by Will Durant
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).
5. Laplace
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
VI. ABOUT THE EARTH
Four sciences studied the earth: meteorology explored its envelope of weather; geodesy estimated its size, shape, density, and such distances as involved its surface curvature; geology delved into its composition, depths, and history; geography charted its lands and seas.
1. Meteorology
Besides the simple rain gauge, the science of weather used four measuring instruments: the thermometer for temperature, the barometer for atmospheric pressure, the anemometer for winds, the hygrometer for moisture in the air.
In or before 1721 Gabriel Daniel Fahrenheit, a German instrument maker in Amsterdam, developed the thermometer, which Galileo had invented in 1603; Fahrenheit used mercury instead of water as the expanding-contracting fluid, and divided the scale into degrees based upon the freezing point of water (32°) and the oral temperature of the normal human body (98.6°). In 1730 René de Réaumur reported to the Académie des Sciences “rules for constructing thermometers with comparable gradations”; he took the freezing point of water as zero, and its boiling point as 80°, and he graduated the scale to make the degrees correspond to equal increments in the rise or fall of the thermometric fluid, for which he used alcohol. Anders Celsius of Uppsala, about 1742, improved Réaumur’s thermometer by returning to the use of mercury, and dividing the scale into a hundred “centigrade” degrees between the freezing and the boiling points of water. By determining these points more precisely, Jean André Deluc of Geneva, in 1772, gave the rival thermometers essentially the form they have today: the Fahrenheit form for English-speaking peoples, the centigrade form for others.
The barometer had been invented by Torricelli in 1643, but its readings of atmospheric pressure were made uncertain by factors for which he had not allowed: the quality of the mercury, the bore of the tube, and the temperature of the air. Various researches, culminating in the experiments and calculations of Deluc (1717–1817), remedied these defects, and brought the mercury barometer into its current form.
Divers crude anemometers were made in the seventeenth century. At his death in 1721 Pierre Huet, the scholarly bishop of Avranches, left a design for an anemometer (the word was apparently his invention) that would measure the force of the wind by funneling it into a tube where its pressure would raise a column of mercury. This was improved by the “wind gauge” (1775) of the Scottish physician James Lind. John Smeaton devised (c. 1750) a mechanism for measuring wind velocity. The best eighteenth-century instrument for measuring moisture was the hygrometer of the versatile Genevan Horace de Saussure (1783), which was based upon the expansion and contraction of a human hair by changes in humidity. William Cullen provided a basis for another type of hygrometer by noting the cooling effect of fluids in evaporation.
With these and other instruments, such as the magnetic needle, science strove to detect regularities in the vagaries of weather. The first requisite was reliable records. Some had been kept for France by the Académie des Sciences since 1688. From 1717 to 1727 a Breslau physician kept daily records of weather reports which he had solicited from many parts of Germany; and in 1724 the Royal Society of London began to compile meteorological reports not only from Britain but also from the Continent, India, and North America. A still wider and more systematic co-ordination
of daily reports was organized in 1780 by J. J. Hemmer at Mannheim, under the patronage of the Elector Palatine Charles Theodore; but this was abandoned (1792) during the wars of the French Revolution.
One meteorological phenomenon that sparked much speculation was the aurora borealis. Edmund Halley carefully studied the outbursts of these “northern lights” on March 16–17, 1716, and ascribed them to magnetic influences emanating from the earth. In 1741 Hjorter and other Scandinavian observers noted that irregular variations of the compass needle occurred at the time of the displays. In 1793 John Dalton, the chemist, pointed out that the streamers of the lights are parallel to the dipping needle, and that their vertex, or point of convergence, lies in the magnetic meridian. The eighteenth century, therefore, recognized the electrical nature of the phenomenon, which is now interpreted as an electrical discharge in the earth’s atmosphere, due to ionization caused by particles shot out from the sun.
The literature of meteorology in the eighteenth century began with Christian von Wolff’s Aerometricae elementa (1709), which summed up the known data to date, and suggested some new instruments. D’Alembert attempted a mathematical formulation of wind motions in Réflexions sur la cause générale des vents, which won a prize offered by the Berlin Academy in 1747. The outstanding treatise in this period was the massive Traité de météorologie (1774) by Louis Cotte, a priest of Montmorency. Cotte gathered and tabulated the results of his own and other observations, described instruments, and applied his findings to agriculture; he gave the flowering and maturation time of various crops, the dates at which swallows came and went, and when the nightingale could be expected to sing; he regarded the winds as the chief causes of changes in the weather; and finally he offered tentative formulas for weather forecasts. Jean Deluc’s Recherches sur les modifications de l’atmosphère (1772) extended the experiments of Pascal (1648) and Halley (1686) on the relations between altitude and atmospheric pressure, and formulated the law that “at a certain temperature the differences between the logarithms of the heights of the mercury [in the barometer] give immediately, in thousandths of a fathom, the difference in heights of the places where the barometer was observed.”71 By attaching a level to his barometer, Deluc was able to estimate barometrically the altitude of various landmarks; so he calculated the height of Mont Blanc as 14,346 feet above sea level. Horace de Saussure, after ascending the mountain and taking barometric readings at its peak (1787), obtained a measurement of 15,700 feet.