Christian Huygens, barring only one, was the outstanding scientist of this age—facile secundus to Newton. His father, Constantijn Huygens, was one of the most distinguished of Holland’s poets and statesmen. Born at The Hague in 1629, Christiaan (as the Dutch spelled him) began at the age of twenty-two to publish mathematical treatises. His discoveries in astronomy and physics soon won him a European renown; he was elected a fellow of the Royal Society in London in 1663, and in 1665 he was invited by Colbert to join the Académie des Sciences in Paris. He moved to the French capital, received a liberal pension, and remained there till 1681; then, uncomfortable under a King turned persecutor of Protestants, he returned to Holland. His correspondence in six languages with Descartes, Roberval, Mersenne, Fermat, Pascal, Newton, Boyle, and many others illustrated the growing unity of the scientific fraternity. “The world is my country,” he said, and “to promote science is my religion.” 15 His mens sana in corpore aegro was one of the marvels of his time—his body always ailing, his mind creative till his death at sixty-six. His work in mathematics was the least part of his achievement; yet geometry, logarithms, and calculus all profited from his labors. In 1673 he established that “law of inverse squares” (that the attraction of bodies for one another varies inversely as the square of the distance between them) which became so vital to Newton’s astronomy.
Newton, of course, was now the central luminary in the galaxy of British science; he deserves a separate chapter; but there were satellites to his star. His friend John Wallis, an Anglican priest, became Savilian professor of geometry at Oxford in 1649 at the age of thirty-three, and held that chair for fifty-four years. Grammar, logic, and theology diverted his pen from science; nevertheless he wrote effectively on mathematics, mechanics, acoustics, astronomy, tides, botany, physiology, geology, and music; he lacked only some amours and wars to make him a full man. His De Algebra Tractatus Historicus et Practicus (1673) not only contributed original ideas to that science, but was the first serious attempt in England to write the history of mathematics. His contemporaries were delighted by his prolonged controversy with Hobbes over the quadrature of the circle; Wallis scored his point, but the old philosopher fought on to the end of his ninety-first year. History remembers Wallis chiefly for his Arithmetica Infinitorum (1655), which applied Cavalieri’s method of indivisibles to the quadrature of curves, and so prepared for infinitesimal calculus.
Calculus meant originally a small stone used by the ancient Romans in calculating; but only the devotees of calculus can now define their science properly.* Archimedes had glimpsed it, Kepler had approached it, Fermat had discovered it but had not published his findings; Cavalieri and Torricelli in Italy, Pascal and Roberval in France, John Wallis and Isaac Barrow in England, James and David Gregory in Scotland, had all carried bricks to the building in this astonishing co-operation of a continent. Newton and Leibniz brought the work to fulfillment.
The term calculus was suggested to Leibniz by Johann Bernoulli, member of a family as remarkable as the Bachs, the Brueghels, and the Couperins for the social heredity of genius. Nikolaus Bernoulli (1623–1708), like his ancestors, was a merchant. In his son Jakob Bernoulli I (1654–1705) mercantile accounting passed into higher forms of reckoning. Taking as his motto Invito patre sidera verso—“Against my father’s will I study the stars”—Jakob dabbled in astronomy, contributed to analytical geometry, advanced the calculus of variations, and became professor of mathematics at the University of Basel. His studies of catenary curves (curves described by a uniform chain suspended between two points) came to later fruition in the designing of suspension bridges and high-voltage transmission lines. His brother Johann (1667–1748), also against paternal plans, took up medicine, then mathematics, and succeeded Jakob as professor at Basel; he contributed to physics, optics, chemistry, astronomy, the theory of tides, and the mathematics of sails; he invented exponential calculus, constructed the first system of integral calculus, and introduced the use of the word integral in this sense. Another brother, Nikolaus I (1662–1716), took his doctor’s degree in philosophy at sixteen, in law at twenty, taught law at Bern and mathematics in St. Petersburg. We shall find six more Bernoulli mathematicians in the eighteenth century, and there were two in the nineteenth. By that time the Bernoulli battery had run down.
The establishment of statistics as almost a science was among the achievements of this age. John Graunt, a haberdasher, amused himself by collecting and studying the burial records of London parishes. Usually these records stated the reported cause of death, including “dead in the street and starved,” “executed and prest to death,” “King’s evil,” “starved at nurse,” and “made away themselves.” 16 In 1662 Graunt published his Natural and Political Observations . . . upon the Bills of Mortality; this is the beginning of modern statistics. He concluded from his tables that thirty-six per cent of all children died before the age of six, twenty-four per cent died in the next ten years, fifteen per cent in the next ten, etc.; 17 the infantile mortality seems much exaggerated here, but suggests the labor of love in keeping up with the angel of death. “Among the several casualties,” said Graunt, “some bear a constant proportion unto the whole number of burials; such are chronical diseases, and the diseases whereunto the city is most subject, as, for example, consumptions, dropsies, jaundice, etc.”; 18 i.e., certain diseases, and other social phenomena, though incalculable in individuals, may be precalculated with relative accuracy for a large community; this principle, here formulated by Graunt, became a foundation of statistical prediction. He noted that in many years the burials in London exceeded the christenings; he concluded that London was especially rich in opportunities for death, as from business anxieties, “smokes, stinks, close air,” and “intemperance in feeding.” As the population of London grew nevertheless, Graunt ascribed the increase to immigration from the countryside and the lesser towns. He reckoned the population of the capital in 1662 at some 384,000 souls.
Statistics were applied to politics by Graunt’s friend Sir William Petty. Again exemplifying a versatility impossible today, Petty, after studying at Caen, Utrecht, Leiden, Amsterdam, and Paris, taught anatomy at Oxford and music at Gresham College, London, and won fortune and knighthood as physician to the royal army in Ireland.* In 1676 he wrote the second classic in English statistics, Political Arithmetic. Politics, Petty held, could approach to a science only by basing its conclusions on quantitative measurements. Therefore he pleaded for a periodical census that would record the birth, sex, marital condition, titles, occupation, religion, etc., of every inhabitant of England. On the basis of mortality bills, number of houses, and annual excess of births over deaths, he estimated the population of London at 696,000 in 1682; of Paris, 488,000; Amsterdam, 187,000; Rome, 125,000. Like Giovanni Botero in 1589 and Thomas Malthus in 1798, Petty thought that population tends to increase faster than the means of subsistence, that this leads to war, and that by the year 3682 the habitable earth would be dangerously overcrowded, with one person to every two acres of land. 20
Insurance companies used statistics to turn their business into an art and science that took account of everything except inflation. From the mortality reports of Breslau Edmund Halley drew up (1693) a table of expectable deaths for all years between one and eighty-four; on its basis he calculated the odds against persons of a given age dying during the calendar year, and deduced the logical price of a policy. The first life insurance companies established in London in the eighteenth century made use of Halley’s tables, and turned mathematics into gold.
III. ASTRONOMY
The stars were subjected to science in a hundred countries. In Italy the Jesuit astronomer Riccioli (1650) discovered the first double star—i.e., a star which to the eye seems one but is seen through the telescope as two stars apparently revolving around each other. In Danzig Johannes Hevelius built an observatory in his own home, made his own instruments, catalogued 1,564 stars, discovered four comets, observed the transit of Mercury, noted the moon’s libr
ations (periodic alternations in the visibility of its parts), charted its surface, and gave to several of its features names that remain on lunar maps today. When he announced to Europe’s stargazers that he could distinguish stellar positions as accurately with a diopter (a sight using only one lens or prism) as with a compound telescope, Robert Hooke challenged the claim; Halley traveled from London to Danzig to test it, and reported that Hevelius had told the truth. 21
Recognizing the importance of astronomy for navigation, Louis XIV provided funds to raise and equip an observatory at Paris (1667–72). From that center Jean Picard led or sent expeditions to study the skies from different points on the earth; he went to Uraniborg to note the exact location from which Tycho Brahe had made his classic map of the stars; and, by a variety of observations ranging from Paris to Amiens, he measured a degree of longitude with such accuracy (within a few yards of the current figure, 69.5 miles) that Newton is supposed to have used Picard’s results to estimate the mass of the earth and verify the theory of gravitation. By similar observations Picard reckoned the equatorial diameter of the earth at 7,801 miles—not far from our present computation of 7,913 miles. 22 These findings made it possible for a ship at sea to determine its location with unprecedented precision. So the commercial expansion and industrial development of Europe urged on the scientific revolution, and profited from it.
At Picard’s suggestion Louis XIV invited to France the Italian astronomer Giovanni Domenico Cassini, who had already acquired European fame by discovering the spheroidal form of Jupiter and the periodic rotation of Jupiter and Mars. Arrived in Paris (1669), he was received by the King as a prince of science. 23 In 1672 he and Picard sent Jean Richer to Cayenne, in South America, to observe Mars at its maximum “opposition” to the sun and nearness to the earth; Cassini noted the same opposition from Paris. The comparison of the simultaneous observations from these two separate points gave new and more precise values to the parallax of Mars and the sun and their distance from the earth, and revealed vaster dimensions in the solar system than had been estimated before. As a pendulum was found to beat more slowly at Cayenne than a similar pendulum at Paris, the astronomers concluded that gravity was less intense near the equator than in higher latitudes; and this suggested that the earth was not a perfect sphere. Cassini thought it was flattened at the equator; Newton thought it was flattened at the poles; further research supported Newton. Meanwhile Cassini discovered four new satellites of Saturn, and the division (now known by his name) of Saturn’s ring into two. After Cassini’s death in 1712 he was succeeded in the Paris observatory by his son Jacques, who measured the arc of the meridian from Dunkirk to Perpignan, and published the first tables of the satellites of Saturn.
Christian Huygens, before joining the cosmopolitan assemblage of scientists in Paris, made at The Hague some important contributions to astronomy. With his brother Constantijn he developed a new method of grinding and polishing lenses; with these he constructed telescopes of greater power and clarity than any known before; thereby he discovered (1655) the sixth satellite of Saturn, and that planet’s mysterious ring. A year later he made the first delineation of the bright region (now bearing his name) in the Orion nebula, and detected the multiple character of its nuclear star.
The great rival to the Paris astronomers was the remarkable group that gathered mostly around Halley and Newton in England. James Gregory of Edinburgh lent distant aid by designing the first reflecting telescope (1663)—i.e., one in which the rays of light from the object are concentrated by a curved mirror instead of a lens; Newton improved this in 1668. In 1675 John Flamsteed and others addressed to Charles II a memorial asking him to finance the building of a national observatory, so that better methods of calculating longitude might guide the English shipping that was now plowing the seas. The King provided for the building, which was raised in the borough of Greenwich near southeast London; this came to be used as the point of zero longitude and standard time. Charles offered Flamsteed a small salary as director, but nothing to pay for assistants or instruments. Flamsteed, frail and sickly, gave his life to that observatory. He took pupils, bought instruments out of his personal funds, received others as gifts from friends, and set himself patiently to chart the sky as seen from Greenwich. Before he died (1719) he had made the most extensive and accurate star catalogue yet known, considerably improving on that which Tycho Brahe had left to Kepler in 1601. Harassed by lack of aid, doing himself the paperwork usually left to assistants, Flamsteed angered Halley and Newton by delays in the calculation and announcement of his results; at last Halley published them without Flamsteed’s permission, and the ailing astronomer shook the stars with his wrath.
Nevertheless Edmund Halley was the finest gentleman of them all. An enthusiastic schoolboy student of the sky, he published at twenty a paper on the planetary orbits; and in that same year (1676) he set out to see how the heavens looked from the southern hemisphere of the earth. On the island of St. Helena he charted the behavior of 341 stars. On the eve of his twenty-first birthday he made the first full observation of a transit of Mercury. Back in England, he was elected a fellow of the Royal Society at twenty-two. He recognized Newton’s genius, financed the first edition of the costly Principia, and prefixed to it some complimentary verse in splendid Latin, ending in the line, Nec fas est proprius mortali attingere divos (It is not allowed to any mortal to come closer to the gods). 24 Halley edited the Greek text of the Conies of Apollonius of Perga, and learned Arabic to translate Greek treatises preserved only in that language.
He wrote his name in the sky by one of the most successful predictions in history. Borelli had paved the way by discovering the parabolic form of cometary paths (1665). When a comet appeared in 1682 Halley found similarities in its course with comets recorded in 1456, 1531, and 1607; he noted that these manifestations had come at intervals of some seventy-five years, and he predicted a reappearance in 1758. He could not live to see the fulfillment of his prophecy, but when the comet returned it received his name, and added to the rising prestige of science. Until late in the seventeenth century comets were considered to be direct acts of God, portending great calamities to mankind; the essays of Bayle and Fontenelle, and the prediction of Halley, laid this superstition. Halley identified another comet, seen in 1680, with one observed in the year of Christ’s death; he traced its recurrence every 575 years, and from this periodicity he computed its orbit and speed around the sun. Commenting on these calculations, Newton concluded that “the bodies of comets are solid, compact, fixed, and durable, like the bodies of the planets,” and are not “vapors or exhalations of the earth, of the sun, and other planets.” 25*
In 1691 Halley was refused the Savilian chair of astronomy at Oxford on suspicion of being a materialist. 26 In 1698, on a commission from William III, he sailed far into the South Atlantic, studied the variations of the compass, and charted stars as seen from the Antarctic. (Compared with this expedition, said Voltaire, “the voyage of the Argonauts was but the crossing of a bark from one side of a river to the other.” 27) In 1718 Halley pointed out that several of the supposedly “fixed stars” had altered their positions since Greek times, and that one of them, Sirius, had changed since Brahe; allowing for errors of observation, he concluded that the stars vary their positions relative to one another over great periods of time; and these “proper motions” are now accepted as real. In 1721 he was appointed to succeed Flamsteed as astronomer royal; but Flamsteed had died so poor that his creditors seized his instruments, and Halley found his own work hampered by inadequate equipment as well as by his own declining energies; nevertheless he began, at sixty-four, to observe and record the phenomena of the moon through its complete cycle of eighteen years. He died in 1742, aged eighty-six, after wisely drinking a glass of wine against his doctor’s orders. Life, like wine, should not be taken in excess.
IV. THE EARTH
In love with science, Halley had ventured into the mists of meteorology with an essay (1697) on trade wi
nds, and a chart that for the first time mapped the movements of the air. He attributed these movements to differences in the temperature and pressure of the atmosphere; so the sun, moving apparently westward, carried heat with it, especially along the equatorial regions of the earth; the air rarefied by this heat sucked in less rarefied air from the east, and created the prevailing equatorial winds that Columbus had relied on to sail from east to west. Francis Bacon had suggested a similar explanation. George Hadley was to develop it in 1735 by adding that the greater eastward speed of the earth’s rotation at the equator creates a contrary westward flow of air.
The development of the barometer and the thermometer made meteorology a science. Guericke’s barometer rightly forecast a severe storm in 1660. Various hygrometers were invented in the sixteenth century to measure humidity. The Accademia del Cimento used a graduated vessel that received the moisture dripping from the outside of an ice-filled metallic cone. Hooke attached a grain bristle, or “beard”—which swelled and bent with increasing moisture in the air—to an indicator needle that turned as the bristle swelled. Hooke invented also a wind gauge, a wheel barometer, and a weather clock. This last instrument, designed on a commission from the Royal Society (1678), measured and recorded the velocity and direction of the wind, the pressure and humidity of the atmosphere, the temperature of the air, and the amount of rainfall; for literal good measure it gave the time of day. Armed with improved instruments, weather stations in diverse cities began to record and compare their simultaneous observations, as between Paris and Stockholm in 1649. Grand Duke Ferdinand II of Tuscany, patron of the Cimento, sent barometers, thermometers, and hygrometers to chosen observers at Paris, Warsaw, Innsbruck, and elsewhere, with instructions for recording meteorological data daily, and transmitting a copy to Florence for comparison. Leibniz persuaded the weather stations at Hanover and Kiel to keep daily records from 1679 to 1714.