Pioneers of Science — Lecture IV: Galileo and the Invention of the Telescope

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 nebulæ.

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 × 16 = 144 feet; in 4 seconds 16 × 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.

[Illustration: FIG. 35. --Curve described by a projectile, showing how it drops from the line of fire, _O D_, in successive seconds, the same distances _AP_, _BQ_, _CR_, &c. , as are stated above for a dropped body.

] 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 £13 a year, or 7-1/2_d.

_ 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 Brahé 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.

[Illustration: FIG. 36. --Two forms of pulsilogy.

The string is wound up till the swinging weight keeps time with the pulse, and the position of a bead or of an index connected with the string is then read on a scale or dial.

] 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 7-1/2_d.

_ 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.

[Illustration: FIG. 37. --Tower of Pisa.

] 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.

[Illustration: FIG. 38. --View of the half-moon in small telescope.

The darker regions, or plains, used to be called "seas."

] 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.

[Illustration: FIG. 39. --Portion of the lunar surface more highly magnified, showing the shadows of a mountain range, deep pits, and other details.

] 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.

[Illustration: FIG. 40. --Another portion of the lunar surface, showing a so-called crater or vast lava pool and other evidences of ancient heat unmodified by water.

] 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.

[Illustration: FIG. 41. --Lunar landscape showing earth.

The earth would be a stationary object in the moon's sky: its only apparent motion being a slow oscillation as of a pendulum (the result of the moon's libration).

] 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).

[Illustration: FIG. 42. --Galileo's method of estimating the height of lunar mountain.

_AB'BC_ is the illuminated half of the moon.

_SA_ is a solar ray just catching the peak of the mountain _M_.

Then by geometry, as _MN_ is to _MA_, so is _MA_ to _MB'_; whence the height of the mountain, _MN_, can be determined.

The earth and spectator are supposed to be somewhere in the direction _BA_ produced, _i.

e. _ towards the top of the page.

] 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.

[Illustration: FIG. 43. --Some clusters and nebulæ.

] [Illustration: FIG. 44. --Jupiter's satellites, showing the stages of their discovery.