Ptolemy was an observer of the heavens, though not of the highest order; but he had all the work of his predecessors, best of all Hipparchus, to build upon. Ptolemy's greatest work was the "Megale Syntaxis," generally known as the Almagest. It forms a nearly complete compendium of the ancient astronomy, and although it embodies much error, because built on a wrong theory, the Almagest nevertheless is competent to follow the motions of all the bodies in the sky with a close approach to accuracy, even at the present day. This marvelous work written at this critical epoch became as authoritative as the philosophy of Aristotle, and for many centuries it was the last word in the science. The old astrology held full sway, and the Ptolemaic theory of the universe supplied everything necessary: further progress, indeed, was deemed impossible.
The Almagest comprises in all thirteen books, the first two of which deal with the simpler observations of the celestial sphere, its own motion and the apparent motions of sun, moon, and planets upon it. He discusses, too, the postulates of his system and exhibits great skill as an original geometer and mathematician. In the third book he takes up the length of the year, and in the fourth book similarly the moon and the length of the month. Here his mathematical powers are at their best, and he made a discovery of an inequality in the moon's motion known as the evection. Book five describes the construction and use of the astrolabe, a combination of graduated circles with which Ptolemy made most of his observations. In the sixth book he follows mainly Hipparchus in dealing with eclipses of sun and moon. In the seventh and eighth books he discusses the motion of the equinox, and embodies a catalogue of 1,028 stars, substantially as in Hipparchus. The five remaining books of the Almagest deal with the planetary motions, and are the most important of all of Ptolemy's original contributions to astronomy. Ptolemy's fundamental doctrines were that the heavens are spherical in form, all the heavenly motions being in circles. In his view, the earth too is spherical, and it is located at the center of the universe, being only a point, as it were, in comparison. All was founded on mere appearance combined with the philosophical notion that the circle being the only perfect curve, all motions of heavenly bodies must take place in earth-centered circles. For fourteen or fifteen centuries this false theory persisted, on the authority of Ptolemy and the Almagest, rendering progress toward the development of the true theory impossible.
Ptolemy correctly argued that the earth itself is a sphere that is curved from east to west, and from north to south as well, clinching his argument, as we do to-day, by the visibility of objects at sea, the lower portions of which are at first concealed from our view by the curved surface of the water which intervenes. To Ptolemy also the earth is at the center of the celestial sphere, and it has no motion of translation from that point; but his argument fails to prove this. Truth and error, indeed, are so deftly intermingled that one is led to wonder why the keen intelligence of this great philosopher permitted him to reject the simple doctrine of the earth's rotation on its axis. But if we reflect that there was then no science of natural philosophy or physics proper, and that the age was wholly undeveloped along the lines of practical mechanics, we shall see why the astronomers of Ptolemy's time and subsequent centuries were content to accept the doctrines of the heavens as formulated by him.
When it came to explaining the movements of the "wandering stars," or planets, as we term them, the Ptolemaic theory was very happy in so far as accuracy was concerned, but very unhappy when it had to account for the actual mechanics of the cosmos in space. Sun and moon were the only bodies that went steadily onward, easterly: whereas all the others, Mercury, Venus, Mars, Jupiter, Saturn, although they moved easterly most of the time, nevertheless would at intervals slow down to stationary points, where for a time they did not move at all, and then actually go backward to the west, or retrograde, then become stationary again, finally resuming their regular onward motion to the east.
To help out of this difficulty, the worst possible mechanical scheme was invented, that known as the epicycle. Each of the five planets was supposed to have a fictitious "double," which traveled eastward with uniformity, attached to the end of a huge but mechanically impossible bar. The earth-centered circle in which this traveled round was called the "deferent." What this bar was made of, what stresses it would be subjected to, or what its size would have to be in order to keep from breaking—none of these questions seems to have agitated the ancient and medieval astronomers, any more than the flat-earth astronomy of the Hindu is troubled by the necessity of something to hold up the tortoise that holds up the elephant that holds up the earth.
But at the end of this bar is jointed or swiveled another shorter bar, to the revolving end of which is attached the actual planet itself; and the second bar, by swinging once round the end of the primary advancing bar, would account for the backward or retrograde motion of the planet as seen in the sky. For every new irregularity that was found, in the motion of Mars, for instance, a new and additional bar was requisitioned, until interplanetary space was hopelessly filled with revolving bars, each producing one of the epicycles, some large, some small, that were needed to take up the vagaries of the several planets.
The Arabic astronomers who kept the science alive through the Middle Ages added epicycle to epicycle, until there was every justification for Milton's verses descriptive of the sphere:
With the fall of Alexandria and the victory of Mohammed throughout the West, and a consequent decline in learning, supremacy in science passed to the East and centered round the caliphs of Bagdad in the seventh and eighth centuries. They were interested in astronomy only as a practical, and to them useful, science, in adjusting the complicated lunar calendar of the Mohammedans, in ascertaining the true direction of Mecca which every Mohammedan must know, and in the revival of astrology, to which the Greeks had not attached any particular significance.
Harun al-Rashid ordered the Almagest and many other Greek works translated, of which the modern world would otherwise no doubt never have heard, as the Greek originals are not extant.
Splendid observatories were built at Damascus and Bagdad, and fine instruments patterned after Greek models were continuously used in observing. The Arab astronomers, although they had no clocks, were nevertheless so fully impressed with the importance of time that they added extreme value to their observations of eclipses, for example, by setting down the altitudes of sun or stars at the same time. On very important occasions the records were certified on oath by a body of barristers and astronomers conjointly—a precedent which fortunately has never been followed.
About the middle of the ninth century, the Caliph Al-Mamun directed his astronomers to revise the Greek measures of the earth's dimensions, and they had less reverence for the Almagest than existed in later centuries: indeed, Tabit ben Korra invented and applied to the tables of the Almagest a theoretical fluctuation in the position of the ecliptic which he called "trepidation," which brought sad confusion into astronomical tables for many succeeding centuries.
Albategnius was another Arab prince whose record in astronomy in the ninth and tenth centuries was perhaps the best: the Ptolemaic values of the precession of the equinoxes and of the obliquity of the ecliptic were improved by new observations, and his excellence as mathematician enabled him to make permanent improvements in the astronomical application of trigonometry.
Abul Wefa was the last of the Bagdad astronomers in the latter half of the tenth century, and his great treatise on astronomy known as the Almagest is sometimes confused with Ptolemy's work. Following him was Ibn Yunos of Cairo, whose labors culminated in the famous Hakemite Tables, which became the standard in mathematical and astronomical computations for several centuries.
Mohammedan astronomy thrived, too, in Spain and northern Africa. Arzachel of Toledo published the Toledan Tables, and his pupils made improvements in instruments and the methods of calculation. The Giralda was built by the Moors in Seville in 1196, the first astronomical observatory on the continent of Europe; but within the next half century both Seville and Cordova became Christian again, and Arab astronomy was at an end.
Through many centuries, however, the science had been kept alive, even if no great original advances had been achieved; and Arab activities have modified our language very materially, adding many such words as almanac, zenith, and radii, and a wealth of star names, as Aldebaran, Rigel, Betelgeuse, Vega, and so on.
Meanwhile, other schools of astronomy had developed in the East, one at Meraga near the modern Persia, where Nassir Eddin, the astronomer of Hulagu Khan, grandson of the Mongol emperor Genghis Khan, built and used large and carefully constructed instruments, translated all the Greek treatises on astronomy, and published a laborious work known as the Ilkhanic Tables, based on the Hakemite Tables of Ibn Yunos.
More important still was the Tartar school of astronomy under Ulugh Beg, a grandson of Tamerlane, who built an observatory at Samarcand in 1420, published new tables of the planets, and made with his excellent instruments the observations for a new catalogue of stars, the first since Hipparchus, the star places being recorded with great precision.
The European astronomy of the Middle Ages amounted to very little besides translation from the Arabic authors into Latin, with commentaries. Astronomers under the patronage of Alfonso X of Leon and Castile published in 1252 the Alfonsine Tables, which superseded the Toledan tables and were accepted everywhere throughout Europe. Alfonso published also the "Libros del Saber," perhaps the first of all astronomical cyclopedias, in which is said to occur the earliest diagram representing a planetary orbit as an ellipse: Mercury's supposed path round the earth as a center.
Purbach of Vienna about the middle of the 15th century began his "Epitome of Astronomy" based on the "Almagest" of Ptolemy, which was finished by his collaborator Regiomontanus, who was an expert in mathematics and published a treatise on trigonometry with the first table of sines calculated for every minute from 0° to 90°, a most helpful contribution to theoretical astronomy.
Regiomontanus had a very picturesque career, finally taking up his residence in Nuremberg, where a wealthy citizen named Walther became his patron, pupil, and collaborator. The artisans of the city were set at work on astronomical instruments of the greatest accuracy, and the comet of 1472 was the first to be observed and studied in true scientific fashion. Regiomontanus was very progressive and the invention of the new art of printing gave him an opportunity to publish Purbach's treatise, which went through several editions and doubtless had much to do in promoting dissatisfaction with the ancient Ptolemaic system, and was thus most significant in preparing a background for the coming of the new Copernican order.
The Nuremberg presses popularized astronomy in other important ways, issuing almanacs, the first precursors of our astronomical Ephemerides. Regiomontanus was practical as well, and invented a new method of getting a ship's position at sea, with tables so accurate that they superseded all others in the great voyages of discovery, and it is probable that they were employed by Columbus in his discovery of the American continent. Regiomontanus had died several years earlier, in 1475 at Rome, where he had gone by invitation of the Pope to effect a reformation in the calendar. He was only forty, and his patron Walther kept on with excellent observations, the first probably to be corrected for the effect of atmospheric refraction, although its influence had been known since Ptolemy. The Nuremberg School lasted for nearly two centuries.
Nearly contemporary with Regiomontanus were Fracastoro and Peter Apian, whose original observations on comets are worthy of mention because they first noticed that the tails of these bodies always point away from the sun. Leonardo da Vinci was the first to give the true explanation of earth-shine on the moon, and similarly the moon-illumination of the earth; and this no doubt had great weight in disposing of the popular notion of an essential difference of nature between the earth and celestial bodies—all of which helped to prepare the way for Copernicus and the great revolution in astronomical thought.
Throughout the Middle Ages the progress of astronomy was held back by a combination of untoward circumstances. A prolonged reaction from the heights attained by the Greek philosophers was to be expected. The uprising of the Mohammedan world, and the savage conquerors in the East did not produce conditions favorable to the origin and development of great ideas.
At the birth of Copernicus, however, in 1473, the time was ripening for fundamental changes from the ancient system, the error of which had helped to hold back the development of the science for centuries. The fifteenth century was most fruitful in a general quickening of intelligence, the invention of printing had much to do with this, as it spread a knowledge of the Greek writers, and led to conflict of authorities. Even Aristotle and Ptolemy were not entirely in harmony, yet each was held inviolate. It was the age of the Reformation, too, and near the end of the century the discovery of America exerted a powerful stimulus in the advance of thought.
Copernicus searched the works of the ancient writers and philosophers, and embodied in this new order such of their ideas as commended themselves in the elaboration of his own system.
Pythagoras alone and his philosophy looked in the true direction. Many believe that he taught that the sun, not the earth, is at the center of our solar system; but his views were mingled with the speculative philosophy of the Greeks, and none of his writings, barring a few meager fragments, have come down to our modern age.
To many philosophers, through all these long centuries, the true theory of the celestial motions must have been obvious, but their views were not formulated, nor have they been preserved in writing. So the fact remains that Copernicus alone first proved the truth of the system which is recognized to-day. This he did in his great treatise entitled "De Revolutionibus Orbium Cœlestium," the first printed copy of which was dramatically delivered to him on his deathbed, in May, 1543. The seventy years of his life were largely devoted to the preparation of this work, which necessitated many observations as well as intricate calculations based upon them. Being a canon in the church, he naturally hesitated about publishing his revolutionary views, his friend Rheticus first doing this for him in outline in 1540.
So simple are the great principles that they may be embodied in very few words; what appears to us as the daily revolution of the heavens is not a real motion, but only an apparent one; that is, the heavens are at rest, while the earth itself is in motion, turning round an axis which passes through its center. And the second proposition is that the earth is simply one of the six known planets; and they all revolve round the sun as the true center. The solar system, therefore, is "heliocentric," or sun-centered, not "geocentric" or earth-centered, as taught by the Ptolemaic theory.
Copernicus demonstrates clearly how his system explains the retrograde motion of the planets and their stationary points, no matter whether they are within the orbit of the earth, as Mercury and Venus, or outside of it, as Mars, Jupiter, and Saturn. His system provides also the means of ascertaining with accuracy the proportions of the solar system, or the relative distances of the planets from the sun and from each other. In this respect also his system possessed a vast advantage over that of Ptolemy, and the planetary distances which Copernicus computed are very close approximations to the measures of the present day.
Reinhold revised the calculations of Copernicus and prepared the "Tabulæ Prutenicæ," based on the "De Revolutionibus," which proved far superior to the Alfonsine Tables, and were only supplanted by the Rudolphine Tables of Kepler. On the whole we may regard the lifework of Copernicus as fundamentally the most significant in the history and progress of astronomy.
Clear as Copernicus had made the demonstration of the truth of his new system, it nevertheless failed of immediate and universal acceptance. The Ptolemaic system was too strongly intrenched, and the motions of all the bodies in the sky were too well represented by it. Accurate observations were greatly needed, and the Landgrave William IV. of Hesse built the Cassel Observatory, which made a new catalogue of stars, and introduced the use of clocks to carry on the time as measured by the uniform motion of the celestial sphere. Three years after the death of Copernicus, Tycho Brahe was born, and when he was 30 the King of Denmark built for him the famous observatory of Uraniborg, where the great astronomer passed nearly a quarter of a century in critically observing the positions of the stars and planets. Tycho was celebrated as a designer and constructor of new types of astronomical instruments, and he printed a large volume of these designs, which form the basis of many in use at the present day. Unfortunately for the genius of Tycho and the significance of his work, the invention of the telescope had not yet been made, so that his observations had not the modern degree of accuracy. Nevertheless, they were destined to play a most important part in the progress of astronomy.
Tycho was sadly in error in his rejection of the Copernican system, although his reasons, in his day, seemed unanswerable. If the outer planets were displaced among the stars by the annual motion of the earth round the sun, he argued, then the fixed stars must be similarly displaced—unless indeed they be at such vast distances that their motions would be too slight to be visible. Of course we know now that this is really true, and that no instruments that Tycho was able to build could possibly have detected the motions, the effects of which we now recognize in the case of the nearer fixed stars in their annual, or parallactic, orbits.
The remarkably accurate instruments devised by Tycho Brahe and employed by him in improving the observations of the positions of the heavenly bodies were no doubt built after descriptions of astrolabes such as Hipparchus used, as described by Ptolemy. In his "Astronomiæ Instauratæ Mechanica" we find illustrations and descriptions of many of them.
One is a polar astrolabe, mounted somewhat as a modern equatorial telescope is, and the meridian circle is adjustable so that it can be used in any place, no matter what its latitude might be. There is a graduated equatorial ring at right angles to the polar axis, so that the astrolabe could be used for making observations outside the meridian as well as on it. This equatorial circle slides through grooves, and is furnished with movable sights, and a plumb line from the zenith or highest point of the meridian circle makes it possible to give the necessary adjustment in the vertical. Screws for adjustment at the bottom are provided, just as in our modern instruments, and two observers were necessary, taking their sights simultaneously; unless, as in one type of the instrument, a clock, or some sort of measure of time, was employed.
Another early type of instrument is called by Tycho the ecliptic astrolabe (Armillæ Zodiacales, or the Zodiacal Rings). It resembles the equatorial astrolabe somewhat, but has a second ring inclined to the equatorial one at an angle equal to the obliquity of the ecliptic. In observing, the equatorial ring was revolved round till the ecliptic ring came into coincidence with the plane of the ecliptic in the sky. Then the observation of a star's longitude and latitude, as referred to the ecliptic plane, could be made, quite as well as that of right ascension and declination on the equatorial plane. But it was necessary to work quickly, as the adjustment on the ecliptic would soon disappear and have to be renewed.
Tycho is often called the father of the science of astronomical observation, because of the improvements in design and construction of the instruments he used. His largest instrument was a mural quadrant, a quarter-circle of copper, turning parallel to the north-and-south face of a wall, its axis turning on a bearing fixed in the wall. The radius of this quadrant was nine feet, and it was graduated or divided so as to read the very small angle of ten seconds of arc—an extraordinary degree of precision for his day.
Tycho built also a very large alt-azimuth quadrant, of six feet radius. Its operation was very much as if his mural quadrant could be swung round in azimuth. At several of the great observatories of the present day, as Greenwich and Washington, there are instruments of a similar type, but much more accurate, because the mechanical work in brass and steel is executed by tools that are essentially perfect, and besides this the power of the telescope is superadded to give absolute direction, or pointing on the object under observation.
Excellent clocks are necessary for precise observation with such an instrument; but neither Tycho Brahe, nor Hevelius was provided with such accessories. Hevelius did not avail himself of the telescope as an aid to precision of observation, claiming that pinhole sights gave him more accurate results. It was a dispute concerning this question that Halley was sent over from London to Danzig to arbitrate.
There could be but one way to decide; the telescope with its added power magnifies any displacement of the instrument, and thereby enables the observer to point his instrument more exactly. So he can detect smaller errors and differences of direction than he can without it. And what is of great importance in more modern astronomy, the telescope makes it possible to observe accurately the position of objects so faint that they are wholly invisible to the naked eye.
Most fortunate it was for the later development of astronomical theory that Tycho Brahe not only was a practical or observational astronomer of the highest order, but that he confined himself studiously for years to observations of the places of the planets. Of Mars he accumulated an especially long and accurate series, and among those who assisted him in his work was a young and brilliant pupil named Johann Kepler.
Strongly impressed with the truth of the Copernican System, Kepler was free to reject the erroneous compromise system devised by Tycho Brahe, and soon after Tycho's death Kepler addressed himself seriously to the great problem that no one had ever attempted to solve, viz: to find out what the laws of motion of the planets round the sun really are. Of course he took the fullest advantage of all that Ptolemy and Copernicus had done before him, and he had in addition the splendid observations of Tycho Brahe as a basis to work upon.
Copernicus, while he had effected the tremendous advance of substituting the sun for the earth as the center of motion, nevertheless clung to the erroneous notion of Ptolemy that all the bodies of the sky must perforce move at uniform speeds, and in circular curves, the circle being the only "perfect curve." Kepler was not long in finding out that this could not be so, and he found it out because Tycho Brahe's observations were much more accurate than any that Copernicus had employed.
Naturally he attempted the nearest planet first, and that was Mars—the planet that Tycho had assigned to him for research. How fortunate that the orbit of Mars was the one, of all the planets, to show practically the greatest divergence from the ancient conditions of uniform motion in a perfectly circular orbit! Had the orbit of Mars chanced to be as nearly circular as is that of Venus, Kepler might well have been driven to abandon his search for the true curve of planetary motion.
However, the facts of the cosmos were on his side, but the calculations essential in testing his various hypotheses were of the most tedious nature, because logarithms were not yet known in his day. His first discovery was that the orbit of Mars is certainly not a circle, but oval or elliptic in figure. And the sun, he soon found, could not be in the center of the ellipse, so he made a series of trial calculations with the sun located in one of the foci of the ellipse instead.
Then he found he could make his calculated places of Mars agree quite perfectly with Tycho Brahe's observed positions, if only he gave up the other ancient requisite of perfectly uniform motion. On doing this, it soon appeared that Mars, when in perihelion, or nearest the sun, always moved swiftest, while at its greatest distance from the sun, or aphelion, its orbital velocity was slowest.
Kepler did not busy himself to inquire why these revolutionary discoveries of his were as they were; he simply went on making enough trials on Mars, and then on the other planets in turn, to satisfy himself that all the planetary orbits are elliptical, not circular in form, and are so located in space that the center of the sun is at one of the two foci of each orbit. This is known as Kepler's first law of planetary motion.
The second one did not come quite so easy; it concerned the variable speed with which the planet moves at every point of the orbit. We must remember how handicapped he was in solving this problem: only the geometry of Euclid to work with, and none of the refinements of the higher mathematics of a later day. But he finally found a very simple relation which represented the velocity of the planet everywhere in its orbit. It was this: if we calculate the area swept, or passed over, by the planet's radius vector (that is, the line joining its center to the sun's center) during a week's time near perihelion, and then calculate the similar area for a week near aphelion, or indeed for a week when Mars is in any intermediate part of its orbit, we shall find that these areas are all equal to each other. So Kepler formulated his second great law of planetary motion very simply: the radius vector of any planet describes, or sweeps over, equal areas in equal times. And he found this was true for all the planets.
But the real genius of the great mathematician was shown in the discovery of his third law, which is more complex and even more significant than the other two—a law connecting the distances of the planets from the sun with their periods of revolution about the sun. This cost Kepler many additional years of close calculation, and the resulting law, his third law of planetary motion is this: The cubes of the mean or average distances of the planets from the sun are proportional to the squares of their times of revolution around him.
So Kepler had not only disposed of the sacred theories of motion of the planets held by the ancients as inviolable, but he had demonstrated the truth of a great law which bound all the bodies of the solar system together. So accurately and completely did these three laws account for all the motions, that the science of astronomy seemed as if finished; and no matter how far in the future a time might be assigned, Kepler's laws provided the means of calculating the planet's position for that epoch as accurately as it would be possible to observe it. Kepler paused here, and he died in 1630.
The fifteenth and sixteenth centuries, containing the lives and work of Copernicus, Tycho, Galileo, Kepler, Huygens, Halley, and Newton, were a veritable Golden Age of astronomy. All these men were truly great and original investigators.
None had a career more picturesque and popular than did Galileo. Born a few years earlier and dying a few years later than Kepler, the work of each of these two great astronomers was wholly independent of the other and in entirely different fields. Kepler was discovering the laws of planetary motion, while Galileo was laying the secure foundations of the new science of dynamics, in particular the laws of falling bodies, that was necessary before Kepler's laws could be fully understood. When only eighteen Galileo's keen power of observation led to his discovery of the laws of pendulum motion, suggested by the oscillation to and fro of a lamp in the cathedral of Pisa.
The world-famous leaning tower of this place, where he was born, served as a physical laboratory from the top of which he dropped various objects, and thus was led to formulate the laws of falling bodies. He proved that Aristotle was all wrong in saying that a heavy body must fall swifter in proportion to its weight than a lighter one. These and other discoveries rendered him unpopular with his associates, who christened him the "Wrangler."
The new system of Copernicus appealed to him; and when he, first of all men, turned a telescope on the heavenly bodies, there was Venus with phases like those of the moon, and Jupiter with satellites traveling about it—a Copernican system in miniature. Nothing could have happened that would have provided a better demonstration of the truth of the new system and the falsity of the old. His marvelous discoveries caused the greatest excitement—consternation even, among the anti-Copernicans. Galileo published the "Sidereus Nuncius," with many observations and drawings of the moon, which he showed to be a body not wholly dissimilar to the earth: this, too, was obviously of great moment in corroboration of the Copernican order and in contradiction to the Ptolemaic, which maintained sharp lines of demarcation between things terrestrial and things celestial.
His telescopes, small as they were, revealed to him anomalous appearances on both sides of the planet Saturn which he called ansæ, or handles. But their subsequent disappearance was unaccountable to him, and later observers, who kept on guessing ineffectively till Huygens, nearly a half century after, showed that the true nature of the appendage was a ring. Spots on the sun were frequently observed by Galileo and led to bitter controversies. He proved, however, that they were objects on the sun itself, not outside it, and by noticing their repeated transits across the sun's disk, he showed that the sun turned round on his axis in a little less than a month—another analogy to the like motion of the earth on the Copernican plan.
Galileo's appointment in 1610 as "First Philosopher and Mathematician" to the Grand Duke of Tuscany gave him abundant time for the pursuit of original investigations and the preparation of books and pamphlets. His first visit to Rome the year following was the occasion of a reception with great honor by many cardinals and others of high rank. His lack of sympathy with others whose views differed from his, and his naturally controversial spirit, had begun to lead him headlong into controversies with the Jesuits and the church, which culminated in his censure by the authorities of the church and persecution by the Inquisition.
In 1618 three comets appeared, and Galileo was again in controversial hot water with the Jesuits. But it led to the publication five years later of "Il Saggiatore" (The Assayer), of no great scientific value, but only a brilliant bit of controversial literature dedicated to the newly elevated Pope, Urban VIII. Later he wrote through several years a great treatise, more or less controversial in character, entitled a "Dialogue on the Two Chief Systems of the World" between three speakers, and extending through four successive days. Simplicio argues for the Aristotelians, Salviati for the Copernicans, while Sagredo does his best to be neutral. It will always be a very readable book, and we are fortunate to have a recent translation by Professor Crew of Evanston.
Here we find the first suggestion of the modern method of getting stellar parallaxes, the relative parallax, that is, of two stars in the same field—a method not put into service till Bessel's time, two centuries later. But the most important chapters of the "Dialogue" deal with Galileo's investigations of the laws of motion of bodies in general, which he applied to the problem of the earth's motion. In this he really anticipated Newton in the first of his three laws of motion, and in a subsequent work, dealing with the theory of projectiles, he reaches substantially the results of Newton's second law of motion, although he gave no general statement of the principle. Nevertheless, in the epoch where his life was lived and his work done, his telescopic discoveries, combined with his dynamic researches in untrodden fields, resulted in the complete and final overthrow of the ancient system of error, and the secure establishment of the Copernican system beyond further question and discussion. Only then could the science of astronomy proceed unhampered to the fullest development by the master minds of succeeding centuries.
Following Kepler and Galileo was a half century of great astronomical progress along many lines laid out by the work of the great masters. The telescope seemed only a toy, but its improvement in size and quality showed almost inconceivable possibilities of celestial discoveries.
Hevelius of Danzig took up the study of the moon, and his "Selenographia" was finely illustrated by plates which he not only drew but engraved himself. Lunar names of mountains, plains, and craters we owe very largely to him. Also he published among other works two on comets, the second of which was published in 1668 and called the "Cometographia," the first detailed account of all the comets observed and recorded to date.
Many were the telescopes turned on the planet Saturn, and every variety of guess was made as to the actual shape and physical nature of the weird appendages discovered by Galileo. The true solution was finally reached by Huygens, whose mechanical genius had enabled him to grind and polish larger and better lenses than his contemporaries; in 1659 he published the "Systema Saturnium" interpreting the ring and the cause of its various configurations, and the first discovery of a Saturnian satellite is due to him.
Gascoigne in England about 1640 was the first to make the important application of the micrometer to enhance the accuracy of measurement of small angles in the telescopic field; an invention made and applied independently many years later by Huygens in Holland and Auzout and Picard in France, where the instrument was first regularly employed as an accessory in the work of an observatory.
Another Englishman, Jeremiah Horrocks, was the first observer of a transit of Venus over the disk of the sun, in 1639. Horrocks was possessed of great ability in calculational astronomy also. This was about the time of the invention of the pendulum clock by Huygens, which in conjunction with the later invention of the transit instrument by Roemer wrought a revolution in the exacting art of practical astronomy. This was because it enabled the time to be carried along continuously, and the revolution of the earth could be utilized in making precise measures of the position of sun, moon, and stars. Louis XIV had just founded the new Observatory at Paris in 1668, and Picard was the first to establish regular time-observations there.
Huygens followed up the motion of the pendulum in theory as well as practice in his "Horologium Oscillatorium" (1673), showing the way to measure the force of gravity, and his study of circular motion showed the fundamental necessity of some force directed toward the center in planetary motions.
The doctrine of the sphericity of the earth being no longer in doubt, the great advance in accuracy of astronomical observation indicated to Willebrord Snell in Holland the best way to measure an arc of meridian by triangulation. Picard repeated the measurements near Paris with even greater accuracy, and his results were of the utmost significance to Newton in establishing his law of gravitation.
Domenico Cassini, an industrious observer, voluminous writer, and a strong personality, devised telescopes of great size, discovered four Saturnian satellites and the main division in the ring of Saturn, determined the rotation periods of Mars and Jupiter, and prepared tables of the eclipses of Jupiter's satellites. At his suggestion Richer undertook an expedition to Cayenne in latitude 5 degrees north, where it was found that the intensity of gravity was less than at Paris, and his clock therefore lost time, thus indicating that the earth was not a perfect sphere as had been thought, but a spheroid instead.
The planet Mars passed a near opposition, and Richer's observations of it from Cayenne, when combined with those of Cassini and others in France, gave a new value of the sun's parallax and distance, really the first actual measurement worth the name in the history of astronomy.
To close this era of signal advance in astronomy we may cite a discovery by Roemer of the first order: no less than that of the velocity of transmission of light through space. At the instigation of Picard, Roemer in studying the motions of Jupiter's satellites found that the intervals between eclipses grew less and less as Jupiter and the earth approached each other, and greater and greater than the average as the two planets separated farther and farther. Roemer correctly attributed this difference to the progressive motion of light and a rough value of its velocity was calculated, though not accepted by astronomers generally for more than a century.
Why the laws of Kepler should be true, Kepler himself was unable to say. Nor could anyone else in that day answer these questions: (1) The planets move in orbits that are elliptical not circular—why should they move in an imperfect curve, rather than the perfect one in which it had always been taught that they moved? (2) Why should our planet vary its velocity at all, and travel now fast, now slow; especially why should the speed so vary that the line of varying length, joining the planet to the sun, always passes over areas proportional to the time of describing them? And (3) Why should there be any definite relation of the distances of planets from the sun to their times of revolution about him? Why should it be exactly as the cube of one to the square of the other?
We must remember that the Copernican system itself was not yet, in the beginning of the seventeenth century, accepted universally; and the great minds of that period were most concerned in overturning the erroneous theory of Ptolemy.
The next step in logical order was to find a basic explanation of the planetary motions, and Descartes and his theory of vortices are worthy of mention, among many unsuccessful attempts in this direction. Descartes was a brilliant French philosopher and mathematician, but his hypothesis of a multitude of whirlpools in the ether, while ingenious in theory, was too vague and indefinite to account for the planetary motions with any approach to the precision with which the laws of Kepler represented them.
Another great astronomer whose labors helped immensely in preparing the way for the signal discoveries that were soon to come was Huygens, a man of versatility as natural philosopher, mechanician, and astronomical observer. Huygens was born thirteen years before the death of Galileo, and to the discovery of the laws of motion by the latter Huygens added researches on the laws of action of centrifugal forces. Neither of them, however, appeared to see the immediate bearing on the great general problem of celestial motions in its true light, and it was reserved for another generation, and an astronomer of another country, to make the one fundamental discovery that should explain the whole by a single simple law.
"How is it that you are able to make these great discoveries?" was once asked of Sir Isaac Newton, facile princeps of all philosophers, and the discoverer of the great law of universal gravitation.
"By perpetually thinking about them," was Newton's terse and illuminating reply. He had set for himself the definite problem of Kepler's laws: why is it that they are true, and is there not some single, general law that will embody all the circumstances of the planetary motions?
Newton was born in 1643, the year after the death of Galileo. He had a thorough training in the mathematics of his day, and addressed himself first to an investigation and definite formulation of the general laws of motion, which he found to be three in number, and which he was able to put in very simple terms. The first one is: Any body, once it is set in motion, will continue to move forward in a straight line with a uniform velocity forever, provided it is acted upon by no force whatever. In other words, a state of motion is as natural as a state of rest (rest in relation to things everywhere adjacent) in which we find all things in general.
Here on earth where gravity itself pulls all objects downward toward the earth, and where resistance of the air tends to hold a moving body back and bring it to rest, and where friction from contact with whatever material substance may be in its path is perpetually tending to neutralize all motion—with all three of these forces always at work to stop a moving body, the truth of this first and fundamental law of motion was not apparent on the surface.
Till Galileo's time everyone had made the mistake of supposing that some force or other must be acting continually on every moving body to keep it in motion. Ptolemy, Copernicus, Kepler, Leonardo da Vinci—all failed to see the truth of this law which Newton developed in the immortal Principia. And at the present day it is not always easy to accept at first, although the progress of mechanical science, by reducing friction and resistance, has produced machines in which motion of large masses may be kept up indefinitely with the application of only the merest minimum of force.
Once a planet is set in motion round the sun, it would go on forever through frictionless, non-resistant space; but there must be a central force, as Huygens saw clearly, to hold it in its orbit. Otherwise it would at any moment take the direction of a tangent to the orbit. Here is where Newton's second law of motion comes in, and he formulated it with great definiteness. When any force acts on a moving body, its deviation from a straight line will be in the direction of the force applied and proportional to that force.
In accord with this law, Newton first began to inquire whether the force of attraction here on earth, which everyone commonly recognizes as gravity, drawing all things down toward the center of the earth, might not extend upward indefinitely. It is found in operation on the summits of mountain peaks, and the clouds above them and the rain falling from them are obviously drawn downward by the same force. May it not extend outward into space, even as far as the moon?
This was an audacious question, but Newton not only asked, but tried to answer it in the year 1665, when he was only twenty-three. On the surface of the earth this attraction is strong enough to draw a falling body downward through a vertical space of sixteen feet in a second of time. What ought it to be at the distance of the moon. The distance of the moon in Newton's time was better known in terms of the earth's size than was the size of the earth itself: the earth's radius was known to be one-sixtieth of the moon's distance, but the earth's diameter was thought to be something under 7,000 miles, so that Newton's first calculations were most disappointing, and he laid them aside for nearly twenty years.
Meanwhile the French astronomers led by Picard had measured the earth anew, and showed it to be nearly 8,000 miles in diameter. As soon as Newton learned of this, he revised his calculations, and found that by the law of the inverse square the moon, in one second, should fall away from a tangent to its orbit one thirty-six hundredth of sixteen feet.
This accorded exactly with his original supposition that the earth's attraction extended to the moon. So he concluded that the force which makes a stone fall, or an apple, as the story goes, is the same force that holds the moon in its orbit, and that this force diminishes in the exact proportion that the square of the distance from the earth's center increases. The moon, indeed, becomes a falling body; only, as Kingdon Clifford puts it: "She is going so fast and is so far off that she falls quite around to the other side of the earth, instead of hitting it; and so goes on forever."