1. Instrumental Prelude
How far did the findings of mathematics, physics, and chemistry illuminate the sky? Of all the audacities of science the most daring is the attempt to fling its measuring rods around the stars, to subject those scintillating beauties to nocturnal spying, to analyze their constituents across a billion miles, and to confine their motions to man-made logic and laws. Mind and the heavens are the poles of our wonder and study, and the greatest wonder is mind legislating for the firmament.
The farseeing instruments had been invented, the major discoveries had been made; the eighteenth century undertook to improve the instruments (Graham, Hadley, Dollond), extend the discoveries (Bradley and Herschel), apply the latest mathematics to the stars (d’Alembert and Clairaut), and organize the results in a new system of cosmic dynamics (Laplace).
The telescope was bettered and enlarged. “Equatorial telescopes” were made which turned on two axes—one parallel, the other perpendicular, to the plane of the axis of the earth; this choice of axes enabled the observer to keep a celestial object in view long enough for detailed study and micrometric measurement. Newton had been discouraged from use of the refracting telescope by the belief that light, in being refracted by lenses, must necessarily be broken up into colors, so confusing observation; he gave up the problem of making a color-free refraction, and turned to the reflecting telescope. In 1733 Chester Moor Hall, a “gentleman amateur,” solved the problem by combining lenses of different refractive media, neutralizing the diversity of color. He did not publish his discovery, and John Dollond had to work out independently the principles and construction of the achromatic telescope, which he announced in the Philosophical Transactions of the Royal Society of London in 1758.
In 1725 George Graham, a Quaker watchmaker, made for Edmund Halley at Greenwich Observatory a mural quadrant—a mechanical quarter-circle graduated into degrees and minutes, and fixed on a wall so as to catch the transit of a star across the meridian. For Halley, James Bradley, and Pierre Lemonnier, Graham made transit instruments combining telescope, axis, clock, and chronograph, to mark such transits with greater accuracy than before. In 1730 Thomas Godfrey, a member of Franklin’s intellectual circle in Philadelphia, described to his friends an instrument for measuring angles and altitudes by means of double reflection through opposed mirrors seen in a telescope; but he did not publish it till 1734. In 1730 John Hadley built a similar instrument, an octant—a graduated arc of an eighth of a circle; in 1757 this was enlarged to a sixth. By enabling a navigator to see at once, in the reflecting telescope, both the horizon and the sun (or a star), Hadley’s “sextant” allowed a more precise measurement of the angle separating the objects. This, combined with Harrison’s marine chronometer, made navigation an almost exact science.
To determine the position of a ship at sea the navigator had to determine the longitude and latitude. To find the longitude he had to ascertain his time at the place and moment by astronomical observation, and to compare this local time with a clock set to keep standard (Greenwich) time wherever the clock might be. The problem was to construct a chronometer that would not be affected by changes of temperature or the motions of the ship. In 1714 the British government offered twenty thousand pounds for a method of finding longitude within half a degree. John Harrison, a Yorkshire clockmaker, submitted to George Graham (1728) plans for a marine chronometer; Graham advanced the money to construct it; completed in 1735, it used two massive and opposed balances instead of a pendulum; four balance springs, moving contrary to one another, compensated for the motions of the vessel; and a manifold of brass and steel rods, expanding with heat and contracting with cold, and connected with the springs, neutralized the variations in temperature. The Board of Longitude sent Harrison with his chronometer on a test voyage to Lisbon. The results encouraged the Board to provide funds for a second, third, and fourth improvement. This fourth chronometer, only five inches wide, was tried on a voyage to the West Indies (1759); on that trip the clock lost no more than five seconds additional to its normal and precalculated loss (when stationary on land) of eighty seconds per thirty days. After some disputes Harrison received the full award of twenty thousand pounds. With this and other marine instruments, the British navy was now (at the height of the Seven Years’ War, 1756–63) equipped to rule the waves.
2. Astronomic Theory
The British and French competed ardently in studying astronomy; this was no remote or “pure” science for them; it entered into the struggle for mastery of the seas, and therefore of the whole colonial and commercial world. Germany and Russia through Euler, Italy through Boscovich, contributed to the contest without sharing in the spoils.
Euler, Clairaut, and d’Alembert aided navigation by their studies of the moon, tabulating its changes of place and phase in relation to the sun and the earth, and its effects upon tides. From Euler’s records Johann Tobias Mayer, at the University of Göttingen, drew up lunar tables which won a gift from the British Board of Longitude. In 1738 the Paris Académie des Sciences offered a prize for a theory of tides. Four authors received awards: Daniel Bernoulli, Euler, Colin Maclaurin, and A. Cavallieri. All but the last based their explanations upon Newton’s, adding the rotation of the earth to the attraction of the sun and the moon as a factor in determining tides. The Académie on several occasions invited essays on the perturbations of the planets—their real or apparent deviations from elliptical orbits. Clairaut’s essay won the prize in 1747, Euler’s in 1756.
Ruggiero Giuseppe Boscovich honored his Jesuit order by illuminating discoveries in astronomy and physics. Born in Ragusa, he entered the novitiate at Rome at fourteen, astonished his teachers at the Collegium Romanum by his precocity in science, and was appointed to the chair of mathematics there at twenty-nine. From that time onward he issued sixty-six publications. He shared in determining the general orbit of comets, and gave the first geometric solution for finding the orbit and equator of a planet. In his treatiseDe materiae divisibilitate (1748) he expounded his view of matter as composed of points, or fields, of force, each a center alternately of repulsion and attraction—a theory recalling Leibniz’ monads and prefiguring the atomic hypotheses of our time. The versatile Jesuit organized practical enterprises—surveying and mapping the Papal States, damming the lakes that threatened to submerge Lucca, making plans to drain the Pontine Marshes, and helping to design the Brera Observatory at Milan. At his urging, in 1757, Pope Benedict XIV abrogated the decree of the Index Expurgatorius against the Copernican system. He was given membership in the Paris Académie des Sciences and the London Royal Society. In 1761–62 he was received with honors in France, England, Poland, and Turkey. In 1772 he accepted appointment by Louis XV as director of optics in the French navy. He returned to Italy in 1783, and died at Milan in 1787, at the age of seventy-six. He left behind him several volumes of poetry.
The most brilliant luminary among British astronomers in the first half of the eighteenth century was James Bradley. His uncle, James Pound, a rector at Wanstead in Essex, was an amateur astronomer, with an observatory of his own; there the boy learned that there was a science as well as an aesthetic of the stars. After taking his M.A. at Oxford, Bradley hurried back to Wanstead, made original observations, reported them to the Royal Society, and was elected to its membership at the age of twenty-six (1718). Three years later he became Savilian professor of astronomy at Oxford. When the great Halley died, in 1742, Bradley was appointed to succeed him at Greenwich as astronomer royal. In that post he remained till his death (1762).
His first major enterprise was to determine the annual parallax of a star—i.e., the difference in its apparent direction as seen (1) from a point on the surface of the earth, and (2) from an imaginary point at the center of the sun. If, as Copernicus had supposed, the earth revolved in orbit around the sun, such a difference should exist; none had been demonstrated; if it could be proved it would corroborate Copernicus. The omniventurous Robert Hooke had tried (1669) to show such a parallax in the case of the star gamma Draconis; he had failed. Samuel Molyneux, a moneyed amateur, resumed the attempt in 1725 at Kew; Bradley joined him there; their results only partly confirmed the Copernican hypothesis. Bradley returned to Wanstead, and engaged George Graham to construct for him a “zenith sector” telescope enabling him to observe not one star but two hundred stars in their transit across the meridian. After thirteen months of observation and calculation, Bradley was able to show an annual cycle of alternating southward and northward deviations in the apparent position of the same star; and he explained this alternation as due to the earth’s orbital motion. This discovery of the “aberration of light” (1729) explained hundreds of hitherto puzzling observations and deviations; it made a revolutionary distinction between the observed position and the “real,” or calculated, position of any star; it agreed handsomely with Copernicus, since it depended upon the revolution of the earth around the sun. Its effect upon astronomy was so illuminating that a French astronomer-historian, Joseph Delambre, proposed to rank Bradley with Kepler, even with Hipparchus himself.53
Bradley went on to his second major discovery: the “nutation”—literally the nodding—of the earth’s axis of rotation, like the axial vacillation of a spinning top. The stars whose apparent motions had been described as performing an annual cycle, due to the revolution of the earth around the sun, did not, in Bradley’s observations, return, after a year, to precisely the same apparent positions as before. It occurred to him that the discrepancy might be due to a slight bending of the earth’s axis by periodic changes in the relation between the moon’s orbit around the earth and the earth’s orbit around the sun. He studied these changes through nineteen years (1728–47); at the end of the nineteenth year he found that the stars had returned to exactly the same apparent positions they had had at the beginning of the first year. He felt certain now that the nutation of the earth’s axis was due to the orbital motion of the moon, and its action upon the equatorial parts of the earth. His report of these findings was an exciting event in the proceedings of the Royal Society for 1748. Patience has its heroes as well as war.
During Bradley’s tenure as astronomer royal, Britain submitted to a painful operation: after 170 years of resistance it accepted the Gregorian calendar, but obstinately named it the Reformed calendar. An act of Parliament (1750) ordered that the eleven days following the second of September, 1752, were to be omitted from the “New Style”; that September 3 was to be called September 14; and that the legal year should thereafter begin not on March 25 but on January 1. This involved complications in business dealings and ecclesiastical holydays; it stirred many protests, and angry Britons demanded, “Give us back our eleven days!”54—but in the end science triumphed over bookkeeping and theology.
English astronomy reached its peak when William Herschel added Uranus to the planets and abandoned his career as a musician. His fatherIV was a musician in the Hanoverian army; the son, born in Hanover in 1738 and named Friedrich Wilhelm, adopted his father’s profession, and served as musician in the first campaign of the Seven Years’ War; but his health was so delicate (he lived to be almost eighty-four) that he was released. In 1757 he was sent to England to seek his fortune in music. At Bath, which then rivaled London as a center of fashionable society, he rose from oboist to conductor to organist in the Octagon Chapel. He composed, taught music, and sometimes gave thirty-five lessons in a week. At night he unbent by studying calculus; thence he passed to optics, finally to astronomy. He brought over from Germany his brother Jacob and, in 1772, his sister Caroline, who managed their household, learned to keep astronomical records, and at last became an astronomer in her own right.
Fired with ambition to chart the skies, Herschel, helped by his brother, made his own telescope. He ground and polished the lenses himself, and on one occasion he continued this operation uninterrupted for sixteen hours, Caroline feeding him as he worked, or relieving the tedium by reading to him from Cervantes, Fielding, or Sterne. This was the first of several telescopes made by Herschel or under his supervision. In 1774, aged thirty-six, he made his first observation, but for many years yet he could give to astronomy only such time as was left him by his work as a musician. Four times he studied every part of the heavens. In the second of these cosmic tours, on March 14, 1781, he made his epochal discovery, whose importance he vastly underestimated:
In examining the small stars in the neighborhood of H. Geminorum I perceived one that appeared visibly larger than the rest. Being struck with its uncommon appearance, I compared it to H. Geminorum and the small star in the quartile between Auriga and Gemini; and finding it so much larger than either of them, I suspected it to be a comet.55
It was not a comet; continued scrutiny soon showed that it revolved around the sun in an almost circular orbit, nineteen times greater than the orbit of the earth, and twice that of Saturn; it was a new planet, the first so recognized in the written records of astronomy. All the learned world acclaimed the discovery, which doubled the diameter of the solar system as previously known. The Royal Society awarded Herschel a fellowship and the Copley Medal; George III persuaded him to give up his career as a musician and become astronomer to the King. Herschel named the new planet Georgium Sidus (Star of the Georges); but astronomers later agreed to call it Uranus, taking it away from the Hanoverian kings and surrendering it, like nearly all its fellows, to the pagan gods.
In 1781 William and Caroline moved to Slough, a pretty town on the way from London to Windsor. His modest salary of two hundred pounds a year could not support him, his sister, and his instruments; he added to it by making and selling telescopes. For himself he built them even larger, until in 1785 he made one forty feet long, with a mirror four feet in diameter. Fanny Burney, daughter of the musician-historian whom we have often quoted, wrote in her diary under December 30, 1786:
This morning my dear father carried me [i.e., drove her, for she was thirty-six] to Dr. Herschel. This great and very extraordinary man received us with almost open arms.… By the invitation of Mr. Herschel I took a walk … through his telescope! and it held me quite upright, and without the least inconvenience; so would it have done had I been dressed in feathers and a bell-hoop—such is its circumference.56
In 1787 Herschel discovered two satellites of Uranus, which he named Oberon and Titania; in 1789 he found the sixth and seventh satellites of Saturn. In 1788 he married a wealthy widow; he no longer had to worry about money, but he continued his investigations with undiminished fervor. Usually he worked all through those nights when the stars were out and were not dimmed by too bright a moon. Most of his observations were made in the open air from a platform reached by a fifty-foot ladder. Sometimes the cold was so severe that the ink froze in the bottle that Caroline took with her to record his findings.
Carrying on more systematically, and with better telescopes, the work of Charles Messier and Nicolas de Lacaille in locating and listing nebulae and star clusters, Herschel submitted to the Royal Society (1782–1802) catalogues of 2,500 nebulae and clusters, and 848 double stars. Of these 848 he had himself discovered 227. He suggested that they might be paired in mutual gravitation and revolution—an illuminating application of Newton’s theory to interstellar relations. In many cases what had looked like one star turned out to be a cluster of individual stars, and some of these clusters, seen in the larger telescopes, proved to be separate stars at vastly different distances from the earth. The Milky Way, in the new magnification, was transformed from a cloud of glowing matter into an immense aggregation and succession of single luminaries. Now the sky, which had seemed to be merely studded with stars, appeared to be crowded with them almost as thickly as drops of water in the rain. And whereas the unaided human eye had seen only stars of the first to the sixth magnitude, Herschel’s telescopes revealed additional stars 1,342 times fainter than the brightest. Like Galileo, Herschel had immensely expanded the known universe. If Pascal had trembled before the “infinity” of the heavens known to his time, what would he have felt before this endless depth beyond depth of stars beyond counting, some, said Herschel, “11,750,000,000,000,000,000,000 miles” from the earth?57 Many of the stars were suns with planets revolving about them. Our own sun and its planets and their satellites were collectively reduced to a speck in a cosmos of light.
One of Herschel’s most brilliant suggestions related to the motion of our solar system through space. Previous observations had indicated that certain associated stars had, in recorded time, decreased or increased their divergence from each other. He wondered might not this variation be due to the motion of the solar system away from the converging—or toward the diverging—stars, as two lamps on opposite sides of a street will seem to converge or diverge as we leave or approach them. He concluded that the solar system as a whole was moving away from certain stars, and toward a star in the constellation Hercules. He published his hypothesis in 1783; a few months later Pierre Prévost announced a similar theory. The rival groups of astronomers, English and French, were in eager competition and close accord.
A contemporary described Herschel, in his eighty-second year, as “a great, simple, good old man. His simplicity, his kindness, his anecdotes, his readiness to explain his own sublime conceptions of the universe, are indescribably charming.”58 In all his work Caroline shared with a devotion as beautiful as in any romance. Not only did she keep careful records of his observations, and make complicated mathematical calculations to guide him, but she herself discovered three nebulae and eight comets. After William’s death (1822) she returned to live with her relatives in Hanover; there she kept up her studies, and catalogued still further the findings of her brother. In 1828 she received the gold medal of the Astronomical Society, and in 1846 a medal from the King of Prussia. She died in 1848, in her ninety-eighth year.
4. Some French Astronomers
Around the Paris Observatory (completed in 1671) there gathered a galaxy of stargazers, in which the Cassini family formed through four generations a successive constellation. Giovanni Domenico Cassini directed the Observatory from 1671 to 1712. Dying, he was succeeded as director by his son Jacques, who was succeeded (1756) by his son César François Cassini de Thury, who in turn was succeeded (1784) by his son Jacques Dominique, who died as the Comte de Cassini in 1845 at the age of ninety-seven. Here was a family worthy to be named with the Bernoullis and the Bachs.
Jean Le Rond d’Alembert had no family, either before or after, but he gathered sciences around him as one would gather children. Applying his mathematics to astronomy, he reduced to law Newton’s theory of the precession of the equinoxes, and Bradley’s hypothesis of the axial nutation of the earth. “The discovery of these results,” said Laplace, “was in Newton’s time beyond the means of analysis and mechanics.… The honor of doing this was reserved to d’Alembert. A year and a half after the publication in which Bradley presented his discovery, d’Alembert offered his treatise [Recherches sur la précession des équinoxes (1749)], a work as remarkable in the history of celestial mechanics and dynamics as that of Bradley in the annals of astronomy.”59
It is a blot on d’Alembert’s record that he did not enjoy the successes of his rivals—but which of us has risen to such saintly delight? He criticized with special zeal the work of Alexis Clairaut. At ten Alexis knew infinitesimal calculus; at twelve he submitted his first paper to the Académie des Sciences; at eighteen he published a book containing such important additions to geometry as won him adjoint membership in the Académie (1731), at an age six years younger than d’Alembert was to be on receiving the same honor in 1741. Clairaut was among the scientists chosen to accompany Maupertuis on the expedition to Lapland (1736) for measuring an arc of the meridian. Returning, he presented to the Académie memoirs on geometry, algebra, conic sections, and calculus. He published in 1743 his Théorie de la figure de la terre, which calculated, by “Clairaut’s theorem,” and more precisely than Newton or Maclaurin had done, the form that a rotating body mechanically assumes from the natural gravitation of its parts. His interest in Newton brought him into touch with Mme. du Châtelet; he helped her with her translation of the Principia, and shared with Voltaire the honor of converting French scientists from Descartes’ vortices to Newton’s gravitation.
In 1746–49 Euler, Clairaut, and d’Alembert worked independently to find, by the new methods of calculus, the apogee of the moon—its moment of maximum distance from the earth; Euler and Clairaut published approximately the same results; d’Alembert followed with a still more accurate computation. A prize offered by the Academy of St. Petersburg for charting the moon’s motion was won by Clairaut, who published his results in Théorie de la lune (1752). Next he applied his mathematics to the perturbations of the earth due to Venus and the moon; from these variations he estimated the mass of Venus to be 66.7 per cent, and that of the moon as 1.49 per cent, that of the earth; our current figures are 81.5 and 1.82 per cent.
In 1757 the astronomers of Europe began to look out for the return of the comet that Halley had predicted. To guide their observations Clairaut undertook to compute the perturbations the comet would have suffered in passing by Saturn and Jupiter. He calculated that these and other experiences had retarded it by 618 days, and advised the Académie des Sciences that the comet would be at perihelion (its point nearest the sun) about April 13, 1759. An amateur watcher discerned it on Christmas Day, 1758; it passed perihelion on March 12, 1759, thirty-two days earlier than Clairaut’s reckoning. Even so the event was a triumph for science and a transient blow to superstition.V Clairaut presented his studies on the subject in Théorie du mouvement des comètes (1760). His successes, and his great personal charm, made him a prize catch for the rival salons. He attended them frequently, and died at fifty-two (1765). “No French savant of this age merited a higher renown.”60
There were many more whom history should commemorate, though it would spoil the story to tell all. There was Joseph Delisle, who studied the spots and corona of the sun, and founded the St. Petersburg Observatory; and Nicolas de Lacaille, who went to the Cape of Good Hope for the Académie des Sciences, spent ten years (1750–60) charting southern skies, and died of overwork at forty-nine; and Pierre Lemonnier, who went with Maupertuis to Lapland at twenty-one, carried on studies of the moon through fifty years, analyzed the motions of Jupiter and Saturn, and observed and recorded Uranus (1768–69) long before Herschel discovered it to be a planet (1781). And Joseph de Lalande, whose Traité de l’astronomie (1764) surveyed every branch of the science, taught it at the Collège de France for forty-six years, and established in 1802 the Lalande Prize, which is still given annually for the best contribution to astronomy. And Jean Baptiste Delambre, who determined the orbit of Uranus, succeeded Lalande at the Collège, and added to Lalande’s ecumenical exposition a history of astronomy in six painstaking volumes (1817–27).
He was born (1749) Pierre Simon Laplace, of a middle-class family in Normandy, and became the Marquis Pierre Simon de Laplace. He made his first mark by his pious theological essays in school, and became the most confirmed atheist of Napoleonic France. At the age of eighteen he was sent to Paris with a letter of introduction to d’Alembert. D’Alembert, who received many such letters and discounted their encomiums, refused to see him. Resolute, Laplace addressed to him a letter on the general principles of mechanics. D’Alembert responded: “Monsieur, you see that I paid little attention to recommendations. You need none; you have introduced yourself better. That is enough for me. My support is your due.”61 Soon, through d’Alembert’s influence, Laplace was appointed teacher of mathematics at the École Militaire. In a later letter to d’Alembert he analyzed his own passion for mathematics:
I have always cultivated mathematics by taste rather than from desire for a vain reputation. My greatest amusement is to study the march of the inventors, to see their genius at grips with the obstacles they have encountered and overcome. I then put myself in their place, and ask myself how I should have gone about surmounting these same obstacles; and although this substitution in the great majority of instances has been humiliating to my self-love, nevertheless the pleasure of rejoicing in their success has amply repaid me for this little humiliation. If I am fortunate enough to add something to their works, I attribute all the merit to their first efforts.62
We detect some pride in this conscious modesty. In any case Laplace’s ambition was grandly immodest, for he undertook to reduce the entire universe to one mathematical system by applying to all celestial bodies and phenomena the Newtonian theory of gravitation. Newton had left the cosmos in a precarious condition: it was, he thought, subject to irregularities that mounted in time, so that God had to intervene now and then to set it right again. Many scientists, like Euler, were not convinced that the world was a mechanism. Laplace proposed to prove it mechanically.
He began (1773) with a paper showing that the variations in the mean distances of each planet from the sun were subject to nearly precise mathematical formulation, and were therefore periodic and mechanical; for this paper the Académie des Sciences elected him to associate membership at the age of twenty-four. Henceforth Laplace, with a unity, direction, and persistence of purpose characteristic of great men, devoted his life to reducing one after another operation of the universe to mathematical equations. “All the effects of nature,” he wrote, “are only the mathematical consequences of a small number of immutable laws.”63
Though his major works did not appear till after the Revolution, their preparation had begun long before. His Exposition du système du monde (1796) was a popular and nonmechanical introduction to his views, notable for its lucid and fluent style, and embodying his famous hypothesis (anticipated by Kant in 1755) as to the origin of the solar system. Laplace proposed to explain the revolution and rotation of the planets and their satellites by postulating a primeval nebula of hot gases, or other minute particles, enveloping the sun and extending to the farthest reaches of the solar system. This nebula, rotating with the sun, gradually cooled, and contracted into rings perhaps like those now seen around Saturn. Further cooling and contraction condensed these rings into planets, which then, by a similar process, evolved their own satellites; and a like condensation of nebulae may have produced the stars. Laplace assumed that all planets and satellites revolved in the same direction, and practically in the same plane; he did not know, at the time, that the satellites of Uranus move in a contrary direction. This “nebular hypothesis” is now rejected as an explanation of the solar system, but is widely accepted as explaining the condensation of stars out of nebulae. Laplace expounded it only in his popular work, and did not take it too seriously. “These conjectures on the formation of the stars and the solar system … I present with all the distrust [défiance] which everything that is not a result of observation or of calculation ought to inspire.”64
Laplace summed up his observations, equations, and theories—and nearly all the starry science of his time—in the five stately volumes of his Mécanique céleste (1799–1825), which Jean Baptiste Fourier called the Almagest of modern astronomy. He stated his aim with sublime simplicity: “given the eighteen known bodies of the solar system, and their positions and motions at any time, to deduce from their mutual gravitation, by … mathematical calculation, their positions and motions at any other time; and to show that these agree with those actually observed.” To realize his plan Laplace had to study the perturbations caused by the cross-influences of the members—sun, planets, and satellites—of the solar system, and reduce these to periodic and predictable regularity. All these perturbations, he believed, could be explained by the mathematics of gravitation. In this attempt to prove the stability and self-sufficiency of the solar system, and of the rest of the world, Laplace assumed a completely mechanistic view, and gave a classic expression to the deterministic philosophy:
We ought to regard the present state of the universe as the effect of its antecedent state, and as the cause of the state that is to follow. An intelligence knowing all the forces acting in nature at a given instant, as well as the momentary positions of all things in the universe, would be able to comprehend in one single formula the motions of the largest bodies as well as of the lightest atoms in the world, provided that its intellect were sufficiently powerful to subject all data to analysis; to it nothing would be uncertain, the future as well as the past would be present to its eyes. [Cf. the Scholastic conception of God.] The perfection that the human mind has been able to give to astronomy affords a feeble outline of such an intelligence. Discoveries in mechanics and geometry, coupled with those in universal gravitation, have brought the mind within reach of comprehending in the same analytical formulas the past and the future state of the system of the world. All the mind’s efforts in the search for truth tend to approximate to the intelligence we have just imagined, although it will forever remain infinitely remote from such an intelligence.65
When Napoleon asked Laplace why his Mécanique céleste had made no mention of God, the scientist is said to have replied, “Je n’avais pas besoin de cette hypothèse-là” (I had no need of that hypothesis).66 But Laplace had his modest moments. In his Théorie analytique des probabilités (1812)—which is the basis of nearly all later work in that field—he deprived science of all certainty:
Strictly speaking, one may even say that nearly all our knowledge is problematical; and in the small number of things which we are able to know with certainty, even in the mathematical sciences themselves, induction and analogy, the principal means for discovering truth, are based on probabilities.67 VI
In addition to his epochal and widely influential formulation of astronomical discoveries and hypotheses to his date, Laplace made specific contributions. He illuminated nearly every department of physics with the “Laplace equations” for a “potential,” which made it easier to ascertain the intensity of energy, or the velocity of motion, at any point in a field of lines of force. He calculated the earth’s dynamical ellipticity from those perturbations of the moon which were ascribed to the oblate form of our globe. He developed an analytical theory of the tides, and from their phenomena he deduced the mass of the moon. He found an improved method for determining the orbit of comets. He discovered the numerical relations between the movements of Jupiter’s satellites. He computed with characteristic precision the secular (century-long) acceleration of the moon’s mean motion. His studies of the moon provided the basis for the improved tables of lunar motions drawn up in 1812 by his pupil Jean Charles Burckhardt. And finally he rose from science to philosophy—from knowledge to wisdom—in a flight of eloquence worthy of Buffon:
Astronomy, by the dignity of its object matter and the perfection of its theories, is the fairest monument of the human spirit, the noblest testimony of human intelligence. Seduced by self-love and the illusions of his senses, man for a long time regarded himself as the center in the movement of the stars, and his vain arrogance was punished by the terrors that these inspired. Then he saw himself on a planet almost imperceptible in the solar system, whose vast extent is itself but an insensible point in the immensity of space. The sublime results to which this discovery has led him are well fitted to console him for the rank that it assigns to the earth, in showing him his own grandeur in the extreme minuteness of the base from which he measures the stars. Let him preserve with care, and augment, the results of these noble sciences, which are the delight of thinking beings. Those sciences have rendered important services to navigation and geography, but their greatest blessing has been to dissipate the fears produced by celestial phenomena, and to destroy the errors born from ignorance of our true relations with nature, errors and fears that will readily be reborn if the torch of science is ever extinguished.68
Laplace found it easier to adjust his life to the convulsions of French politics than his mathematics to the irregularities of the stars. When the Revolution came he weathered it by being more valuable alive than dead: with Lagrange he was employed to manufacture saltpeter for gunpowder and to calculate trajectories for cannon balls. He was made a member of the commission for weights and measures that formulated the metric system. In 1785 he had examined and passed, as a candidate for an artillery corps, the sixteen-year-old Bonaparte; in 1798 General Bonaparte took him to Egypt to study the stars from the Pyramids. In 1799 the First Consul appointed him minister of the interior; after six weeks he dismissed him because “Laplace sought subtleties everywhere, … and carried the spirit of the infinitely small into administration.”69 To console him Bonaparte nominated him to the new Senate, and made him a count. Now, in the gold and lace of his rank, his portrait was painted by Jacques André Naigeon: a handsome and noble face, eyes saddened as if with the consciousness that death mocks all majesty, that astronomy is a groping in the dark, and that science is a speck of light in a sea of night. On his deathbed (1827) all vanity left him, and almost his last words were: “That which we know is but a little thing; that which we do not know is immense.”70