Science in the Age of Galileo

(Napisao: gosp. Marko Marelić -  S. Francisco - USA)
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Tools and Methods of Science

First there had to be scientific instruments. The eyes could not see clearly enough, far enough, minutely enough. The flesh could not feel with required accuracy the pressure, warmth, and weight of things. The mind could not measure space, time quantity, quality, or density without mingling its personal equation with the facts. Microscopes were needed, telescopes, thermometers, barometers, hydrometers, better watches, finer scales. And one by one they came. In his Magia naturalis (1589) Giambattista della Porta wrote, "With a concave lens things appear smaller but plainer; with a convex lens you see them larger but less distinct. If, however, you know how to combine the two sorts properly, you will see near and far both large and clear." Here was the principle of the microscope, the field glass, the opera glass, the telescope, a whole array of inventions, and all histology. The simple microscope, a single convex lens had long been known. The invention that transformed biology was the compound microscope which combined several converging lenses. The industry of grinding and polishing lenses was especially developed in the Netherlands - Spinoza lived and died by it. About 1590 Zacharias Janssen, a spectacle-maker of Middleburg, combined a double convex lens and a double concave lens to make the earliest known compound microscope. From that invention came modern biology and modern medicine.

A further application of these principles transformed astronomy. On October 2, 1608, another spectacle-maker of Middleburg, Hans Lippershey, presented to the States-General of the United Provinces (still at war with Spain) the description of an instrument for seeing objects at a distance. Lippershey had placed a double convex lens (the "object glass") at the farther end of a tube, and a double concave lens (the "eyepiece") at the nearer end. The legislators saw the military value of the invention and awarded Lippershey nine hundred florins. On October 17 another Dutchman, Jacobus Metius, stated that he had independently made a similar instrument. Hearing of these developments, Galileo made his own telescopes at Padua in 1609, which magnified to three diameters; these were the instruments with which he began to enlarge the world. In 1611 Kepler suggested that still better results could be obtained by reversing the Galilean position of the lenses, using the convex lens as the "eyepiece" and the concave lens as the "object glass. And in 1613-17 the Jesuit Christoph Scheiner made an improved telescope on this plan.

Meanwhile, on principles known to Hero of Alexandria in or before the third century A.D., Galileo had invented a thermometer (c. 1603). He placed the open end of a glass tube into a vessel of water. The other end of the tube was an empty glass bulb which he warmed by the touch of his hand. When he withdrew his hand the bulb cooled and water rose in the tube. Galileo's friend Giovanni Sagredo (1613) marked off the tube into a hundred degrees.

A pupil of Galileo, Evangelista Torricelli, closed a long glass tube at one end, filled it with mercury, and stood with its open end submerged in a dish of mercury. The mercury in the tube did not flow down into the dish. Scholastic physics explained it as due to the pressure of the surrounding atmosphere upon the mercury in the dish. He reasoned that this outside pressure would raise the mercury in the vessel into an empty tube freed from air and the experiment proved him right. He showed that variations in the height of the mercury in the tube could be used as a measure of variations in atmospheric pressure. So in 1643 he constructed the first barometer - still the basic instrument of meteorology.

Armed with these new tools, the sciences called to mathematicians for improved methods of calculation, measurement, and notation. Napier and Burgi responded with logarithms, Oughtred responded with the slide rule, but a greater help came with the decimal system. Tentative suggestions, as usual, had prepared the way. Al-Kashi of Samarkand (.1436) had expressed the ratio of the circumference of a circle to the diameter as 3 1415926535898 732 which is a decimal using a space instead of a point. Francesco Pellos of Nice in 1492 used a point. Simon Stevinum expounded the new system in an epochal treatise, The Decimal (1585), in which he offered the "teach with unheard of ease how to perform all calculations . . . by whole numbers without fractions." The metric system in Continental Europe carried out his ideas in the measurement of lengths, volumes, and currencies. But the circle and the clock paid tribute to Babylonian mathematics by retaining a sexagesimal division.

Gerard Desargues published a classic treatise on conic sections in 1639. Francois Viete of Paris revived the languishing study of algebra by using letters for known as well as unknown quantities, and he anticipated Descartes by applying algebra to geometry. Descartes established analytical geometry in a flash of inspiration when he proposed that numbers and equations can be represented by geometrical figures and vice versa (so the progressive depreciation of currency in a course of time can be shown as a statistical graph), and that from an algebraic equation representing a geometrical figure consequences can be algebraically drawn which will prove geometrically true; algebra could therefore be used to solve difficult geometrical problems. Descartes was so charmed with his discoveries that he thought his geometry was far superior to that of his predecessors as the eloquence of Cicero above the A B C of children. His analytical geometry, Cavalieri's theory of indivisibles (1629), Kepler's approximate squaring of the circle, and the squaring of the cycloid by Roberval, Torricelli, and Descartes all prepared Leibniz and Newton to discover calculus.

Mathematics was now the goal as well as the indispensable tool of all the sciences. Kepler observed that when the mind leaves the realm of quantity it wanders in darkness and doubt. "Philosophy," said Galileo, meaning "natural philosophy" or science, "is written in this grand book of the universe, which stands continually open to our gaze. But the book cannot be understood unless we first learn to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics."

Descartes and Spinoza
longed to reduce metaphysics itself to mathematical form.

Science now began to liberate itself from the placenta of its mother, philosophy. It shrugged Aristotle from its back, turned its face from metaphysics to Nature, developed its own distinctive methods, and looked to improve the life of man on the earth. This movement belonged to the heart of the Age of Reason, but it did not put its faith in "pure reason" - reason independent of experience and experiment. Too often such reasoning had woven mythical webs. Reason, as well as tradition and authority was now to be checked by the study and recording of lowly facts; and whatever "logic" might say, science would aspire to accept only what could be quantitatively measured, mathematically expressed and experimentally proved.

Science and Matter

The sciences advanced in logical progression through modern history: mathematics and physics in the seventeenth century, chemistry in the eighteenth, biology in the nineteenth and psychology in the twentieth century.

The great name in the physics of this period is Galileo, but many lesser heroes merit remembrance. Stevinus helped to determine the laws of the pulley and the lever; he made valuable studies in water pressure, the center of gravity, the parallelogram of forces, and the inclined plane; and at Delft about 1690 he anticipated Galileo's alleged experiment at Pisa by showing, contrary to immemorial belief, that when two like objects of however different weight are let fall together from a height they reach the ground at the same time. Descartes laid down quite clearly the law of inertia - that a body persists in its state of rest or in rectilinear motion unless affected by some external force. He and Gassendi anticipated the molecular theory of heat. He based his Meteores (1637) on a cosmology no longer accepted, but the treatise did much to establish meteorology as a science. Torricelli (1642) extended his studies of atmospheric pressure to the mechanics of winds. These, he held, were the equalizing currents set up by local differences in the density of the air. Gassendi, that remarkable priest of all the sciences, carried on experiments for measuring the speed of sound - his results gave 1,473 feet per second. His friar friend, Marin Mersenne, repeated the experiment and reported 1,380 feet, closer to the correct figure of 1.087 feet per second. Mersenne in 1636 established the whole series of overtones produced by a sounding string.

Research in optics centered on the complex problems of reflection and refraction, especially as seen in the rainbow. About 1591 Marco Antonio de Dominis, Archbishop of Spalato (Split) composed a treatise, De radiis visus et lucis . . . et iride published 1611), in which he explained the formation of the primary rainbow (the only one generally visible) as due to two refractions and one reflection of light in drops of moisture in sky or spray, and that of the secondary rainbow (an arc of colors in reversed order, sometimes faintly seen outside the primary bow) as due to two refractions and two reflections. In 1611 Kepler's Dioptrice studies the refraction of light by lenses; and ten years later Willebrord Snell of Leiden formulated the laws of refraction with a precision that made possible a more accurate computation of the action of lenses on light and the construction of better microscopes and telescopes. Descartes applied these laws to a mechanical calculation of radiation angles in the rainbow. Explanation of the color arrangement had to wait for Newton.

Gilbert's epochal discussion of terrestrial magnetism set off a train of theories and experiments. Famianus Strada of the Society of Jesus, suggested telegraphy (1617) by proposing that two men might communicate through a distance by utilizing the sympathetic action of two magnetic needles made to point simultaneously to the same letter of the alphabet. Another Jesuit, Niccolo Cabeo (1629), gave the first known description of electrical repulsion. Still another, Athanasius Kircher described in his Magnes (1641) a measurement of magnetism by suspending a magnet from one pan of a balance and counterpoising its influence by weights in the other. Descartes ascribed magnetism to the conflict of particles thrown off by the great vortex from which he believed the universe had evolved.

Alchemy was still popular, especially as a royal substitute for debasing the currency. Emperor Rudolf II, the electors of Saxony, Brandenburg, and the Palatinate, the Duke of Brunswick, the Landgrave of Hesse, all engaged alchemists to manufacture silver or gold. From these experiments, from the needs of metallurgy and the dyeing industry, and from the emphasis of Paracelsus on chemical medicine, the science of chemistry was taking form. Andreas Libavius personified the transition. His Defense of Transmutatory Alchemy (1604) continued the old quest, but his Alchymia (1597) was the first systematic treatise on scientific chemistry. He discovered stannic chloride, was the first to make ammonium sulfate, and was among the first to suggest blood transfusions as therapy. His laboratory at Coburg was one of the wonders of the city. Jan Baptista van Helmont, a wealthy nobleman who devoted himself to science and the medical service of the poor, placed his name among the founders of chemistry by distinguishing gases from air and analyzing their varieties and composition; he coined the word chemistry from the Greek chaos. He made many discoveries in his chosen field, ranging from the explosive gases of gunpowder to the inflammatory possibilities of human wind. He suggested the use of alkalis to correct undue acidity in the digestive tract. Johann Glauber recommended crystalline sodium sulfate as "a splendid medicine for internal and external use," and "Glauber's salt" is still used as an aperient. Both he and Helmont dabbled in alchemy.

All these "natural sciences" shared in improving industrial production and martial slaughter. Technicians applied the new knowledge of movements and pressures in liquids and gases, the composition of forces, the laws of the pendulum, the course of projectiles, the refining of metals. Gunpowder was used in mine blasting (1613). In 1612 Simon Sturtevant devised a method of producing coke - i.e., "coking" (cooking or heating) bituminous coal to rid it of volatile ingredients; this coke was valuable in metallurgy, as the impurities in coal affected iron; it replaced charcoal and saved forests. The making of glass was cheapened so as a result windowpanes became common in this age. Mechanical inventions multiplied as industry grew, for they were due less frequently to the researches of scientists than to the skill of artisans anxious to save time. So we first hear of the screw lathe in 1578, the knitting frame in 1589, the revolving stage in 1597, and the threshing machine and the fountain pen in 1636.

Engineers were accomplishing feats that even today would merit admiration. Domenico Fontana aroused Rome by erecting an obelisk in St. Peter's Square. Stevinus, as an engineer for Maurice of Nassau, developed a system of sluices to control dykes - guardian of the Dutch Republic. Giant bellows ventilated mines; complicated pumps raised water into towers to give pressure for houses and fountains in cities like Augsburg, Paris and London. Truss bridges were built on the simple principle that a triangle cannot be deformed without changing the length of a side. In 1624 a submarine traveled two miles under water in the Thames. Jerome Cardan, Giambattista della Porta and Salomon de Caus advanced the theory of the steam engine; Caus in 1615 described a machine for raising water by the expansive power of steam.

Geology was still unborn, even as a word; the study of the earth was called mineralogy and respect for the Biblical story of Creation checked all ventures in cosmonology. Bernard Palissy was denounced as a heretic for reviving the ancient view that fossils were the petrified remains of dead organisms. Descartes ventured to suggest that the planets, including the earth, had once been glowing masses, like the sun, and that as the planet cooled it formed a crust of liquids and solids over a central fire, whose exhalations produced geysers, volcanoes and earthquakes.

Geography progressed as missionaries, explorers and merchants strove to extend their faith, their knowledge, or their sales. Spanish navigators (1567) explored the South Seas and discovered Guadalcanal and others of the Solomon Islands - so named in the hope of finding there Solomon's mines. Pecho Paes, a Portuguese missionary, taken prisoner in Abyssinia (1588), visited the Blue Nile and solved an ancient riddle by showing that the periodic inundations of the Nile Valley were due to the rainy season in the Abyssinian highlands. Willem Janszoon was apparently the first European to touch Australia (1606), and Abel Tasman discovered Tasmania, New Zealand (1642), and the Fiji Islands (1643). Dutch traders entered Siam, Burma, and Indochina, but information about these countries and China came chiefly from Jesuit missionaries. Samuel Champlain, under orders of Henry IV of France, explored the coast of Nova Scotia and ascended the St. Lawrence River to the vicinity of Montreal. His followers founded Quebec and charted the lake that bears his name.

The mapmakers struggled to keep not too far behind the explorers. Gerardus Mercator (Gerhard Kremer) studied at Louvain and established there a shop for making maps, scientific instruments, and celestial globes. In 1544 he was arrested and prosecuted for heresy, but escaped serious consequences; however, he thought it prudent to accept an invitation to the University of Duisburg, where he became a cartographer to the Duke of Julich-Cleves (1559). During the eighty-two years of his life he labored tirelessly to map Flanders, Lorraine, Europe, indeed the earth. His famous Novus et acuta terrae descripto ad usum navigantius accomodata (1568) introduced the "Mercator's projection" maps, which facilitated navigation by representing all meridians of longitude as parallel to one another, all parallels of latitude as straight lines, and both sets of lines at right angles to each other. In 1585 he began to issue his great Atlas (we owe this use of the word to him), containing fifty-one regional maps of unprecedented precision and accuracy, describing the whole earth as then known. His friend Abraham Oertel rivaled him with a comprehensive Theatrum orbis terrarium (Antwerp, 1570). Together these men freed geography from its millennial bondage to Ptolemy and established it in its modern form. Because of them the Dutch maintained almost a monopoly on mapmaking for a century.

Science and Life

Biology still had to wait two centuries for its heyday. Botany grew leisurely through medical studies of curative herbs and the importation of exotic plants into Europe. Jesuit missionaries brought in Peruvian bark (quinine), vanilla, and rhubarb. About 1560 the potato was introduced from Peru to Spain and then it spread across the Continent. Prospero Alpini, professor of botany at Padua, described fifty foreign plants newly cultivated in Europe. From his studies of the date palm he deduced the doctrine of sexual reproduction in plants, which Theophrastus had expressed in the third century B.C. "The female date trees," said Alpini, "do not bear fruit unless the branches of the male and female plants are mixed together, or as is generally done, unless the dust found in the male sheath or male flowers is sprinkled over the female flowers." Linnaeus would later classify plants according to their mode of reproduction; but meanwhile (1583) Andrea Cesalpino of Florence offered the first systematic classification of plants - 1500 of them - on the basis of their different seeds and fruits. Gaspard Bauhin, of Basel, in his massive Pinas theatric botanici (1623), classified 6000 plants, anticipating Linnaeus' binomial nomenclature by genus and species. Bauhin devoted forty years to preparing this Table of the Botanic World, and he died a year after its publication. For three centuries it remained a standard text.

The private herbariums of physicians were now evolving into botanical gardens maintained for the public by universities or governments. The earliest, established at Pisa in 1543, achieved renown under Cesalpino; Zurich had one in 1560, then Bologna, Cassel, Leiden, Leipzig, Breslau, Basel, Heidelburg, and Oxford. Bui de La Brosse, physician to Louis XIII, organized the famous Jardin des Plantes Medicinales at Paris in 1653. Zoological gardens, as menageries for public amusement, had existed in China (1100 B.C.), ancient Rome, and Aztec Mexico (c. 1450); modern forms were opened at Dresden in 1554 and under Louis XIII at Versailles.

Zoology received less attention than botany, since it offered fewer cures, except in mythical medicine. Ulisse Aldrovandi began in 1599 the publication of thirteen great volumes on "natural history"; he lived to see six through the press. The Senate of Bologna published the remaining seven from his manuscripts and at public cost. They were superceded only by the Histoire naturelle (1749-1804) of Buffon. The Jesuit polymath Athanasius Kircher began histology with his Ars magna lucis et umbrae (1646), in which he described the minute "worms" that his microscope had found in decaying substances. The belief in the spontaneous generation of tiny organisms out of rotten flesh - or even out of slime - was still almost universal, though Harvey was soon to reject it in his De generatione animalium (1651). Zoology was backward partly because only a few thinkers saw in animals the progenitors of men. But in 1632 Galileo wrote to the Grand Duke of Tuscany: "Though the differences between man and the other animals is enormous, one might say reasonably that it is little more than the difference among men themselves." The modern mind was slowly climbing back to what the Greeks had known two thousand years before.

Anatomy was resting after its labors under Vesalius. Dissection of cadavers was still opposed - as by Hugo Grotius - but the numerous "anatomy lessons" in Dutch art reflect a general acceptance of the procedure. The great name here, as well as in surgery, is Girolamo Fabrizio d"Acquapendente, pupil of Fallopio and teacher of Harvey. During his reign at the University of Padua the great anatomical theater was built there - the only structure still completely preserved from that era. His discovery of the valves in the veins and his studies of the effect of ligatures led to Harvey's demonstration of the circulation of the blood. Knowledge of circulation of body fluids was advanced by Gasparo Aselli's discovery of the lacteals (1632), lymphatic vessels carrying milk-like chyle from the small intestine. Indeed, Aselli, despite his ""the little ass") described the circulation of the blood six years before Harvey published his theory. Andrea Cesalpino had expounded the essential theory in 1571, half a century before Harvey; he still clung to the old view that some blood passes through the septum of the heart, but he came closer than Harvey to explaining - by capillamenta - how the blood finds its way from the arteries to the veins. On a hundred fronts the noblest of all armies was advancing in the greatest of all wars.

Science and Health

In that war for the conquest of knowledge the central battle is that battle of life against death - a battle which individually is always lost and collectively is regularly won. In fighting disease and pain the physicians and the hospitals had many human enemies; personal uncleanliness, public filth, noisome prisons, quacks and magical potions, "scientific" mystics, hernia setters, stone melters, cataract couchers, tooth drawers, amateur uroscopists. And new diseases ran a race with new cures.

Leprosy had disappeared, and protective devices had reduced syphilis; Fallopio had invented (1564) a linen sheath against such infection. (This soon came to be used as a contraceptive and was sold by barbers and bawds.) But epidemics of typhus, typhoid fever, malaria, diphtheria, scurvy, influenza, smallpox, and dysentery appeared in several countries of Europe in this period, especially in Germany. Probably exaggerated figures report 4,000 deaths from a plague of boils in Basel in 1563-64; twenty-five percent of the inhabitants of Freiburg-im-Breisgau carried off by plague in 1564; 9,000 in Rostock and 5,000 in Frankfurt au der Oder in 1565; 4,000 at Hanover and 6,000 at Brunswick in 1566. Terrified citizens ascribed some plagues to deliberate poisoning; at Frankenstein, in Silesia, seventeen persons were burned to death on suspicion of "strewing poison." In 1604 the bubonic plague was so severe in Frankfurt am Main that there were not enough people to bury the dead. These are palpable exaggerations, but it is reported that during a recurrence of the bubonic plague in Italy in 1629-31 Milan lost 86,000 and "no less than 500,000 died in the Venetian Republic . . . Between 1630 and 1631 there were 1,000,000 victims of the plague in northern Italy alone." The fertility of women barely kept up with the resourcefulness of death. Childbirth was made doubly painful by its frequent futility; two-fifths of all children died before completing their second year. Families were large, populations were small.

Public sanitation was improving, hospitals were multiplying. Medical education was taking a more rigorous form - though one could still practice medicine without a degree. Bologna, Padua, Basel, Leiden, Montpellier, and Paris had famous medical school drawing students from all Western Europe. There is a peculiar example of patient medical research in the thirty year experiment by which Sanctorius tried to reduce physiological processes to quantitative measurement. He did much of his work while sitting at a table on a large scale; he recorded the changes in his weight from the intake and the outlet of solids and liquids and he even weighed his sweat. He found that the human body gives off several pounds daily through normal perspiration, and he concluded that this is a vital form of elimination. He invented a clinical thermometer (1612) and pulsimeter as aids to diagnosis.

Therapy was graduating from toads to leeches. Some reputable physicians prescribed dried toads sewn in a bag and hung on the breast, as a trap to catch and absorb the poisonous air that surrounded the body in plague areas. Bloodletting by leeches or cupping was combined with plentiful drinking of water, on the theory that some of the intaken fluid would form fresh uninfected blood. Two schools of treatment contended for the victim; the iatromechanical, stemming from Descartes' teaching that all bodily processes are mechanical; and the iatrochemical, originating with Paracelsus, developed by Helmont, and interpreting all physiology as chemical. Hydrotherapy was popular. Curative waters were taken at England's Bath, the Netherlands' Spa, France's Plombieres, and a dozen places along the Rhine and in Italy. New drugs like valerian (c. 1580), antimony (c. 1603), ipecac (1625), and quinine (1632) were introduced to Europe. The London pharmacopoeia of 1618 listed 1,960 drugs. Montaigne tells of special treats which a few doctors kept for patient patients: the left foot of a tortoise, the urine of a lizard, an elephant's dung, a mole's liver, blood drawn from the right wing of a white pigeon, and, for us who have the stone . . . the pulverized droppings of a rat; and such other tomfooleries that are more suggestive of magic and spells than of a serious science.

Such delicacies were impressively expensive, and people in the seventeenth century moaned over druggists' charges more that over doctors' bills.

Dentistry was left to barbers and consisted almost entirely of extractions. The "barber-surgeons" now included skilled practitioners like Ambroise Pare, Francois Rousset, who revived the Caesarean section, and Gasparo Tagliacozzi, specialist in the plastic reconstruction of ears, noses, and lips. He was condemned by moralists for interfering with the handiwork of God. His body was exhumed from consecrated ground and was reburied in unhallowed soil. Wilhelm Fabry, "father of German surgery," was the first to recommend amputation of a limb above the diseased part. And Giovanni Colle of Padua gave the oldest known description of a blood transfusion (1628).

As in every age, the patients resented the doctor's fees; the comedians laughed at his long robe, red shoes, and bedside gravity. If we trust the satires of the comic dramatists, his social status was not much above that of a teacher. But when we note the history of Rembrandt's Anatomy Lesson we see a class of men holding a respected position in society and able to pay well for even a share in a great picture. And the most famous philosopher of the age, dreaming like all of us of a better future for mankind, thought of this as depending upon the improvement of human character, and of medical science as the likeliest agent of this basic revolution. "For even the mind," said Descartes, "depends so much on the temperament and disposition of the bodily organs that if it is possible to find some means by which men might commonly be made wiser and abler . . . I believe it is in medicine that it ought to be looked for."

From Copernicus to Kepler

We have left astronomy to the last, for its heroes come toward the end of this period and constitute its pieces de resistance.

The same Church that was to silence Galileo led the way in a major achievement of modern astronomy - the reform of the calendar. The revision that Sosigenes had made for Caesar about 46 B.C. had overestimated the year by eleven minutes and fourteen seconds. Consequently, by 1577 the Julian calendar lagged behind the progress of the seasons by some twelve days, and ecclesiastical feasts had fallen out of the season for which they had been intended. Several attempts at calendar reform had been made - under Clement VI, Sixtus IV, and Leo X - but difficulties had been found in securing general agreement and requisite astronomical knowledge. In 1576 a revised calendar drawn up by Luigi Giglio was presented to Gregory XIII. The Pope submitted it to a commission of theologians, lawyers, and scientists, including the Bavarian Jesuit Christopher Clavius, famous in mathematics and astronomy; the final draft was apparently his work. Long negotiations were carried out with the princes and prelates to secure their co-operation. Many objections were made and the effort to win the consent of the Eastern churches failed. On February 24, 1582, Gregory XIII signed the decree that established the Gregorian calendar in Roman-Catholic lands. The equate the old calendar with astronomic realities, ten days were to be omitted in October 1582, the fifth was to be counted as the fifteenth, and complicated allowances were to be made for the reckoning of interest and other commercial relations. To offset the error in the Julian calendar, only such century years as are divisible by 400 were to have a 29th day in February. Protestant nations resisted the change. In Frankfurt am Main and Bristol the people rioted in the belief that the Pope wished to rob it of ten days; even Montaigne, avid of time, complained, "The eclipsing or abridging of ten days, which the Pope hath lately caused, hath taken me so low that I can hardly recover myself." But slowly the new calendar - which would need no further correction for 3,333 years - won acceptance: by the German states in 1700, in England in 1752, Sweden in 1753 and Russia in 1918.

A similar lag occurred in the acceptance of the Copernican astronomy. In Italy it might be studied and taught if presented as hypothesis rather than demonstrated fact. Giordano Bruno defended it, and Campanella already wondered whether the inhabitants of other planets thought themselves, as earthlings do, the center and purpose of all things. Generally, Protestant theologians vied with Catholic in denouncing the new system. Bacon and Bodin alike repudiated it. More surprising was its rejection by the greatest astronomer of the half century that followed Copernicus' death (1543).

Tycho Brahe was born in 1546 in the then Danish province of Scania which is now the southern extremity of Sweden. His father was a member of the Danish Council of State; his mother was mistress of the robes of the Queen. His rich uncle Jorgen, disconsolately childless, abducted him, wheedled his parents into consent, and gave the boy every advantage of education. At thirteen Tycho entered the University of Copenhagen. According to Gassendi, he was drawn to astronomy when he heard a teacher discuss a forthcoming eclipse of the sun. He watched the eclipse come as predicted and marveled at the science that had reached prophetic power. He bought a copy of Ptolemy's Almagest, pored over it to the neglect of other studies, and never abandoned the geocentric view there presented in the second century of our era.

At sixteen he was transferred to the University of Leipzig, where he studied law by day and the stars by night. He was warned that this regime would lead to physical and nervous breakdown. Tycho persisted, and he spent his allowance on astronomical instruments. In 1565 his uncle died, leaving him a large fortune. After settling his business affairs, Tycho hurried to Wittenberg for more mathematics and astronomy; and then driven by the plague he went to Rostock. There he fought a duel and had part of his nose cut off; he ordered a bright new nose of silver and gold and wore it the rest of his life. He dabbled in astrology and predicted the coming death of Suleiman the Magnificent, only to find that the Sultan had already died. After much travel in Germany he returned to Denmark, busied himself with chemistry, and was brought back to astronomy by discovering a new star in the constellation Cassiopeia (1572). His carefree observations of this transitory star and his account of it in his first publication, De nova stella, gave him a European reputation, but shocked some great Danes, who considered authorship a form of exhibitionism incompatible with blue blood. Tycho confounded everyone by marrying a peasant girl. He seems to have felt that a simple housewife was the best mate for an absorbed astronomer and was the best match open to a man with a golden nose.

Dissatisfied with astronomical facilities in Copenhagen, he set out for Cassel, where Landgrave William IV had built (1561) the first observatory with a revolving roof, and Joost Burgi had developed a pendulum clock which made possible an unprecedented accuracy in timing the observation and movements of stars. Fired with new zeal, Tycho went back to Copenhagen and interested Frederick II in projects for an observatory. The King gave him the island of Hveen (Venus) in the Sound, and a good pension. With this and his own means Tycho built a castle and gardens there which he called Uraniburg (Heavenly City), with living quarters, library, laboratory, several observatories, and a workshop to make his own instruments. He had no telescope; twenty-eight years were to pass before its invention; yet it was his observations that guided Kepler to epochal discoveries.

In twenty-one years at Hveen Tycho and his pupils gathered a body of data exceeding in extent and accuracy anything hitherto known. He took records of the sun's apparent motion every day for many years. He was one of the first astronomers to allow for the refraction of light and the fallibility of observers and instruments; so he repeated the same observation time and again. He discovered and reduced to law the variations in the motion of the moon. His meticulous tracing of a comet in 1577 led him to the now universally accepted belief that comets, instead of being generated in the earth's atmosphere, are true celestial bodies moving in fixed and regular courses. When Tycho published his catalogue of 777 stars, and marked them with loving care on the great celestial globe in his library, he had justified his life.

In 1588 Frederick II died. The new King was a boy of eleven. The regents who ruled him were not as patient with the pride, temper, and extravagance of Brahe as Frederick had been; soon the government grants ran low, and in 1597 they ceased. Tycho left Denmark and settled in Benatek Castle, near Prague, as the guest of Emperor Rudolf II, who looked to him for astrological predictions. Brahe imported his instruments and records from Hveen, and advertised for an assistant. Johann Kepler can (1600) and worked fitfully but devotedly for his difficult master. Just as Brahe was hoping to develop his massive accumulation of data into a reasoned theory of the heavens, he was struck down at table by a burst bladder. He lingered in pain for eleven days, and died (1601) mourning that he had not completed his work. The funeral orator said that he had "coveted nothing but time."

Kepler 1571 - 1630

It turned out well for science that Tycho moved to Prague, for there Kepler inherited his observations, and deduced from them the planetary laws that prepared for Newton's theory of gravitation. From Brahe to Kepler to Newton and from Copernicus to Galileo to Newton are the basic and converging lines of modern astronomy.

Kepler was born at Weil, near Stuttgart, son of an army officer who repeatedly went off to war as preferable to domesticity. Returning at last, the father opened a tavern, in which Johann served as a waiter. The boy was sickly; smallpox crippled his hands and permanently impaired his vision. The Duke of Wurttemberg saw in him the possibility of a good preacher and paid for his education. At Tubingen Michael Maestlin, who as professor taught the Ptolemaic astronomy, privately converted Kepler to the Copernican theory, and the youth became so enthusiastic about the stars that he abandoned all thought of an ecclesiastical career.

After taking his degree he became a schoolmaster at Graz, in Styria, teaching Latin, rhetoric, and mathematics for 150 gulden a year, with free lodging, and adding twenty gulden by editing annually an astrological calendar. At twenty-five he married a woman of twenty-three who had buried one husband and divorced another. She brought him a dowry and a daughter; he added six children in due course. A year after his marriage he was forced as a Protestant to leave Graz (1597), for the new Archduke of Styria, Ferdinand, was a resolute Catholic who ordered all Protestant clergymen and teachers out of Styria. Kepler had given further offense by publishing Mysterium cosmographicum (1596), ardently advocating the Copernican system; hopefully he sent copies to Brahe and Galileo. After a year of despondent poverty he was saved by Tycho's invitation to Prague. But Tycho was hard to get along with; there were difficulties with religion and bread, his wife developed epilepsy. Then Tycho died, and Kepler was appointed his successor, at five hundred florins a year.

Brahe had bequeathed his records to him, but not his instruments. Unable to buy the best, Kepler found himself driven to study Brahe's observations rather than add to them. He could not have said with Newton, "I do not invent hypotheses"; on the contrary, his head hummed with them; "I have much store of fantasy." His peculiar skill lay in testing hypotheses and his wisdom lay in casting them aside when the consequences that he had mathematically deduced from them proved incompatible with the observed phenomena. In seeking to plot the orbit of Mars he tried seventy hypotheses through four years.

Finally (1604) he reached his basic and epochal discovery - that the orbit of Mars around the sun is an ellipse, not a circle as astronomers from Plato to and including Copernicus had supposed. Only an elliptical orbit harmonized with the repeated observations of Brahe and others. Kepler's agile mind leaped to the question, What if all the planetary orbits are elliptical? Rapidly he tested the idea with the recorded observations; it agreed with them almost completely. In a Latin treatise on the motions of Mars, Astronomia nova de motibus stellae Martis (1609), he published the first two of "Kepler's Laws": first, each planet moves in an elliptical orbit, in which one focus is the sun; second, each planet moves more rapidly when near the sun than when farther from it, and a radius drawn from the sun to the planet covers, in its motion, equal areas in equal time. Kepler ascribed the differences in planetary speed to the greater emanation of solar energy felt by the planet as it neared the sun. In this connection he evolved from Gilbert an idea of magnetic attraction closely akin to Newton's theory of gravitation.

When Emperor Rudolf died (1612) Kepler moved to Linz and again he lived by teaching school. His wife having passed away, he married a poor orphan girl. In providing his new home with wine he was fascinated by the difficulty of measuring the contents of a cask with curved sides. The essay that he published on the problem helped to prepare the discovery of infinitesimal calculus.

After puzzling for ten years over the relation between the speed of a planet and the size of its orbit, Kepler published, in his book The Harmony of the World (1619), his third law: the square of the time of the revolution of a planet around the sun is proportioned to the cube root of its mean distance from the sun. (For example: Mars's time of revolution is demonstrably 1.88 times that of the earth; the square of this is 3.53; the cube root of this is 1.52; i.e. the mean distance of Mars from the sun will be 1.52 times that of the earth from the sun.) Kepler was so overjoyed by having reduced the behavior of the planets to such order and regularity that he likened each orbital speed to a note on a musical scale, and concluded that the combined motions make a "harmony of the spheres," which, however, is audible only to the "soul" of the sun. Kepler mingled mysticism with his science, illustrating again Goethe's generous saying that a man's defects are the faults of his time, while his virtues are his own. We can forgive the pride that wrote, in the preface to The Harmony of the World:

"What I promised my friends in the title of this book . . . what sixteen years ago, I urged as a thing to be sought - that for which I joined Tycho Brahe, . . . to which I have devoted the best part of my life - I have at length brought to light. . . .It Is not eighteen months since the unveiled sun . . . burst upon me. Nothing holds me; I will indulge my sacred fury. . . . 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 a discoverer!"

In an Epitome of the Copernican Astronomy (1618-21) Kepler showed how his laws supported, clarified, and amended the Copernican system. "I have attested it as true in my inmost soul," he said, "and I contemplate its beauty with incredible and ravishing delight." The treatise was placed on the Index of Prohibited Books because it argued that the Copernican theory had been proved. Kepler, a pious Protestant, was not disturbed. For a while he enjoyed prosperity and acclaim. His salary as Imperial astronomer was generally paid. From faraway Britain James I invited him (1620) to come and adorn the English court, but Kepler refused, saying that he would suffer from being cooped up in an island.

He shared the prevailing belief in witchcraft. His mother was charged with practicing it; witnesses alleged that their cattle, or they themselves, had become ill because Frau Kepler had touched them. One witness swore that her eight-year-old daughter had been made ill by Mother Kepler's witchery, and she threatened to kill the "witch" if she did not at once cure the girl. The accused woman denied all guilt, but she was arrested and chained in a cell. Kepler fought for her at every stage of the proceedings. The state's attorney proposed that a confession be drawn from her by torture. She was taken to the torture chamber and was shown the instruments to be used upon her but she still asserted her innocence. After thirteen months imprisonment she was released, but she died soon afterward (1622).

This tragedy, and the impact of the spreading war, darkened Kepler's final years. In 1620 Linz was occupied by Imperialist troops, and its inhabitants neared starvation. Through all the chaos he continued his labor of formulating the observations of Brahe, others, and himself, in the Rudolphine tables (1627), which catalogued and charted 1,005 stars and remained standard for a century. In 1626 he moved to Ulm. His Imperial salary fell far in arrears, and he was hard pressed to feed his family. He applied to Wallenstein for employment as astrologer; he was hired and for some years he followed the general, casting horoscopes for him and publishing astrological almanacs. In 1630 he went to Regensburg to appeal to the Diet for the remainder of his salary. The effort consumed his last physical resources; he was seized with fever and died within a few days (November 15, 1630) when he was only 59 years of age. All traces of his grave were swept away by the war.

His function in the history of astronomy was to mediate between Copernicus and Newton. He advanced beyond Copernicus by replacing circular with elliptical orbits, by abandoning eccentrics and epicycles, and by placing the sun not at the center of a circle but at one focus of an ellipse. By these changes he freed the Copernican system from many of the difficulties that had almost justified Tycho Brahe in rejecting it. Through him the heliocentric view now won a rapidly widening acceptance. He transformed what had been a brilliant guess into a hypothesis worked out in impressive mathematical detail. He provided Newton with the planetary laws that led to the theory of gravitation. While keeping his religious faith fervent and undiminished, he revealed the universe as a structure of law, as a cosmos of order in which the same laws ruled the earth and the stars. "My wish," he said, "is that I may perceive the God whom I find everywhere in the external world in like manner within me."

Compiled by Marko Marelich
Retired Mechanical Engineer
San Francisco, California USA
Aug 15, 2006