 Lecture 3 of Pioneers of Science. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Recording by Rick Rodstrom. Pioneers of Science by Sir Oliver Lodge. Lecture 3. Kepler and the Laws of Planetary Motion. Summary of Facts for Lecture 3. Life and Work of Kepler. Kepler was born in December 1571 at Vile in Wirtenburg. Father and officer in the Duke's army, mother something of a varago, both very poor. Kepler was utilized as a tavern pot boy, but ultimately sent to a charity school, and thence to the University of Tübingen. Health extremely delicate. He was liable to violent attacks all his life, studied mathematics, and accepted an astronomical lectureship at Graz at the first post which offered. Endeavored to discover some connection between the number of the planets, their times of revolution, and their distances from the sun. Ultimately hit upon his fanciful regular solid hypothesis, and published his first book in 1597. In 1599 was invited by Tycho to Prague, and their appointed imperial mathematician, at a handsome but seldom paid salary. Observed the new star of 1604. Endeavored to find the law of refraction of light from Vitello's measurements, but failed. Analyzed Tycho's observations to find the true law of motion of Mars. After incredible labor, through innumerable wrong guesses, and six years of almost incessant calculation, he at length emerged in his two laws, discoveries which swept away all epicycles, deference, equants, and other remnants of the Greek system, and ushered in the dawn of modern astronomy. Law one. Planets move in ellipses with the sun in one focus. Law two. The radius vector, or line joining sun and planet, sweeps out equal areas in equal times. Published his second book containing these laws in 1609, Death of Rudolph in 1612, and subsequent increased misery and misfortune of Kepler. Ultimately discovered the connection between the times and distances of the planets, for which he had been groping all his mature life, and announced it in 1618. Law three. The square of the time of revolution, or year of each planet, is proportional to the cube of its mean distance from the sun. The book in which this law was published, on celestial harmonies, was dedicated to James of England. In 1620, had to intervene to protect his mother from being tortured for witchcraft, except at a professorship at Linn's. Published the Rudolfine Tables in 1627, embodying Tycho's observations and his own theory, made a last effort to overcome his poverty by getting the arrears of his salary paid at Prague, but was unsuccessful, and, contracting brain fever on the journey, died in November 1630, aged 59. A man of keen imagination, indomitable perseverance, and uncompromising love of truth, Kepler overcame ill health, poverty, and misfortune, and placed himself in the very highest rank of scientific men. His laws, so extraordinarily discovered, introduced order and simplicity into what else would have been a chaos of detailed observations, and they served as a secure basis for the splendid erection made on them by Newton. Seven planets of the Ptolemaic system, Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn. Six planets of the Copernican system, Mercury, Venus, Earth, Mars, Jupiter, Saturn. The five regular solids in appropriate order, octahedron, icosahedron, dodecahedron, tetrahedron, cube. Table illustrating Kepler's third law, planet, Mercury, mean distance from Sun, D, 0.3871, length of year, T, 0.24084, cube of the distance, D cubed, 0.05801, square of the time, T squared, 0.05801. Planet, Venus, mean distance from Sun, D, 0.7233, length of year, T, 0.61519, cube of the distance, D cubed, 0.37845, square of the time, T squared, 0.37846. Planet, Earth, mean distance from Sun, D, 1, length of year, T, 1, cube of the distance, D cubed, 1, square of the time, T squared, 1. Planet, Mars, mean distance from Sun, 1.5237, length of year, T, 1.8808, cube of the distance, D cubed, 3.5375, square of the time, T squared, 3.5375. Planet, Jupiter, mean distance from Sun, D, 5.2028, length of year, T, 11.862, cube of the distance, D cubed, 140.83, square of the time, T squared, 140.70. Planet, Saturn, mean distance from Sun, D, 9.5388, length of year, T, 29.457, cube of the distance, D cubed, 867.92, square of the time, T squared, 867.70. The length of the Earth's year is 365.256 days. Its mean distance from the Sun, taken above its unity, is 92 million miles. Lecture 3, Kepler and the Laws of Planetary Motion. It is difficult to imagine a stronger contrast between two men engaged in the same branch of science, than exists between Tycho Brahe, the subject of last lecture, and Kepler, our subject on the present occasion. The one, rich, noble, vigorous, passionate, strong in mechanical ingenuity and experimental skill, but not above the average in theoretical and mathematical power. The other, poor, sickly, devoid of experimental gifts, and unfitted by nature for accurate observation, but strong almost beyond competition in speculative subtlety and innate mathematical perception. The one is the complement of the other, and from the fact of their following each other so closely arose the most surprising benefits to science. The outward life of Kepler is to a large extent a mere record of poverty and misfortune. I shall only sketch, in its broad features, so that we may have more time to attend to his work. He was born, so his biographer assures us, in longitude 29 degrees 7 minutes, latitude 48 degrees 54 minutes, on the 21st of December 1571. His parents seem to have been of fair condition, but by reason it is said of his becoming a charity for a friend, the father lost all his slender income and was reduced to keeping a tavern. Young John Kepler was thereupon taken from school and employed as pot boy between the ages of 9 and 12. He was a sickly lad, subject to violent illnesses from the cradle, so that his life was frequently despaired of. Ultimately he was sent to a monastic school, and thence to the University of Tübingen, where he graduated second on the list. Meanwhile home affairs had gone to rack and ruin. His father abandoned the home and later died abroad. The mother quarreled with all her relations, including her son John, who is therefore glad to get away as soon as possible. All his connection with astronomy up to this time had been the hearing of the Copernican theory expounded in university lectures and defending it in a college debating society. An astronomical lectureship at Graz, happening to offer itself, he was urged to take it and agreed to do so, though stipulating that it should not debar him from some more brilliant profession when there was a chance. For astronomy in those days seems to have ranked as a minor science, like mineralogy or meteorology now. It had little of the special dignity with which the labors of Kepler himself were destined so greatly to aid in endowing it. Well, he speedily became a thorough Copernican, and as he had a most singularly restless and inquisitive mind, full of appreciation of everything relating to number and magnitude, was a born speculator and thinker, just as Mozart was a born musician, a bitter, a born calculator. He was agitated by questions such as these. Why are there exactly six planets? Is there any connection between their orbital distances or between their orbits and the times of describing them? These things tormented him, and he thought about them day and night. It is characteristic of the spirit of the times, this questioning why there should be six planets. Nowadays we should simply record the fact and look out for a seventh. Then some occult property of the number six was groped for, such as that it was equal to one plus two plus three, and likewise equal to one times two times three, and so on. Many fine reasons had been given for the seven planets of the Ptolemaic system, but for the six planets of the Copernican system the reasons were not so cogent. Again, with respect to their successive distances from the Sun, some law would seem to regulate their distance, but it was not known. Parenthetically I may remark that it is not known even now. A crude empirical statement known as Bode's law is all that has been discovered. Once more the further the planet, the slower it moved. There seemed to be some law connecting speed and distance. This also Kepler made continual attempts to discover. One of his ideas concerning the law of the successive distances was based on the inscription of a triangle in a circle. If you inscribe in a circle a large number of equilateral triangles, they envelop another circle bearing a definite ratio to the first. These might do for the orbits of two planets. Then try inscribing and circumscribing squares, hexagons, and other figures, and see if the circles thus defined would correspond to the several planetary orbits. But they would not give any satisfactory result. Rooting over this disappointment, the idea of trying solid figures suddenly strikes him. What have plain figures to do with the celestial orbits, he cries out, inscribe the regular solids. And then, brilliant idea, he remembers that there are but five. Euclid had shown that there could be only five regular solids. The number evidently corresponds to the gaps between the six planets. The reason of their being only six seems to be attained. This coincidence assures him he is on the right track, and with great enthusiasm and hope, he represents the Earth's orbit by a sphere as the norm and measure of all. Round it, he circumscribes a dodecahedron and puts another sphere round that, which is approximately the orbit of Mars. Round that, again, a tetrahedron, the corners of which mark the sphere of the orbit of Jupiter. Round that sphere, again, he places a cube, which roughly gives the orbit of Saturn. On the other hand, he inscribes in the sphere of the Earth's orbit an icosahedron, and inside the sphere determined by that an octahedron, which figures he takes to enclose the spheres of Venus and of Mercury, respectively. The imagined discovery is purely fictitious and accidental. First of all, eight planets are now known, and secondly, their real distances agree only very approximately with Kepler's hypothesis. Nevertheless, the idea gave him great delight. He says, The intense pleasure I have received from this discovery can never be told in words. I regretted no more of the time wasted. I tired of no labor. I shunned no toil of reckoning. Days and nights spent in calculation until I could see whether my hypothesis would agree with the orbits of Copernicus or whether my joy was to vanish into air. He then went on to speculate as to the cause of the planet's motion. The old idea was that they were carried round by angels or celestial intelligences. Kepler tried to establish some propelling force emanating from the sun, like the spokes of a windmill. This first book of his brought him into notice and served as an introduction to Tycho and to Galileo. Tycho Brahe was at this time at Prague, under the patronage of the Emperor Rudolf, and as he was known to have by far the best planetary observations of any man living, Kepler wrote to him to know if he might come and examine them so as to perfect his theory. Tycho immediately replied, Come, not as a stranger, but as a very welcome friend. Come and share in my observations with such instruments as I have with me and as a dearly beloved associate. After this visit, Tycho wrote again, offering him the post of mathematical assistant, which, after hesitation, was accepted. Part of the hesitation Kepler expresses by saying that, for observations, his sight was dull, and for mechanical operations, his hand was awkward. He suffered much from weak eyes and dared not expose himself to night air. In all this he was, of course, the antipodes of Tycho, but in mathematical skill he was greatly his superior. On his way to Prague he was seized with one of his periodical illnesses, and all his means were exhausted by the time he could set forward again, so that he had to apply for help to Tycho. It is clear indeed that for some time now he subsisted entirely on the bounty of Tycho, and he expresses himself most deeply grateful for all the kindness he received from that noble and distinguished man, the head of the scientific world at that date. To illustrate Tycho's kindness and generosity, I must read you a letter written to him by Kepler. It seems that Kepler, on one of his absences from Prague, driven half mad with poverty and trouble, fell foul of Tycho, whom he thought to be behaving badly in money matters to him and his family, and wrote him a violent letter full of reproaches and insults. Tycho's secretary replied quietly enough, pointing out the groundlessness and ingratitude of the accusation. Kepler repents instantly and replies, Most noble Tycho! These are the words of his letter. How shall I enumerate or rightly estimate your benefits conferred on me? For two months you have liberally and gratuitously maintained me, and my whole family. You have provided for all my wishes. You have done me every possible kindness. You have communicated to me everything you hold most dear. No one, by word or deed, has intentionally injured me in anything. In short, not to your children, your wife, or yourself, have you shown more indulgence than to me. This being so, as I am anxious to put on record, I cannot reflect without consternation that I should have been so given up by God to my own intemperance as to shut my eyes on all these benefits. That, instead of modest and respectful gratitude, I should indulge for three weeks in continual morose-ness towards all your family, in headlong passion and the utmost insolence towards yourself, who possess so many claims on my veneration, from your noble family, your extraordinary learning, and distinguished reputation. Whatever I have said or written against a person, the fame, the honor, and the learning of your excellency, or whatever in any other way I have injuriously spoken or written, if they admit no other more favorable interpretation, as to my grief I have spoken and written many things and more than I can remember, all and everything I recant, and freely and honestly declare and profess to be groundless, false, and incapable of proof. 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 matter 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 deathbed he entrusted 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 preceded 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 honored 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, Wille Brode 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 1. 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 center, the main planetary orbit was called an eccentric, 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 center, 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 especially 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 centers, both being supposed eccentric 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 Figure 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 labor 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. Grop 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 observations 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 vibrate 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. 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 graduation 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 eccentric 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 calculations, 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, vis, 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 over 100,000 of the radius, and he remembered that the optical inequality of Mars was also about 429 over 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 around 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 equivocal 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 equivocal 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 equivocal description of areas is filled good with an ellipse. The above is a tracing of it. Such is a crude and bold 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, eccentric, and the like were swept at once away, with the benefit 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' relations, Father Jupiter, 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 arrears, 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 smallpox, 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 Linn's, and withdrew with his two quite young remaining children. He provided for himself now partly by publishing a prophesizing almanac, 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 eight thousand 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 lawsuit for some years near their old home in Wirtenburg. 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 Linn's 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 and 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 cubed to t squared for every planet is the same. Or again, the length of a planet's year depends on the 3 over 2 th 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 prophesized 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 honor 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, the Revolutionabus Orbium Celestium. This honor, 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 Rudolfine 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 almanac. After this, the Grand Duke of Tuscany sent Kepler a golden chain, which is interesting in as much as it must really have come from Galileo, who was in high favor 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 traveled 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 overstudy, and disheartened by the failure, he caught a fever and died in his 59th year. His body was buried at Ratisbaum, 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 traveled. He maps out his route like a traveler. 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 labor 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 chimera 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 recognize 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 Hoon and our numerous meteorological observations 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, 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 endeavor to reconcile theories with facts. A life of such labor, crowned by three brilliant discoveries, the world owes and too late recognizes its obligation to the harshly treated German genius Kepler. End of lecture three, recording by Rick Rodstrom. Summary of facts for lectures four and five. In 1564 Michelangelo 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 burned at the stake on the 16th of February 1600 AD. A natural death in the dungeons of the Inquisition saved Antonio de Domines the explainer of the rainbow from the same fate, but his body and books were publicly burned in 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 and noble Thorntine, 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 Aristotleians 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 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 satellites. Observed the mountains of the moon and roughly measured their height. Explained the visibility of the new moon by Earthshine. Was invited to the Grand Ducal Court of Tuscany by Cosmodo Medici and appointed philosopher to that personage. Discovered innumerable new stars and the nebulae. Observed a triple appearance of Saturn. Discovered the faces of Venus predicted by Copernicus and spots on the Sun. Wrote on floating bodies. Tried to get his satellites utilised to determine 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 22 June 1633. Forbidden ever more to publish anything or to teach or to receive friends. Retired to archetry and broken down health. Death of his favourite daughter, sister Maria Celeste wrote and meditated on the laws of motion. Discovered the moon's vibration. In 1637 he became blind. The rigor 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 satellites illustrating their obedience to Kepler's third law. Satellite 1 diameter 2437 miles. Time of revolution 42.47 hours. Distance from Jupiter 6.049 Jovian radii. Period squared 1,803.7. Distance cubed 221.44. Period squared divided by distance cubed 8.149. Satellite 2 diameter 2,188 miles. Time of revolution 85.23 hours. Distance from Jupiter 9.623 Jovian radii. Period squared 7264.1. Distance cubed 891.11. Period squared divided by distance cubed 8.152. Satellite 3 diameter 3,575 miles. Time of revolution 177.72 hours. Distance from Jupiter 15.350 Jovian radii. Period squared 29,488. Distance cubed 3,916.8. Period squared divided by distance cubed 8.153. Satellite 4 diameter 3,059 miles. Time of revolution 400.53 hours. Distance from Jupiter 26.998 Jovian radii. Period squared 160,426. Distance cubed 19,679. Period squared divided by distance cubed 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. There's 16 feet in the first, and 48 feet in the 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, and what is rather absurdly called the square of the time, i.e. the time multiplied by itself. For instance, in three seconds it drops 9 times 16 equals 144 feet. In four seconds, 16 times 16, or 256 feet, and so on. The distance is travelled in 1, 2, 3, 4, etc. seconds by a body dropped from rest and not appreciably resisted by the air, 1, 4, 9, 16, 25, etc., respectively, each multiplied by the constant 16 feet. Another way of stating the law is to say that the heights travelled in successive seconds precede in the proportion 1, 3, 5, 7, 9, and so on, 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 1 foot. A bullet thrown or shot in any direction falls just as much as if it merely dropped, but instead of falling from the starting point, it drops vertically from the line of fire. See figure 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, 3, 600ths 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. 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, 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 4 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, 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 our comedies, 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 will find his equal in the domain of purely experimental science until we come to Faraday. Faraday was no doubt his superior, but a 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 Michelangelo 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 Galeray, a descendant of the important Bono duty family, was himself a mathematician and a musician, and in a book of his still-excellent 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 imbibe 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 skillfully 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 woolen 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. Albincenzo'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 two thousand scuddy a year, the professor of mathematics had only sixty, that is, thirteen pounds a year, or seven and a half pence 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 some great lamp which, after lighting it, the verger had left swing into and fro. Galileo proceeded to time its swings by the only watch he possessed, there's 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 Huygens soon applied it to the astronomical clock which up to that time had been accrued 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 Osterlio Ricci, a distinguished mathematician an old friend of the Galileo family. The youth visited him and one day it is said had a lesson in Euclid being given by Ricci 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 mustered 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. Olbinchenzo 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 seven and a half pence 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 the 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. Now this was clean contrary to what 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 was so. The idea of making an experiment would have savoured of impiety because it seemed to tend towards skepticism and to 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 the 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 in 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 the method was not to make an experiment but to turn over the pages of Aristotle and he who 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 realise the state of things clearly and the pursuit of the learned of these days towards every new discovery seemed stupid and almost insane. They had a crystallised 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 and 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 lifeblood of science is growth, expansion, freedom, development. Before it could appear it must throw off those old shackles of centuries it must burst its old skin and emerge worn with struggle, weakly and unprotected but free 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 five pound weight would fall five times as quick as a one pound weight a fifty pound weight, fifty times as quick 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 poo-pooed and snubbed he knew he was right and he was determined to make everyone see the facts as he saw them so one morning before the assembled university he ascended the famous leaning tower taking with him a one hundred pound shot and a one pound 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 nail 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 hence forward would be liable to drift along with the tide not knowing wither they dared not do this no they must cling to the old traditions they could not cast away their rotting ropes and sail out onto 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 aleo 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 over much to say that they acted as they did is to say that they were human were now reminded 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 adogma and refuse to rise with the tide of advancing knowledge there may be some even now well the unpopularity of Galileo smoldered 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 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 Taiko 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 lecture was overcrowded so he had to adjourn to a hall holding one thousand 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 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 aristotially indoctrin 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 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 synosure of creation but, as it were, an insect crawling on the surface of this little speck all this not set down in crab 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 recent convert and a master of language had a bombshell been exploded amongst the fossilised professors it had been less disturbing but there was worse in store for them a Dutch optician Hans Lipergy by name 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 weathercock of a neighbouring church spire was seen nearer and upside down the tale goes that the Marquis Benola happening to call it 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 reconnoitering 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 years 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 opticians 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 and 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 Dutchmen'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 is 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 this their power of forming real images the power on which their use is 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 for a magnifying glass or eyepiece 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 as 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 a 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 a way he went with it to Venice and showed it to the senioria 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 50 miles off clear 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 30 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 planes rocks and apparently seas you may imagine the hostility excited amongst the Aristotle 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 fought it and making it harsh and rugged and like so vile and ignoble a body is 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 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 a peculiar brilliancy of Venus is that she is a very cloudy planet 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 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 its 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 the 7th 1610 he noticed three little stars near it which he noted down as fixing its then position on the following night Jupiter 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 rush in patience 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 reappeared 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 around 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 thus be 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 afterward I hope, says Gallo 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 of five regular solids he says 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 eyeglass 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 into thinking how there could be any addition to the number of planets without overturning my mysterious cosmographic published 13 years ago according to which Euclid's five regular solids do not allow more than six planets around the sun but I am so far from disbelieving the existence of the four circumgivial planets that I long for a telescope to anticipate you if possible in discovering two around Mars as the proportion seems to me to require six or eight around Saturn and one each around Mercury and Venus as an illustration of the opposite school I will take the following extract from Francesco Sitzzi 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 unproperitius two luminaries and Mercury alone undecided and indifferent from which and many other similar phenomena of nature such as the seven metals etc. 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 for the seven planets now if we increase the number of 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 laboring before the Grand Duke with logical arguments as if with magical incantations to charm the new planets out of the sky a young German protégé of Kepler, Martin Horky 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 in optical illusions with 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 Shine accounted five, right at 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 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 End of lecture four read by Magnago