by Will Durant
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 treatise De 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.
3. Herschel
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.