of experiment. Mars was finally conquered, and remains in his prison-house to this day. The orbit was found.



In a paroxysm of delight Kepler celebrates his victory by a triumphant figure, sketched actually on his geometrical diagram—the diagram which proves that the law of equable description of areas can hold good with an ellipse. The above is a tracing of it.

Such is a crude and bald sketch of the steps by which Kepler rose to his great generalizations—the two laws which have immortalized his name.

All the complications of epicycle, equant, deferent, excentric, and the like, were swept at once away, and an orbit of striking and beautiful properties substituted. Well might he be called, as he was, "the legislator," or law interpreter, "of the heavens."



He concludes his book on the motions of Mars with a half comic appeal to the Emperor to provide him with the sinews of war for an attack on Mars's relations—father Jupiter, brother Mercury, and the rest—but the death of his unhappy patron in 1612 put an end to all these schemes, and reduced Kepler to the utmost misery. While at Prague his salary was in continual arrear, and it was with difficulty that he could provide sustenance for his family. He had been there eleven years, but they had been hard years of poverty, and he could leave without regret were it not that he should have to leave Tycho's instruments and observations behind him. While he was hesitating what best to do, and reduced to the verge of despair, his wife, who had long been suffering from low spirits and despondency, and his three children, were taken ill; one of the sons died of small-pox, and the wife eleven days after of low fever and epilepsy. No money could be got at Prague, so after a short time he accepted a professorship at Linz, and withdrew with his two quite young remaining children.

He provided for himself now partly by publishing a prophesying almanack, a sort of Zadkiel arrangement—a thing which he despised, but the support of which he could not afford to do without. He is continually attacking and throwing sarcasm at astrology, but it was the only thing for which people would pay him, and on it after a fashion he lived. We do not find that his circumstances were ever prosperous, and though 8,000 crowns were due to him from Bohemia he could not manage to get them paid.

About this time occurred a singular interruption to his work. His old mother, of whose fierce temper something has already been indicated, had been engaged in a law-suit for some years near their old home in Wuertemberg. A change of judge having in process of time occurred, the defendant saw his way to turn the tables on the old lady by accusing her of sorcery. She was sent to prison, and condemned to the torture, with the usual intelligent idea of extracting a "voluntary" confession. Kepler had to hurry from Linz to interpose. He succeeded in saving her from the torture, but she remained in prison for a year or so. Her spirit, however, was unbroken, for no sooner was she released than she commenced a fresh action against her accuser. But fresh trouble was averted by the death of the poor old dame at the age of nearly eighty.

This narration renders the unflagging energy shown by her son in his mathematical wrestlings less surprising.

Interspersed with these domestic troubles, and with harassing and unsuccessful attempts to get his rights, he still brooded over his old problem of some possible connection between the distances of the planets from the sun and their times of revolution, i.e. the length of their years.

It might well have been that there was no connection, that it was purely imaginary, like his old idea of the law of the successive distances of the planets, and like so many others of the guesses and fancies which he entertained and spent his energies in probing. But fortunately this time there was a connection, and he lived to have the joy of discovering it.

The connection is this, that if one compares the distance of the different planets from the sun with the length of time they take to go round him, the cube of the respective distances is proportional to the square of the corresponding times. In other words, the ratio of r^3 to T^2 for every planet is the same. Or, again, the length of a planet's year depends on the 3/2th power of its distance from the sun. Or, once more, the speed of each planet in its orbit is as the inverse square-root of its distance from the sun. The product of the distance into the square of the speed is the same for each planet.

This (however stated) is called Kepler's third law. It welds the planets together, and shows them to be one system. His rapture on detecting the law was unbounded, and he breaks out into an exulting rhapsody:—

"What I prophesied two-and-twenty years ago, as soon as I discovered the five solids among the heavenly orbits—what I firmly believed long before I had seen Ptolemy's Harmonies—what I had promised my friends in the title of this book, which I named before I was sure of my discovery—what sixteen years ago, I urged as a thing to be sought—that for which I joined Tycho Brahe, for which I settled in Prague, for which I have devoted the best part of my life to astronomical contemplations, at length I have brought to light, and recognized its truth beyond my most sanguine expectations. It is not eighteen months since I got the first glimpse of light, three months since the dawn, very few days since the unveiled sun, most admirable to gaze upon, burst upon me. Nothing holds me; I will indulge my sacred fury; I will triumph over mankind by the honest confession that I have stolen the golden vases of the Egyptians to build up a tabernacle for my God far away from the confines of Egypt. If you forgive me, I rejoice; if you are angry, I can bear it; the die is cast, the book is written, to be read either now or by posterity, I care not which; it may well wait a century for a reader, as God has waited six thousand years for an observer."

Soon after this great work his third book appeared: it was an epitome of the Copernican theory, a clear and fairly popular exposition of it, which had the honour of being at once suppressed and placed on the list of books prohibited by the Church, side by side with the work of Copernicus himself, De Revolutionibus Orbium Coelestium.

This honour, however, gave Kepler no satisfaction—it rather occasioned him dismay, especially as it deprived him of all pecuniary benefit, and made it almost impossible for him to get a publisher to undertake another book.

Still he worked on at the Rudolphine tables of Tycho, and ultimately, with some small help from Vienna, completed them; but he could not get the means to print them. He applied to the Court till he was sick of applying: they lay idle four years. At last he determined to pay for the type himself. What he paid it with, God knows, but he did pay it, and he did bring out the tables, and so was faithful to the behest of his friend.

This great publication marks an era in astronomy. They were the first really accurate tables which navigators ever possessed; they were the precursors of our present Nautical Almanack.

After this, the Grand Duke of Tuscany sent Kepler a golden chain, which is interesting inasmuch as it must really have come from Galileo, who was in high favour at the Italian Court at this time.

Once more Kepler made a determined attempt to get his arrears of salary paid, and rescue himself and family from their bitter poverty. He travelled to Prague on purpose, attended the imperial meeting, and pleaded his own cause, but it was all fruitless; and exhausted by the journey, weakened by over-study, and disheartened by the failure, he caught a fever, and died in his fifty-ninth year. His body was buried at Ratisbon, and a century ago a proposal was made to erect a marble monument to his memory, but nothing was done. It matters little one way or the other whether Germany, having almost refused him bread during his life, should, a century and a half after his death, offer him a stone.



The contiguity of the lives of Kepler and Tycho furnishes a moral too obvious to need pointing out. What Kepler might have achieved had he been relieved of those ghastly struggles for subsistence one cannot tell, but this much is clear, that had Tycho been subjected to the same misfortune, instead of being born rich and being assisted by generous and enlightened patrons, he could have accomplished very little. His instruments, his observatory—the tools by which he did his work—would have been impossible for him. Frederick and Sophia of Denmark, and Rudolph of Bohemia, are therefore to be remembered as co-workers with him.

Kepler, with his ill-health and inferior physical energy, was unable to command the like advantages. Much, nevertheless, he did; more one cannot but feel he might have done had he been properly helped. Besides, the world would have been free from the reproach of accepting the fruits of his bright genius while condemning the worker to a life of misery, relieved only by the beauty of his own thoughts and the ecstasy awakened in him by the harmony and precision of Nature.

Concerning the method of Kepler, the mode by which he made his discoveries, we must remember that he gives us an account of all the steps, unsuccessful as well as successful, by which he travelled. He maps out his route like a traveller. In fact he compares himself to Columbus or Magellan, voyaging into unknown lands, and recording his wandering route. This being remembered, it will be found that his methods do not differ so utterly from those used by other philosophers in like case. His imagination was perhaps more luxuriant and was allowed freer play than most men's, but it was nevertheless always controlled by rigid examination and comparison of hypotheses with fact.

Brewster says of him:—"Ardent, restless, burning to distinguish himself by discovery, he attempted everything; and once having obtained a glimpse of a clue, no labour was too hard in following or verifying it. A few of his attempts succeeded—a multitude failed. Those which failed seem to us now fanciful, those which succeeded appear to us sublime. But his methods were the same. When in search of what really existed he sometimes found it; when in pursuit of a chimaera he could not but fail; but in either case he displayed the same great qualities, and that obstinate perseverance which must conquer all difficulties except those really insurmountable."

To realize what he did for astronomy, it is necessary for us now to consider some science still in its infancy. Astronomy is so clear and so thoroughly explored now, that it is difficult to put oneself into a contemporary attitude. But take some other science still barely developed: meteorology, for instance. The science of the weather, the succession of winds and rain, sunshine and frost, clouds and fog, is now very much in the condition of astronomy before Kepler.

We have passed through the stage of ascribing atmospheric disturbances—thunderstorms, cyclones, earthquakes, and the like—to supernatural agency; we have had our Copernican era: not perhaps brought about by a single individual, but still achieved. Something of the laws of cyclone and anticyclone are known, and rude weather predictions across the Atlantic are roughly possible. Barometers and thermometers and anemometers, and all their tribe, represent the astronomical instruments in the island of Huen; and our numerous meteorological observatories, with their continual record of events, represent the work of Tycho Brahe.

Observation is heaped on observation; tables are compiled; volumes are filled with data; the hours of sunshine are recorded, the fall of rain, the moisture in the air, the kind of clouds, the temperature—millions of facts; but where is the Kepler to study and brood over them? Where is the man to spend his life in evolving the beginnings of law and order from the midst of all this chaos?

Perhaps as a man he may not come, but his era will come. Through this stage the science must pass, ere it is ready for the commanding intellect of a Newton.

But what a work it will be for the man, whoever he be that undertakes it—a fearful monotonous grind of calculation, hypothesis, hypothesis, calculation, a desperate and groping endeavour to reconcile theories with facts.

A life of such labour, crowned by three brilliant discoveries, the world owes (and too late recognizes its obligation) to the harshly treated German genius, Kepler.



SUMMARY OF FACTS FOR LECTURES IV AND V

In 1564, Michael Angelo died and Galileo was born; in 1642, Galileo died and Newton was born. Milton lived from 1608 to 1674.

For teaching the plurality of worlds, with other heterodox doctrines, and refusing to recant, Bruno, after six years' imprisonment in Rome, was burnt at the stake on the 16th of February, 1600 A.D. A "natural" death in the dungeons of the Inquisition saved Antonio de Dominis, the explainer of the rainbow, from the same fate, but his body and books were publicly burned at Rome in 1624.

The persecution of Galileo began in 1615, became intense in 1632, and so lasted till his death and after.

* * * * *

Galileo Galilei, eldest son of Vincenzo de Bonajuti de Galilei, a noble Florentine, was born at Pisa, 18th of February, 1564. At the age of 17 was sent to the University of Pisa to study medicine. Observed the swing of a pendulum and applied it to count pulse-beats. Read Euclid and Archimedes, and could be kept at medicine no more. At 26 was appointed Lecturer in Mathematics at Pisa. Read Bruno and became smitten with the Copernican theory. Controverted the Aristotelians concerning falling bodies, at Pisa. Hence became unpopular and accepted a chair at Padua, 1592. Invented a thermometer. Wrote on astronomy, adopting the Ptolemaic system provisionally, and so opened up a correspondence with Kepler, with whom he formed a friendship. Lectured on the new star of 1604, and publicly renounced the old systems of astronomy. Invented a calculating compass or "Gunter's scale." In 1609 invented a telescope, after hearing of a Dutch optician's discovery. Invented the microscope soon after. Rapidly completed a better telescope and began a survey of the heavens. On the 8th of January, 1610, discovered Jupiter's satellites. Observed the mountains in the moon, and roughly measured their height. Explained the visibility of the new moon by earth-shine. Was invited to the Grand Ducal Court of Tuscany by Cosmo de Medici, and appointed philosopher to that personage. Discovered innumerable new stars, and the nebulae. Observed a triple appearance of Saturn. Discovered the phases of Venus predicted by Copernicus, and spots on the sun. Wrote on floating bodies. Tried to get his satellites utilized for determining longitude at sea.

Went to Rome to defend the Copernican system, then under official discussion, and as a result was formally forbidden ever to teach it. On the accession of Pope Urban VIII. in 1623, Galileo again visited Rome to pay his respects, and was well received. In 1632 appeared his "Dialogues" on the Ptolemaic and Copernican systems. Summoned to Rome, practically imprisoned, and "rigorously questioned." Was made to recant 22nd of June, 1633. Forbidden evermore to publish anything, or to teach, or receive friends. Retired to Arcetri in broken down health. Death of his favourite daughter, Sister Maria Celeste. Wrote and meditated on the laws of motion. Discovered the moon's libration. In 1637 he became blind. The rigour was then slightly relaxed and many visited him: among them John Milton. Died 8th of January, 1642, aged 78. As a prisoner of the Inquisition his right to make a will or to be buried in consecrated ground was disputed. Many of his manuscripts were destroyed.

Galileo, besides being a singularly clear-headed thinker and experimental genius, was also something of a musician, a poet, and an artist. He was full of humour as well as of solid common-sense, and his literary style is brilliant. Of his scientific achievements those now reckoned most weighty, are the discovery of the Laws of Motion, and the laying of the foundations of Mechanics.

Particulars of Jupiter's Satellites, Illustrating their obedience to Kepler's third law.

Distance T^2 Time of from Satellite. Diameter revolution Jupiter, T^2 d^3 d^3 miles. in hours. in Jovian which is miles (T) radii. practically (d) constant. - - - - No. 1. 2437 42.47 6.049 1803.7 221.44 8.149 No. 2. 2188 85.23 9.623 7264.1 891.11 8.152 No. 3. 3575 177.72 15.350 29488. 3916.8 8.153 No. 4. 3059 400.53 26.998 160426. 19679. 8.152

The diameter of Jupiter is 85,823 miles.

Falling Bodies.

Since all bodies fall at the same rate, except for the disturbing effect of the resistance of the air, a statement of their rates of fall is of interest. In one second a freely falling body near the earth is found to drop 16 feet. In two seconds it drops 64 feet altogether, viz. 16 feet in the first, and 48 feet in the next second; because at the beginning of every second after the first it has the accumulated velocity of preceding seconds. The height fallen by a dropped body is not proportional to the time simply, but to what is rather absurdly called the square of the time, i.e. the time multiplied by itself.

For instance, in 3 seconds it drops 9 x 16 = 144 feet; in 4 seconds 16 x 16, or 256 feet, and so on. The distances travelled in 1, 2, 3, 4, &c., seconds by a body dropped from rest and not appreciably resisted by the air, are 1, 4, 9, 16, 25, &c., respectively, each multiplied by the constant 16 feet.

Another way of stating the law is to say that the heights travelled in successive seconds proceed in the proportion 1, 3, 5, 7, 9, &c.; again multiplied by 16 feet in each case.



All this was experimentally established by Galileo.

A body takes half a second to drop 4 feet; and a quarter of a second to drop 1 foot. The easiest way of estimating a quarter of a second with some accuracy is to drop a bullet one foot.

A bullet thrown or shot in any direction falls just as much as if merely dropped; but instead of falling from the starting-point it drops vertically from the line of fire. (See fig. 35).

The rate of fall depends on the intensity of gravity; if it could be doubled, a body would fall twice as far in the same time; but to make it fall a given distance in half the time the intensity of gravity would have to be quadrupled. At a place where the intensity of gravity is 1/3600 of what it is here, a body would fall as far in a minute as it now falls in a second. Such a place occurs at about the distance of the moon (cf. page 177).

The fact that the height fallen through is proportional to the square of the time proves that the attraction of the earth or the intensity of gravity is sensibly constant throughout ordinary small ranges. Over great distances of fall, gravity cannot be considered constant; so for things falling through great spaces the Galilean law of the square of the time does not hold.

The fact that things near the earth fall 16 feet in the first second proves that the intensity of ordinary terrestrial gravity is 32 British units of force per pound of matter.

The fact that all bodies fall at the same rate (when the resistance of the air is eliminated), proves that weight is proportional to mass; or more explicitly, that the gravitative attraction of the earth on matter near its surface depends on the amount of that matter, as estimated by its inertia, and on nothing else.



LECTURE IV

GALILEO AND THE INVENTION OF THE TELESCOPE

Contemporary with the life of Kepler, but overlapping it at both ends, comes the great and eventful life of Galileo Galilei,[5] a man whose influence on the development of human thought has been greater than that of any man whom we have yet considered, and upon whom, therefore, it is necessary for us, in order to carry out the plan of these lectures, to bestow much time. A man of great and wide culture, a so-called universal genius, it is as an experimental philosopher that he takes the first rank. In this capacity he must be placed alongside of Archimedes, and it is pretty certain that between the two there was no man of magnitude equal to either in experimental philosophy. It is perhaps too bold a speculation, but I venture to doubt whether in succeeding generations we find his equal in the domain of purely experimental science until we come to Faraday. Faraday was no doubt his superior, but I know of no other of whom the like can unhesitatingly be said. In mathematical and deductive science, of course, it is quite otherwise. Kepler, for instance, and many men before and since, have far excelled Galileo in mathematical skill and power, though at the same time his achievements in this department are by no means to be despised.

Born at Pisa three centuries ago, on the very day that Michael Angelo lay dying in Rome, he inherited from his father a noble name, cultivated tastes, a keen love of truth, and an impoverished patrimony. Vincenzo de Galilei, a descendant of the important Bonajuti family, was himself a mathematician and a musician, and in a book of his still extant he declares himself in favour of free and open inquiry into scientific matters, unrestrained by the weight of authority and tradition.

In all probability the son imbibed these precepts: certainly he acted on them.

Vincenzo, having himself experienced the unremunerative character of scientific work, had a horror of his son's taking to it, especially as in his boyhood he was always constructing ingenious mechanical toys, and exhibiting other marks of precocity. So the son was destined for business—to be, in fact, a cloth-dealer. But he was to receive a good education first, and was sent to an excellent convent school.

Here he made rapid progress, and soon excelled in all branches of classics and literature. He delighted in poetry, and in later years wrote several essays on Dante, Tasso, and Ariosto, besides composing some tolerable poems himself. He played skilfully on several musical instruments, especially on the lute, of which indeed he became a master, and on which he solaced himself when quite an old man. Besides this he seems to have had some skill as an artist, which was useful afterwards in illustrating his discoveries, and to have had a fine sensibility as an art critic, for we find several eminent painters of that day acknowledging the value of the opinion of the young Galileo.

Perceiving all this display of ability, the father wisely came to the conclusion that the selling of woollen stuffs would hardly satisfy his aspirations for long, and that it was worth a sacrifice to send him to the University. So to the University of his native town he went, with the avowed object of studying medicine, that career seeming the most likely to be profitable. Old Vincenzo's horror of mathematics or science as a means of obtaining a livelihood is justified by the fact that while the University Professor of Medicine received 2,000 scudi a year, the Professor of Mathematics had only 60, that is L13 a year, or 7-1/2d. a day.

So the son had been kept properly ignorant of such poverty-stricken subjects, and to study medicine he went.

But his natural bent showed itself even here. For praying one day in the Cathedral, like a good Catholic as he was all his life, his attention was arrested by the great lamp which, after lighting it, the verger had left swinging to and fro. Galileo proceeded to time its swings by the only watch he possessed—viz., his own pulse. He noticed that the time of swing remained as near as he could tell the same, notwithstanding the fact that the swings were getting smaller and smaller.

By subsequent experiment he verified the law, and the isochronism of the pendulum was discovered. An immensely important practical discovery this, for upon it all modern clocks are based; and Huyghens soon applied it to the astronomical clock, which up to that time had been a crude and quite untrustworthy instrument.

The best clock which Tycho Brahe could get for his observatory was inferior to one that may now be purchased for a few shillings; and this change is owing to the discovery of the pendulum by Galileo. Not that he applied it to clocks; he was not thinking of astronomy, he was thinking of medicine, and wanted to count people's pulses. The pendulum served; and "pulsilogies," as they were called, were thus introduced to and used by medical practitioners.

The Tuscan Court came to Pisa for the summer months, for it was then a seaside place, and among the suite was Ostillio Ricci, a distinguished mathematician and old friend of the Galileo family. The youth visited him, and one day, it is said, heard a lesson in Euclid being given by Ricci to the pages while he stood outside the door entranced. Anyhow he implored Ricci to help him into some knowledge of mathematics, and the old man willingly consented. So he mastered Euclid and passed on to Archimedes, for whom he acquired a great veneration.

His father soon heard of this obnoxious proclivity, and did what he could to divert him back to medicine again. But it was no use. Underneath his Galen and Hippocrates were secreted copies of Euclid and Archimedes, to be studied at every available opportunity. Old Vincenzo perceived the bent of genius to be too strong for him, and at last gave way.



With prodigious rapidity the released philosopher now assimilated the elements of mathematics and physics, and at twenty-six we find him appointed for three years to the University Chair of Mathematics, and enjoying the paternally dreaded stipend of 7-1/2d. a day.

Now it was that he pondered over the laws of falling bodies. He verified, by experiment, the fact that the velocity acquired by falling down any slope of given height was independent of the angle of slope. Also, that the height fallen through was proportional to the square of the time.

Another thing he found experimentally was that all bodies, heavy and light, fell at the same rate, striking the ground at the same time.[6]

Now this was clean contrary to what he had been taught. The physics of those days were a simple reproduction of statements in old books. Aristotle had asserted certain things to be true, and these were universally believed. No one thought of trying the thing to see if it really were so. The idea of making an experiment would have savoured of impiety, because it seemed to tend towards scepticism, and cast a doubt on a reverend authority.

Young Galileo, with all the energy and imprudence of youth (what a blessing that youth has a little imprudence and disregard of consequences in pursuing a high ideal!), as soon as he perceived that his instructors were wrong on the subject of falling bodies, instantly informed them of the fact. Whether he expected them to be pleased or not is a question. Anyhow, they were not pleased, but were much annoyed by his impertinent arrogance.

It is, perhaps, difficult for us now to appreciate precisely their position. These doctrines of antiquity, which had come down hoary with age, and the discovery of which had reawakened learning and quickened intellectual life, were accepted less as a science or a philosophy, than as a religion. Had they regarded Aristotle as a verbally inspired writer, they could not have received his statements with more unhesitating conviction. In any dispute as to a question of fact, such as the one before us concerning the laws of falling bodies, their method was not to make an experiment, but to turn over the pages of Aristotle; and he who could quote chapter and verse of this great writer was held to settle the question and raise it above the reach of controversy.

It is very necessary for us to realize this state of things clearly, because otherwise the attitude of the learned of those days towards every new discovery seems stupid and almost insane. They had a crystallized system of truth, perfect, symmetrical—it wanted no novelty, no additions; every addition or growth was an imperfection, an excrescence, a deformity. Progress was unnecessary and undesired. The Church had a rigid system of dogma, which must be accepted in its entirety on pain of being treated as a heretic. Philosophers had a cast-iron system of truth to match—a system founded upon Aristotle—and so interwoven with the great theological dogmas that to question one was almost equivalent to casting doubt upon the other.

In such an atmosphere true science was impossible. The life-blood of science is growth, expansion, freedom, development. Before it could appear it must throw off these old shackles of centuries. It must burst its old skin, and emerge, worn with the struggle, weakly and unprotected, but free and able to grow and to expand. The conflict was inevitable, and it was severe. Is it over yet? I fear not quite, though so nearly as to disturb science hardly at all. Then it was different; it was terrible. Honour to the men who bore the first shock of the battle!

Now Aristotle had said that bodies fell at rates depending on their weight.

A 5 lb. weight would fall five times as quick as a 1 lb. weight; a 50 lb. weight fifty times as quick, and so on.

Why he said so nobody knows. He cannot have tried. He was not above trying experiments, like his smaller disciples; but probably it never occurred to him to doubt the fact. It seems so natural that a heavy body should fall quicker than a light one; and perhaps he thought of a stone and a feather, and was satisfied.

Galileo, however, asserted that the weight did not matter a bit, that everything fell at the same rate (even a stone and a feather, but for the resistance of the air), and would reach the ground in the same time.

And he was not content to be pooh-poohed and snubbed. He knew he was right, and he was determined to make every one see the facts as he saw them. So one morning, before the assembled University, he ascended the famous leaning tower, taking with him a 100 lb. shot and a 1 lb. shot. He balanced them on the edge of the tower, and let them drop together. Together they fell, and together they struck the ground.

The simultaneous clang of those two weights sounded the death-knell of the old system of philosophy, and heralded the birth of the new.

But was the change sudden? Were his opponents convinced? Not a jot. Though they had seen with their eyes, and heard with their ears, the full light of heaven shining upon them, they went back muttering and discontented to their musty old volumes and their garrets, there to invent occult reasons for denying the validity of the observation, and for referring it to some unknown disturbing cause.

They saw that if they gave way on this one point they would be letting go their anchorage, and henceforward would be liable to drift along with the tide, not knowing whither. They dared not do this. No; they must cling to the old traditions; they could not cast away their rotting ropes and sail out on to the free ocean of God's truth in a spirit of fearless faith.



Yet they had received a shock: as by a breath of fresh salt breeze and a dash of spray in their faces, they had been awakened out of their comfortable lethargy. They felt the approach of a new era.

Yes, it was a shock; and they hated the young Galileo for giving it them—hated him with the sullen hatred of men who fight for a lost and dying cause.

We need scarcely blame these men; at least we need not blame them overmuch. To say that they acted as they did is to say that they were human, were narrow-minded, and were the apostles of a lost cause. But they could not know this; they had no experience of the past to guide them; the conditions under which they found themselves were novel, and had to be met for the first time. Conduct which was excusable then would be unpardonable now, in the light of all this experience to guide us. Are there any now who practically repeat their error, and resist new truth? who cling to any old anchorage of dogma, and refuse to rise with the tide of advancing knowledge? There may be some even now.

Well, the unpopularity of Galileo smouldered for a time, until, by another noble imprudence, he managed to offend a semi-royal personage, Giovanni de Medici, by giving his real opinion, when consulted, about a machine which de Medici had invented for cleaning out the harbour of Leghorn. He said it was as useless as it in fact turned out to be. Through the influence of the mortified inventor he lost favour at Court; and his enemies took advantage of the fact to render his chair untenable. He resigned before his three years were up, and retired to Florence.

His father at this time died, and the family were left in narrow circumstances. He had a brother and three sisters to provide for.

He was offered a professorship at Padua for six years by the Senate of Venice, and willingly accepted it.

Now began a very successful career. His introductory address was marked by brilliant eloquence, and his lectures soon acquired fame. He wrote for his pupils on the laws of motion, on fortifications, on sundials, on mechanics, and on the celestial globe: some of these papers are now lost, others have been printed during the present century.

Kepler sent him a copy of his new book, Mysterium Cosmographicum, and Galileo in thanking him for it writes him the following letter:—[7]

"I count myself happy, in the search after truth, to have so great an ally as yourself, and one who is so great a friend of the truth itself. It is really pitiful that there are so few who seek truth, and who do not pursue a perverse method of philosophising. But this is not the place to mourn over the miseries of our times, but to congratulate you on your splendid discoveries in confirmation of truth. I shall read your book to the end, sure of finding much that is excellent in it. I shall do so with the more pleasure, because I have been for many years an adherent of the Copernican system, and it explains to me the causes of many of the appearances of nature which are quite unintelligible on the commonly accepted hypothesis. I have collected many arguments for the purpose of refuting the latter; but I do not venture to bring them to the light of publicity, for fear of sharing the fate of our master, Copernicus, who, although he has earned immortal fame with some, yet with very many (so great is the number of fools) has become an object of ridicule and scorn. I should certainly venture to publish my speculations if there were more people like you. But this not being the case, I refrain from such an undertaking."

Kepler urged him to publish his arguments in favour of the Copernican theory, but he hesitated for the present, knowing that his declaration would be received with ridicule and opposition, and thinking it wiser to get rather more firmly seated in his chair before encountering the storm of controversy.

The six years passed away, and the Venetian Senate, anxious not to lose so bright an ornament, renewed his appointment for another six years at a largely increased salary.

Soon after this appeared a new star, the stella nova of 1604, not the one Tycho had seen—that was in 1572—but the same that Kepler was so much interested in.

Galileo gave a course of three lectures upon it to a great audience. At the first the theatre was over-crowded, so he had to adjourn to a hall holding 1000 persons. At the next he had to lecture in the open air.

He took occasion to rebuke his hearers for thronging to hear about an ephemeral novelty, while for the much more wonderful and important truths about the permanent stars and facts of nature they had but deaf ears.

But the main point he brought out concerning the new star was that it upset the received Aristotelian doctrine of the immutability of the heavens. According to that doctrine the heavens were unchangeable, perfect, subject neither to growth nor to decay. Here was a body, not a meteor but a real distant star, which had not been visible and which would shortly fade away again, but which meanwhile was brighter than Jupiter.

The staff of petrified professorial wisdom were annoyed at the appearance of the star, still more at Galileo's calling public attention to it; and controversy began at Padua. However, he accepted it; and now boldly threw down the gauntlet in favour of the Copernican theory, utterly repudiating the old Ptolemaic system which up to that time he had taught in the schools according to established custom.

The earth no longer the only world to which all else in the firmament were obsequious attendants, but a mere insignificant speck among the host of heaven! Man no longer the centre and cynosure of creation, but, as it were, an insect crawling on the surface of this little speck! All this not set down in crabbed Latin in dry folios for a few learned monks, as in Copernicus's time, but promulgated and argued in rich Italian, illustrated by analogy, by experiment, and with cultured wit; taught not to a few scholars here and there in musty libraries, but proclaimed in the vernacular to the whole populace with all the energy and enthusiasm of a recent convert and a master of language! Had a bombshell been exploded among the fossilized professors it had been less disturbing.

But there was worse in store for them.

A Dutch optician, Hans Lippershey by name, of Middleburg, had in his shop a curious toy, rigged up, it is said, by an apprentice, and made out of a couple of spectacle lenses, whereby, if one looked through it, the weather-cock of a neighbouring church spire was seen nearer and upside down.

The tale goes that the Marquis Spinola, happening to call at the shop, was struck with the toy and bought it. He showed it to Prince Maurice of Nassau, who thought of using it for military reconnoitring. All this is trivial. What is important is that some faint and inaccurate echo of this news found its way to Padua, and into the ears of Galileo.

The seed fell on good soil. All that night he sat up and pondered. He knew about lenses and magnifying glasses. He had read Kepler's theory of the eye, and had himself lectured on optics. Could he not hit on the device and make an instrument capable of bringing the heavenly bodies nearer? Who knew what marvels he might not so perceive! By morning he had some schemes ready to try, and one of them was successful. Singularly enough it was not the same plan as the Dutch optician's, it was another mode of achieving the same end.

He took an old small organ pipe, jammed a suitably chosen spectacle glass into either end, one convex the other concave, and behold, he had the half of a wretchedly bad opera glass capable of magnifying three times. It was better than the Dutchman's, however; it did not invert.

It is easy to understand the general principle of a telescope. A general knowledge of the common magnifying glass may be assumed. Roger Bacon knew about lenses; and the ancients often refer to them, though usually as burning glasses. The magnifying power of globes of water must have been noticed soon after the discovery of glass and the art of working it.

A magnifying glass is most simply thought of as an additional lens to the eye. The eye has a lens by which ordinary vision is accomplished, an extra glass lens strengthens it and enables objects to be seen nearer and therefore apparently bigger. But to apply a magnifying glass to distant objects is impossible. In order to magnify distant objects, another function of lenses has also to be employed, viz., their power of forming real images, the power on which their use as burning-glasses depends: for the best focus is an image of the sun. Although the object itself is inaccessible, the image of it is by no means so, and to the image a magnifier can be applied. This is exactly what is done in the telescope; the object glass or large lens forms an image, which is then looked at through a magnifying glass or eye-piece.

Of course the image is nothing like so big as the object. For astronomical objects it is almost infinitely less; still it is an exact representation at an accessible place, and no one expects a telescope to show distant bodies as big as they really are. All it does is to show them bigger than they could be seen without it.

But if the objects are not distant, the same principle may still be applied, and two lenses may be used, one to form an image, the other to magnify it; only if the object can be put where we please, we can easily place it so that its image is already much bigger than the object even before magnification by the eye lens. This is the compound microscope, the invention of which soon followed the telescope. In fact the two instruments shade off into one another, so that the reading telescope or reading microscope of a laboratory (for reading thermometers, and small divisions generally) goes by either name at random.

The arrangement so far described depicts things on the retina the unaccustomed way up. By using a concave glass instead of a convex, and placing it so as to prevent any image being formed, except on the retina direct, this inconvenience is avoided.



Such a thing as Galileo made may now be bought at a toy-shop for I suppose half a crown, and yet what a potentiality lay in that "glazed optic tube," as Milton called it. Away he went with it to Venice and showed it to the Signoria, to their great astonishment. "Many noblemen and senators," says Galileo, "though of advanced age, mounted to the top of one of the highest towers to watch the ships, which were visible through my glass two hours before they were seen entering the harbour, for it makes a thing fifty miles off as near and clear as if it were only five." Among the people too the instrument excited the greatest astonishment and interest, so that he was nearly mobbed. The Senate hinted to him that a present of the instrument would not be unacceptable, so Galileo took the hint and made another for them.



They immediately doubled his salary at Padua, making it 1000 florins, and confirmed him in the enjoyment of it for life.

He now eagerly began the construction of a larger and better instrument. Grinding the lenses with his own hands with consummate skill, he succeeded in making a telescope magnifying thirty times. Thus equipped he was ready to begin a survey of the heavens.



The first object he carefully examined was naturally the moon. He found there everything at first sight very like the earth, mountains and valleys, craters and plains, rocks, and apparently seas. You may imagine the hostility excited among the Aristotelian philosophers, especially no doubt those he had left behind at Pisa, on the ground of his spoiling the pure, smooth, crystalline, celestial face of the moon as they had thought it, and making it harsh and rugged and like so vile and ignoble a body as the earth.



He went further, however, into heterodoxy than this—he not only made the moon like the earth, but he made the earth shine like the moon. The visibility of "the old moon in the new moon's arms" he explained by earth-shine. Leonardo had given the same explanation a century before. Now one of the many stock arguments against Copernican theory of the earth being a planet like the rest was that the earth was dull and dark and did not shine. Galileo argued that it shone just as much as the moon does, and in fact rather more—especially if it be covered with clouds. One reason of the peculiar brilliancy of Venus is that she is a very cloudy planet.[8] Seen from the moon the earth would look exactly as the moon does to us, only a little brighter and sixteen times as big (four times the diameter).



Galileo made a very good estimate of the height of lunar mountains, of which many are five miles high and some as much as seven. He did this simply by measuring from the half-moon's straight edge the distance at which their peaks caught the rising or setting sun. The above simple diagram shows that as this distance is to the diameter of the moon, so is the height of the sun-tipped mountain to the aforesaid distance.

Wherever Galileo turned his telescope new stars appeared. The Milky Way, which had so puzzled the ancients, was found to be composed of stars. Stars that appeared single to the eye were some of them found to be double; and at intervals were found hazy nebulous wisps, some of which seemed to be star clusters, while others seemed only a fleecy cloud.



Now we come to his most brilliant, at least his most sensational, discovery. Examining Jupiter minutely on January 7, 1610, he noticed three little stars near it, which he noted down as fixing its then position. On the following night Jupiter had moved to the other side of the three stars. This was natural enough, but was it moving the right way? On examination it appeared not. Was it possible the tables were wrong? The next evening was cloudy, and he had to curb his feverish impatience. On the 10th there were only two, and those on the other side. On the 11th two again, but one bigger than the other. On the 12th the three re-appeared, and on the 13th there were four. No more appeared.

Jupiter then had moons like the earth, four of them in fact, and they revolved round him in periods which were soon determined.

The reason why they were not all visible at first, and why their visibility so rapidly changes, is because they revolve round him almost in the plane of our vision, so that sometimes they are in front and sometimes behind him, while again at other times they plunge into his shadow and are thus eclipsed from the light of the sun which enables us to see them. A large modern telescope will show the moons when in front of Jupiter, but small telescopes will only show them when clear of the disk and shadow. Often all four can be thus seen, but three or two is a very common amount of visibility. Quite a small telescope, such as a ship's telescope, if held steadily, suffices to show the satellites of Jupiter, and very interesting objects they are. They are of habitable size, and may be important worlds for all we know to the contrary.

The news of the discovery soon spread and excited the greatest interest and astonishment. Many of course refused to believe it. Some there were who having been shown them refused to believe their eyes, and asserted that although the telescope acted well enough for terrestrial objects, it was altogether false and illusory when applied to the heavens. Others took the safer ground of refusing to look through the glass. One of these who would not look at the satellites happened to die soon afterwards. "I hope," says Galileo, "that he saw them on his way to heaven."

The way in which Kepler received the news is characteristic, though by adding four to the supposed number of planets it might have seemed to upset his notions about the five regular solids.

He says,[9] "I was sitting idle at home thinking of you, most excellent Galileo, and your letters, when the news was brought me of the discovery of four planets by the help of the double eye-glass. Wachenfels stopped his carriage at my door to tell me, when such a fit of wonder seized me at a report which seemed so very absurd, and I was thrown into such agitation at seeing an old dispute between us decided in this way, that between his joy, my colouring, and the laughter of us both, confounded as we were by such a novelty, we were hardly capable, he of speaking, or I of listening....

"On our separating, I immediately fell to thinking how there could be any addition to the number of planets without overturning my Mysterium Cosmographicon, published thirteen years ago, according to which Euclid's five regular solids do not allow more than six planets round the sun.

"But I am so far from disbelieving the existence of the four circumjovial planets that I long for a telescope to anticipate you if possible in discovering two round Mars (as the proportion seems to me to require) six or eight round Saturn, and one each round Mercury and Venus."



As an illustration of the opposite school, I will take the following extract from Francesco Sizzi, a Florentine astronomer, who argues against the discovery thus:—

"There are seven windows in the head, two nostrils, two eyes, two ears, and a mouth; so in the heavens there are two favourable stars, two unpropitious, two luminaries, and Mercury alone undecided and indifferent. From which and many other similar phenomena of nature, such as the seven metals, &c., which it were tedious to enumerate, we gather that the number of planets is necessarily seven.

"Moreover, the satellites are invisible to the naked eye, and therefore can have no influence on the earth, and therefore would be useless, and therefore do not exist.

"Besides, the Jews and other ancient nations as well as modern Europeans have adopted the division of the week into seven days, and have named them from the seven planets: now if we increase the number of the planets this whole system falls to the ground."

To these arguments Galileo replied that whatever their force might be as a reason for believing beforehand that no more than seven planets would be discovered, they hardly seemed of sufficient weight to destroy the new ones when actually seen.

Writing to Kepler at this time, Galileo ejaculates:

"Oh, my dear Kepler, how I wish that we could have one hearty laugh together! Here, at Padua, is the principal professor of philosophy whom I have repeatedly and urgently requested to look at the moon and planets through my glass, which he pertinaciously refuses to do. Why are you not here? What shouts of laughter we should have at this glorious folly! And to hear the professor of philosophy at Pisa labouring before the grand duke with logical arguments, as if with magical incantations, to charm the new planets out of the sky."

A young German protege of Kepler, Martin Horkey, was travelling in Italy, and meeting Galileo at Bologna was favoured with a view through his telescope. But supposing that Kepler must necessarily be jealous of such great discoveries, and thinking to please him, he writes, "I cannot tell what to think about these observations. They are stupendous, they are wonderful, but whether they are true or false I cannot tell." He concludes, "I will never concede his four new planets to that Italian from Padua though I die for it." So he published a pamphlet asserting that reflected rays and optical illusions were the sole cause of the appearance, and that the only use of the imaginary planets was to gratify Galileo's thirst for gold and notoriety.

When after this performance he paid a visit to his old instructor Kepler, he got a reception which astonished him. However, he pleaded so hard to be forgiven that Kepler restored him to partial favour, on this condition, that he was to look again at the satellites, and this time to see them and own that they were there.

By degrees the enemies of Galileo were compelled to confess to the truth of the discovery, and the next step was to outdo him. Scheiner counted five, Rheiter nine, and others went as high as twelve. Some of these were imaginary, some were fixed stars, and four satellites only are known to this day.[10]

Here, close to the summit of his greatness, we must leave him for a time. A few steps more and he will be on the brow of the hill; a short piece of table-land, and then the descent begins.



LECTURE V

GALILEO AND THE INQUISITION

One sinister event occurred while Galileo was at Padua, some time before the era we have now arrived at, before the invention of the telescope—two years indeed after he had first gone to Padua; an event not directly concerning Galileo, but which I must mention because it must have shadowed his life both at the time and long afterwards. It was the execution of Giordano Bruno for heresy. This eminent philosopher had travelled largely, had lived some time in England, had acquired new and heterodox views on a variety of subjects, and did not hesitate to propound them even after he had returned to Italy.

The Copernican doctrine of the motion of the earth was one of his obnoxious heresies. Being persecuted to some extent by the Church, Bruno took refuge in Venice—a free republic almost independent of the Papacy—where he felt himself safe. Galileo was at Padua hard by: the University of Padua was under the government of the Senate of Venice: the two men must in all probability have met.

Well, the Inquisition at Rome sent messengers to Venice with a demand for the extradition of Bruno—they wanted him at Rome to try him for heresy.

In a moment of miserable weakness the Venetian republic gave him up, and Bruno was taken to Rome. There he was tried, and cast into the dungeons for six years, and because he entirely refused to recant, was at length delivered over to the secular arm and burned at the stake on 16th February, Anno Domini 1600.

This event could not but have cast a gloom over the mind of lovers and expounders of truth, and the lesson probably sank deep into Galileo's soul.

In dealing with these historic events will you allow me to repudiate once for all the slightest sectarian bias or meaning. I have nothing to do with Catholic or Protestant as such. I have nothing to do with the Church of Rome as such. I am dealing with the history of science. But historically at one period science and the Church came into conflict. It was not specially one Church rather than another—it was the Church in general, the only one that then existed in those countries. Historically, I say, they came into conflict, and historically the Church was the conqueror. It got its way; and science, in the persons of Bruno, Galileo, and several others, was vanquished.

Such being the facts, there is no help but to mention them in dealing with the history of science.

Doubtless now the Church regards it as an unhappy victory, and gladly would ignore this painful struggle. This, however, is impossible. With their creed the Churchmen of that day could act in no other way. They were bound to prosecute heresy, and they were bound to conquer in the struggle or be themselves shattered.

But let me insist on the fact that no one accuses the ecclesiastical courts of crime or evil motives. They attacked heresy after their manner, as the civil courts attacked witchcraft after their manner. Both erred grievously, but both acted with the best intentions.

We must remember, moreover, that his doctrines were scientifically heterodox, and the University Professors of that day were probably quite as ready to condemn them as the Church was. To realise the position we must think of some subjects which to-day are scientifically heterodox, and of the customary attitude adopted towards them by persons of widely differing creeds.

If it be contended now, as it is, that the ecclesiastics treated Galileo well, I admit it freely: they treated him as well as they possibly could. They overcame him, and he recanted; but if he had not recanted, if he had persisted in his heresy, they would—well, they would still have treated his soul well, but they would have set fire to his body. Their mistake consisted not in cruelty, but in supposing themselves the arbiters of eternal truth; and by no amount of slurring and glossing over facts can they evade the responsibility assumed by them on account of this mistaken attitude.

I am not here attacking the dogma of Papal Infallibility: it is historically, I believe, quite unaffected by the controversy respecting the motion of the earth, no Papal edict ex cathedra having been promulgated on the subject.

We left Galileo standing at his telescope and beginning his survey of the heavens. We followed him indeed through a few of his first great discoveries—the discovery of the mountains and other variety of surface in the moon, of the nebulae and a multitude of faint stars, and lastly of the four satellites of Jupiter.

This latter discovery made an immense sensation, and contributed its share to his removal from Padua, which quickly followed it, as I shall shortly narrate; but first I think it will be best to continue our survey of his astronomical discoveries without regard to the place whence they were made.

Before the end of the year Galileo had made another discovery—this time on Saturn. But to guard against the host of plagiarists and impostors, he published it in the form of an anagram, which, at the request of the Emperor Rudolph (a request probably inspired by Kepler), he interpreted; it ran thus: The furthest planet is triple.

Very soon after he found that Venus was changing from a full moon to a half moon appearance. He announced this also by an anagram, and waited till it should become a crescent, which it did.

This was a dreadful blow to the anti-Copernicans, for it removed the last lingering difficulty to the reception of the Copernican doctrine.



Copernicus had predicted, indeed, a hundred years before, that, if ever our powers of sight were sufficiently enhanced, Venus and Mercury would be seen to have phases like the moon. And now Galileo with his telescope verifies the prediction to the letter.

Here was a triumph for the grand old monk, and a bitter morsel for his opponents.

Castelli writes: "This must now convince the most obstinate." But Galileo, with more experience, replies:—"You almost make me laugh by saying that these clear observations are sufficient to convince the most obstinate; it seems you have yet to learn that long ago the observations were enough to convince those who are capable of reasoning, and those who wish to learn the truth; but that to convince the obstinate, and those who care for nothing beyond the vain applause of the senseless vulgar, not even the testimony of the stars would suffice, were they to descend on earth to speak for themselves. Let us, then, endeavour to procure some knowledge for ourselves, and rest contented with this sole satisfaction; but of advancing in popular opinion, or of gaining the assent of the book-philosophers, let us abandon both the hope and the desire."



What a year's work it had been!

In twelve months observational astronomy had made such a bound as it has never made before or since.

Why did not others make any of these observations? Because no one could make telescopes like Galileo.

He gathered pupils round him however, and taught them how to work the lenses, so that gradually these instruments penetrated Europe, and astronomers everywhere verified his splendid discoveries.

But still he worked on, and by March in the very next year, he saw something still more hateful to the Aristotelian philosophers, viz. spots on the sun.



If anything was pure and perfect it was the sun, they said. Was this impostor going to blacken its face too?

Well, there they were. They slowly formed and changed, and by moving all together showed him that the sun rotated about once a month.

Before taking leave of Galileo's astronomical researches, I must mention an observation made at the end of 1612, that the apparent triplicity of Saturn (Fig. 46) had vanished.



"Looking on Saturn within these few days, I found it solitary, without the assistance of its accustomed stars, and in short perfectly round and defined, like Jupiter, and such it still remains. Now what can be said of so strange a metamorphosis? Are perhaps the two smaller stars consumed like spots on the sun? Have they suddenly vanished and fled? Or has Saturn devoured his own children? Or was the appearance indeed fraud and illusion, with which the glasses have so long time mocked me and so many others who have so often observed with me? Now perhaps the time is come to revive the withering hopes of those, who, guided by more profound contemplations, have fathomed all the fallacies of the new observations and recognized their impossibility! I cannot resolve what to say in a chance so strange, so new, so unexpected. The shortness of time, the unexampled occurrence, the weakness of my intellect, the terror of being mistaken, have greatly confounded me."

However, he plucked up courage, and conjectured that the two attendants would reappear, by revolving round the planet.



The real reason of their disappearance is well known to us now. The plane of Saturn's rings oscillates slowly about our line of sight, and so we sometimes see them edgeways and sometimes with a moderate amount of obliquity. The rings are so thin that, when turned precisely edgeways, they become invisible. The two imaginary attendants were the most conspicuous portions of the ring, subsequently called ansae.

I have thought it better not to interrupt this catalogue of brilliant discoveries by any biographical details; but we must now retrace our steps to the years 1609 and 1610, the era of the invention of the telescope.

By this time Galileo had been eighteen years at Padua, and like many another man in like case, was getting rather tired of continual lecturing. Moreover, he felt so full of ideas that he longed to have a better opportunity of following them up, and more time for thinking them out.

Now in the holidays he had been accustomed to return to his family home at Pisa, and there to come a good deal into contact with the Grand-Ducal House of Tuscany. Young Cosmo di Medici became in fact his pupil, and arrived at man's estate with the highest opinion of the philosopher. This young man had now come to the throne as Cosmo II., and to him Galileo wrote saying how much he should like more time and leisure, how full he was of discoveries if he only had the chance of a reasonable income without the necessity of consuming so large a portion of his time in elementary teaching, and practically asking to be removed to some position in the Court. Nothing was done for a time, but negotiations proceeded, and soon after the discovery of Jupiter's satellites Cosmo wrote making a generous offer, which Galileo gladly and enthusiastically accepted, and at once left Padua for Florence. All his subsequent discoveries date from Florence.

Thus closed his brilliant and happy career as a professor at the University of Padua. He had been treated well: his pay had become larger than that of any Professor of Mathematics up to that time; and, as you know, immediately after his invention of the telescope the Venetian Senate, in a fit of enthusiasm, had doubled it and secured it to him for life wherever he was. To throw up his chair and leave the place the very next year scarcely seems a strictly honourable procedure. It was legal enough no doubt, and it is easy for small men to criticize a great one, but nevertheless I think we must admit that it is a step such as a man with a keen sense of honour would hardly have taken.

One quite feels and sympathizes with the temptation. Not emolument, but leisure; freedom from harassing engagements and constant teaching, and liberty to prosecute his studies day and night without interference: this was the golden prospect before him. He yielded, but one cannot help wishing he had not.

As it turned out it was a false step—the first false step of his public career. When made it was irretrievable, and it led to great misery.

At first it seemed brilliant enough. The great philosopher of the Tuscan Court was courted and flattered by princes and nobles, he enjoyed a world-wide reputation, lived as luxuriously as he cared for, had his time all to himself, and lectured but very seldom, on great occasions or to a few crowned heads.

His position was in fact analogous to that of Tycho Brahe in his island of Huen.

Misfortune overtook both. In Tycho's case it arose mainly from the death of his patron. In Galileo's it was due to a more insidious cause, to understand which cause aright we must remember the political divisions of Italy at that date.

Tuscany was a Papal State, and thought there was by no means free. Venice was a free republic, and was even hostile to the Papacy. In 1606 the Pope had placed it under an interdict. In reply it had ejected every Jesuit.

Out of this atmosphere of comparative enlightenment and freedom into that hotbed of mediaevalism and superstition went Galileo with his eyes open. Keen was the regret of his Paduan and Venetian friends; bitter were their remonstrances and exhortations. But he was determined to go, and, not without turning some of his old friends into enemies, he went.

Seldom has such a man made so great a mistake: never, I suppose, has one been so cruelly punished for it.



We must remember, however, that Galileo, though by no means a saint, was yet a really religious man, a devout Catholic and thorough adherent of the Church, so that he would have no dislike to place himself under her sway. Moreover, he had been born a Tuscan, his family had lived at Florence or Pisa, and it felt like going home. His theological attitude is worthy of notice, for he was not in the least a sceptic. He quite acquiesces in the authority of the Bible, especially in all matters concerning faith and conduct; as to its statements in scientific matters, he argues that we are so liable to misinterpret their meaning that it is really easier to examine Nature for truth in scientific matters, and that when direct observation and Scripture seem to clash, it is because of our fallacious interpretation of one or both of them. He is, in fact, what one now calls a "reconciler."

It is curious to find such a man prosecuted for heresy, when to-day his opinions are those of the orthodox among the orthodox. But so it ever is, and the heresy of one generation becomes the commonplace of the next.

He accepts Joshua's miracle, for instance, not as a striking poem, but as a literal fact; and he points out how much more simply it could be done on the Copernican system by stopping the earth's rotation for a short time, than by stopping the sun and moon and all the host of heaven as on the old Ptolemaic system, or again by stopping only the sun and not any of the other bodies, and so throwing astronomy all wrong.

This reads to us like satire, but no doubt it was his genuine opinion.

These Scriptural reconciliations of his, however, angered the religious authorities still more. They said it was bad enough for this heretic to try and upset old scientific beliefs, and to spoil the face of Nature with his infidel discoveries, but at least he might leave the Bible alone; and they addressed an indignant remonstrance to Rome, to protect it from the hands of ignorant laymen.

Thus, wherever he turned he encountered hostility. Of course he had many friends—some of them powerful like Cosmo, all of them faithful and sincere. But against the power of Rome what could they do? Cosmo dared no more than remonstrate, and ultimately his successor had to refrain from even this, so enchained and bound was the spirit of the rulers of those days; and so when his day of tribulation came he stood alone and helpless in the midst of his enemies.

You may wonder, perhaps, why this man should excite so much more hostility than many another man who was suffered to believe and teach much the same doctrines unmolested. But no other man had made such brilliant and exciting discoveries. No man stood so prominently forward in the eyes of all Christendom as the champion of the new doctrines. No other man stated them so clearly and forcibly, nor drove them home with such brilliant and telling illustrations.

And again, there was the memory of his early conflict with the Aristotelians at Pisa, of his scornful and successful refutation of their absurdities. All this made him specially obnoxious to the Aristotelian Jesuits in their double capacity both of priests and of philosophers, and they singled him out for relentless official persecution.

Not yet, however, is he much troubled by them. The chief men at Rome have not yet moved. Messages, however, keep going up from Tuscany to Rome respecting the teachings of this man, and of the harm he is doing by his pertinacious preaching of the Copernican doctrine that the earth moves.

At length, in 1615, Pope Paul V. wrote requesting him to come to Rome to explain his views. He went, was well received, made a special friend of Cardinal Barberino—an accomplished man in high position, who became in fact the next Pope. Galileo showed cardinals and others his telescope, and to as many as would look through it he showed Jupiter's satellites and his other discoveries. He had a most successful visit. He talked, he harangued, he held forth in the midst of fifteen or twenty disputants at once, confounding his opponents and putting them to shame.

His method was to let the opposite arguments be stated as fully and completely as possible, himself aiding, and often adducing the most forcible and plausible arguments against his own views; and then, all having been well stated, he would proceed to utterly undermine and demolish the whole fabric, and bring out the truth in such a way as to convince all honest minds. It was this habit that made him such a formidable antagonist. He never shrank from meeting an opposing argument, never sought to ignore it, or cloak it in a cloud of words. Every hostile argument he seemed to delight in, as a foe to be crushed, and the better and stronger they sounded the more he liked them. He knew many of them well, he invented a number more, and had he chosen could have out-argued the stoutest Aristotelian on his own grounds. Thus did he lead his adversaries on, almost like Socrates, only to ultimately overwhelm them in a more hopeless rout. All this in Rome too, in the heart of the Catholic world. Had he been worldly-wise, he would certainly have kept silent and unobtrusive till he had leave to go away again. But he felt like an apostle of the new doctrines, whose mission it was to proclaim them even in this centre of the world and of the Church.

Well, he had an audience with the Pope—a chat an hour long—and the two parted good friends, mutually pleased with each other.

He writes that he is all right now, and might return home when he liked. But the question began to be agitated whether the whole system of Copernicus ought not to be condemned as impious and heretical. This view was persistently urged upon the Pope and College of Cardinals, and it was soon to be decided upon.

Had Galileo been unfaithful to the Church he could have left them to stultify themselves in any way they thought proper, and himself have gone; but he felt supremely interested in the result, and he stayed. He writes:—

"So far as concerns the clearing of my own character, I might return home immediately; but although this new question regards me no more than all those who for the last eighty years have supported those opinions both in public and private, yet, as perhaps I may be of some assistance in that part of the discussion which depends on the knowledge of truths ascertained by means of the sciences which I profess, I, as a zealous and Catholic Christian, neither can nor ought to withhold that assistance which my knowledge affords, and this business keeps me sufficiently employed."

It is possible that his stay was the worst thing for the cause he had at heart. Anyhow, the result was that the system was condemned, and both the book of Copernicus and the epitome of it by Kepler were placed on the forbidden list,[11] and Galileo himself was formally ordered never to teach or to believe the motion of the earth.

He quitted Rome in disgust, which before long broke out in satire. The only way in which he could safely speak of these views now was as if they were hypothetical and uncertain, and so we find him writing to the Archduke Leopold, with a presentation copy of his book on the tides, the following:—

"This theory occurred to me when in Rome whilst the theologians were debating on the prohibition of Copernicus's book, and of the opinion maintained in it of the motion of the earth, which I at that time believed: until it pleased those gentlemen to suspend the book, and declare the opinion false and repugnant to the Holy Scriptures. Now, as I know how well it becomes me to obey and believe the decisions of my superiors, which proceed out of more knowledge than the weakness of my intellect can attain to, this theory which I send you, which is founded on the motion of the earth, I now look upon as a fiction and a dream, and beg your highness to receive it as such. But as poets often learn to prize the creations of their fancy, so in like manner do I set some value on this absurdity of mine. It is true that when I sketched this little work I did hope that Copernicus would not, after eighty years, be convicted of error; and I had intended to develop and amplify it further, but a voice from heaven suddenly awakened me, and at once annihilated all my confused and entangled fancies."

This sarcasm, if it had been in print, would probably have been dangerous. It was safe in a private letter, but it shows us his real feelings.

However, he was left comparatively quiet for a time. He was getting an old man now, and passed the time studiously enough, partly at his house in Florence, partly at his villa in Arcetri, a mile or so out of the town.

Here was a convent, and in it his two daughters were nuns. One of them, who passed under the name of Sister Maria Celeste, seems to have been a woman of considerable capacity—certainly she was of a most affectionate disposition—and loved and honoured her father in the most dutiful way.

This was a quiet period of his life, spoiled only by occasional fits of illness and severe rheumatic pains, to which the old man was always liable. Many little circumstances are known of this peaceful time. For instance, the convent clock won't go, and Galileo mends it for them. He is always doing little things for them, and sending presents to the Lady Superior and his two daughters.

He was occupied now with problems in hydrostatics, and on other matters unconnected with astronomy: a large piece of work which I must pass over. Most interesting and acute it is, however.

In 1623, when the old Pope died, there was elected to the Papal throne, as Urban VIII., Cardinal Barberino, a man of very considerable enlightenment, and a personal friend of Galileo's, so that both he and his daughters rejoice greatly, and hope that things will come all right, and the forbidding edict be withdrawn.

The year after this election he manages to make another journey to Rome to compliment his friend on his elevation to the Pontifical chair. He had many talks with Urban, and made himself very agreeable.

Urban wrote to the Grand Duke Ferdinand, son of Cosmo:—

"For We find in him not only literary distinction but also love of piety, and he is strong in those qualities by which Pontifical good will is easily obtainable. And now, when he has been brought to this city to congratulate Us on Our elevation, We have very lovingly embraced him; nor can We suffer him to return to the country whither your liberality recalls him without an ample provision of Pontifical love. And that you may know how dear he is to Us, We have willed to give him this honourable testimonial of virtue and piety. And We further signify that every benefit which you shall confer upon him, imitating or even surpassing your father's liberality, will conduce to Our gratification."

Encouraged, doubtless, by these marks of approbation, and reposing too much confidence in the individual good will of the Pope, without heeding the crowd of half-declared enemies who were seeking to undermine his reputation, he set about, after his return to Florence, his greatest literary and most popular work, Dialogues on the Ptolemaic and Copernican Systems. This purports to be a series of four conversations between three characters: Salviati, a Copernican philosopher; Sagredo, a wit and scholar, not specially learned, but keen and critical, and who lightens the talk with chaff; Simplicio, an Aristotelian philosopher, who propounds the stock absurdities which served instead of arguments to the majority of men.

The conversations are something between Plato's Dialogues and Sir Arthur Helps's Friends in Council. The whole is conducted with great good temper and fairness; and, discreetly enough, no definite conclusion is arrived at, the whole being left in abeyance as if for a fifth and decisive dialogue, which, however, was never written, and perhaps was only intended in case the reception was favourable.

The preface also sets forth that the object of the writer is to show that the Roman edict forbidding the Copernican doctrine was not issued in ignorance of the facts of the case, as had been maliciously reported, and that he wishes to show how well and clearly it was all known beforehand. So he says the dialogue on the Copernican side takes up the question purely as a mathematical hypothesis or speculative figment, and gives it every artificial advantage of which the theory is capable.

This piece of caution was insufficient to blind the eyes of the Cardinals; for in it the arguments in favour of the earth's motion are so cogent and unanswerable, and are so popularly stated, as to do more in a few years to undermine the old system than all that he had written and spoken before. He could not get it printed for two years after he had written it, and then only got consent through a piece of carelessness or laziness on the part of the ecclesiastical censor through whose hands the manuscript passed—for which he was afterwards dismissed.

However, it did appear, and was eagerly read; the more, perhaps, as the Church at once sought to suppress it.

The Aristotelians were furious, and represented to the Pope that he himself was the character intended by Simplicio, the philosopher whose opinions get alternately refuted and ridiculed by the other two, till he is reduced to an abject state of impotence.

The idea that Galileo had thus cast ridicule upon his friend and patron is no doubt a gratuitous and insulting libel: there is no telling whether or not Urban believed it, but certainly his countenance changed to Galileo henceforward, and whether overruled by his Cardinals, or actuated by some other motive, his favour was completely withdrawn.

The infirm old man was instantly summoned to Rome. His friends pleaded his age—he was now seventy—his ill-health, the time of year, the state of the roads, the quarantine existing on account of the plague. It was all of no avail, to Rome he must go, and on the 14th of February he arrived.



His daughter at Arcetri was in despair; and anxiety and fastings and penances self-inflicted on his account, dangerously reduced her health.

At Rome he was not imprisoned, but he was told to keep indoors, and show himself as little as possible. He was allowed, however, to stay at the house of the Tuscan Ambassador instead of in gaol.

By April he was removed to the chambers of the Inquisition, and examined several times. Here, however, the anxiety was too much, and his health began to give way seriously; so, before long, he was allowed to return to the Ambassador's house; and, after application had been made, was allowed to drive in the public garden in a half-closed carriage. Thus in every way the Inquisition dealt with him as leniently as they could. He was now their prisoner, and they might have cast him into their dungeons, as many another had been cast. By whatever they were influenced—perhaps the Pope's old friendship, perhaps his advanced age and infirmities—he was not so cruelly used.

Still, they had their rules; he must be made to recant and abjure his heresy; and, if necessary, torture must be applied. This he knew well enough, and his daughter knew it, and her distress may be imagined. Moreover, it is not as if they had really been heretics, as if they hated or despised the Church of Rome. On the contrary, they loved and honoured the Church. They were sincere and devout worshippers, and only on a few scientific matters did Galileo presume to differ from his ecclesiastical superiors: his disagreement with them occasioned him real sorrow; and his dearest hope was that they could be brought to his way of thinking and embrace the truth.

Every time he was sent for by the Inquisition he was in danger of torture unless he recanted. All his friends urged him repeatedly to submit. They said resistance was hopeless and fatal. Within the memory of men still young, Giordano Bruno had been burnt alive for a similar heresy. This had happened while Galileo was at Padua. Venice was full of it. And since that, only eight years ago indeed, Antonio de Dominis, Archbishop of Salpetria, had been sentenced to the same fate: "to be handed over to the secular arm to be dealt with as mercifully as possible without the shedding of blood." So ran the hideous formula condemning a man to the stake. After his sentence, this unfortunate man died in the dungeons in which he had been incarcerated six years—died what is called a "natural" death; but the sentence was carried out, notwithstanding, on his lifeless body and his writings. His writings for which he had been willing to die!