1. Matter, Motion, Heat, and Light
Mathematics grew because it was the basic and indispensable tool of all science, reducing experience and experiment to quantitative formulations that made possible precise prediction and practical control. The first step was to apply it to matter in general: to discover the regularities and establish the “laws” of energy, motion, heat, sound, light, magnetism, electricity; here were mysteries enough waiting to be explored.
Pierre Louis Moreau de Maupertuis abandoned a career in the French army to devote himself to science. He preceded Voltaire in introducing Newton to France, and in appreciating and instructing Mme. du Châtelet. In 1736, as we shall see, he directed an expedition to Lapland to measure a degree of the meridian. In 1740 he accepted an invitation to visit Frederick II; he followed Frederick into the battle of Mollwitz (1741), was captured by the Austrians, but was soon released. In 1745 he joined the Academy of Sciences at Berlin, and a year later he became its president. To the Paris Académie des Sciences in 1744, and to the Berlin Academy in 1746, he expounded his principle of least action: “Whenever any change occurs in nature, the quantity of action employed for this change is always the least possible.” This, he thought, proved a rational order in nature, and therefore the existence of a rational God.12 Euler and Lagrange developed the principle, and in our own time it played a part in the quantum theory. In an Essai de cosmologie (1750) Maupertuis revived an indestructible heresy: while still recognizing design in nature, he confessed to seeing in it also signs of stupidity or evil, as if a demon were competing with a benevolent deity in the management of the cosmos.13Maupertuis might have agreed with his merciless enemy Voltaire that St. Augustine should have remained a Manichaean.
We have noted the birth of d’Alembert as the unpremeditated issue of a passing contact between an artilleryman and an ex-nun. The Paris police found him, a few hours old, on the steps of the Church of St.-Jean-le-Rond (1717); they had him baptized Jean Baptiste Le Rond, and sent him to a nurse in the country. His father, the Chevalier Destouches, claimed him, gave him (for reasons unknown to us) the name d’Arembert, and paid Mme. Rousseau, a glazier’s wife, to adopt the child. She proved a model stepmother, and Jean a model and precocious boy. When he was seven the father proudly displayed him to the mother, Mme. de Tencin, but she decided that her career as mistress and salonnière would be impeded by accepting him. She contributed nothing to his support, so far as we know, but the Chevalier, before dying in 1726, left him an annuity of twelve hundred livres.
Jean studied at the Collège des Quatre-Nations, then at the University of Paris, where he received the degree in law. There, about 1738, he changed his name from d’Arembert to d’Alembert. Tiring of law, he turned to medicine; but an incidental interest in mathematics became a passion: “mathematics,” he said, “was for me my mistress.”14 He continued till he was forty-eight to live with Mme. Rousseau, looking upon her gratefully as his only mother. She thought it disgraceful that a man should so abandon himself to study and show no economic itch. “You will never be anything better than a philosopher,” she mourned, adding, “And what is a philosopher? ’Tis a madman who torments himself all his life so that people may talk about him when he is dead.”15
Probably his inspiring motives were not a desire for posthumous fame but a proud rivalry with established savants, and that beaver instinct which takes delight in building, in forging order upon a chaos of materials or ideas. In any case he began at twenty-two to submit papers to the Académie des Sciences: one on integral calculus (1739), another on the refraction of light (1741); this gave the earliest explanation of the bending of light rays in passing from one fluid to another of greater density; for this the Académie admitted him to “adjoint” membership. Two years later he published his main scientific work, Traité de dynamique, which sought to reduce to mathematical equations all problems of matter in motion; this anticipated by forty-two years Lagrange’s superiorMécanique analytique; it keeps historical significance because it formulated the basic theorem now known as “D’Alembert’s principle,” too technical for our general digestion, but immensely helpful in mechanical calculations. He applied it in a Traité de l’équilibre et du mouvement des fluides (1744); this so impressed the Académie that it awarded him a pension of five hundred livres, which must have appeased Mme. Rousseau.
Partly from his principle, partly from an original equation in calculus, d’Alembert arrived at a formula for the motion of winds. He dedicated his Réflexions sur la cause générale des vents (1747) to Frederick the Great, who responded by inviting him to settle in Berlin; d’Alembert refused, showing at thirty more wisdom than Voltaire was to show at fifty-six. In an Essai d’une nouvelle théorie de la résistance des fluides (1752) he tried to find mechanical formulas for the resistance of water to a body moving on it; he failed, but in 1775, under a commission from Turgot, he and Condorcet and the Abbé Bossut made experiments that helped to determine the laws of fluid resistance to surface-moving bodies. Late in life he studied the motion of vibrating chords, and issued (1779)Eléments de musique théorique et pratique, following and modifying the system of Rameau; this book won the praise of the famous musicologist Charles Burney. All in all, d’Alembert had one of the keenest minds of the century.
When Maupertuis resigned as president of the Berlin Academy Frederick the Great offered the post to d’Alembert. The mathematician-physicist-astronomer-encyclopedist was poor, but he courteously refused; he cherished his freedom, his friends, and Paris. Frederick respected his motives, and, with the permission of Louis XV, sent him a modest pension of twelve hundred livres. In 1762 Catherine the Great invited him to Russia and the Academy of St. Petersburg; he declined, for he was now in love. Perhaps informed of this, Catherine persisted, bade him come “avec tous vos amis,” with all his friends, and offered him a salary of 100,000 francs a year. She took his refusals graciously, and continued to correspond with him, discussing with him her mode and problems of government. In 1763 Frederick urged him at least to visit Potsdam; d’Alembert went, and dined with the King for two months. He again declined the presidency of the Berlin Academy; instead he induced Frederick to raise the salary of Euler, who had a large family.16 We hope to meet d’Alembert again.
The amazing Bernoullis made some incidental contributions to mechanics. Johann I formulated (1717) the principle of virtual velocities: “In all equilibrium of forces whatsoever, in whatever manner they are applied, and in whatever directions they act upon one another, whether directly or indirectly, the sum of the positive energies will be equal to the sum of the negative energies taken positively.” Johann and his son Daniel (1735) proclaimed that the sum of vis viva (living force) in the world is always constant; this principle was reformulated in the nineteenth century as the conservation of energy. Daniel applied the conception to good effect in his Hydrodynamics (1738), a modern classic in an especially difficult field. In that volume he founded the kinetic theory of gases: a gas is composed of tiny particles moving about with great rapidity, and exerting pressure upon the container by their repeated impacts; heat increases the velocity of the particles and therefore the pressure of the gas; and the lessening of the volume (as Boyle had shown) proportionately increases the pressure.
In the physics of heat the great name for the eighteenth century is Joseph Black. Born in Bordeaux to a Scot born in Belfast, he studied chemistry in the University of Glasgow, and at the age of twenty-six (1754) made experiments in what we would now call oxidation or corrosion; these indicated the action of a gas distinct from common air; he detected this in the balance, and called it “fixed air” (now called carbon dioxide); Black had come close to the discovery of oxygen. In 1756, as lecturer in chemistry, anatomy, and medicine at the university, he began observations that led him to his theory of “latent heat”: when a substance is in process of changing from a solid to a liquid state, or from a liquid to a gas, the changing substance absorbs from the atmosphere an amount of heat not detectable as a change of temperature; and this latent heat is given back to the atmosphere when a gas changes into a liquid or a liquid into a solid. James Watt applied this theory in his improvement of the steam engine. Black, like nearly all predecessors of Priestley, thought of heat as a material substance (“caloric”) added to or subtracted from matter rising or falling in warmth; not until 1798 did Benjamin Thompson, Count Rumford, show that heat is not a substance but a mode of motion, now conceived as an accelerated motion of a body’s constituent parts.
Meanwhile Johan Carl Wilcke of Stockholm, independently of Black, arrived at a similar theory of latent heat (1772). In a series of experiments reported in 1777 the Swedish scientist introduced the term “radiant heat”—the invisible heat given off by hot materials; he distinguished it from light, described its lines of motion and its reflection and concentration by mirrors, and prepared for the later correlation of both heat and light as kindred forms of radiation. Wilcke, Black, Lavoisier, Laplace, and other investigators determined the approximate value of “absolute zero” (the lowest temperature possible in principle). The British adopted as the unit of heat that quantity which raises the temperature of a pound of water one degree Fahrenheit; the French, and the Continent in general, preferred to use that quantity of heat which raises the temperature of a kilogram of water one degree centigrade.
The eighteenth century made little progress in the theory of light, because nearly all physicists accepted Newton’s “corpuscular hypothesis”—that light is the emission of particles from the object to the eye. Euler led a minority that defended a wave theory. Following Huygens, he assumed that the “empty” space between the heavenly bodies, and between other visible objects, is filled with “ether,” a material too fine to be perceived by our senses or our instruments, but strongly suggested by the phenomena of gravity, magnetism, and electricity. Light, in Euler’s view, is an undulation in the ether, just as sound is an undulation in the air. He distinguished colors as due to different periods of vibration in light waves, and anticipated the current assignment of blue light to the shortest period of vibration, and red light to the longest.—Pierre Bouguer verified by experiment what Kepler had worked out theoretically, that the intensity of light varies inversely as the square of the distance from its source. Johann Lambert devised ways of measuring the intensity of light, and reported that the brightness of the sun is 277,000 times that of the moon; this, like our childhood theology, we must take on faith.
The most brilliant advances in eighteenth-century physics were in the field of electricity. Frictional electricity had long been known; Thales of Miletus (600 B.C.) was familiar with the power of amber, jet, and a few other substances, when rubbed, to attract light objects like feathers or straw. William Gilbert, physician to Queen Elizabeth, called this attractive power “electron” (from the Greek ēlektron, amber) and, in Latin, vis electrica. The next step was to find a way to conduct and use this static electricity. Guericke and Hauksbee had sought such means in the seventeenth century; it remained for Stephen Gray to make the decisive discovery (1729).
Gray was an old irascible pensioner in a London almshouse. Having “electrified,” by rubbing, a glass tube corked at both ends, he found that the corks, as well as the tube, would attract a feather. He inserted one end of a wooden rod into one of the corks, and the other end into an ivory ball; when he rubbed the tube the ball, as well as the tube and the corks, attracted a feather; the vis electrica had been conducted along the rod. Using packthread or strong twine instead of the rod, he was able to conduct the electricity through a distance of 765 feet. When he used hair, silk, resin, or glass as a connection there was no conduction; in this way Gray remarked the difference between conductors and non-conductors, and he discovered that non-conductors could be used for the preservation or storage of electric charges. When he suspended 666 feet of conductive packthread from a long succession of inclined poles, and sent the electric “virtue” (as he called it) through that distance, he in effect anticipated the telegraph.
France took up the quest. Jean Desaguliers, continuing (1736) Gray’s experiments, divided substances into conductors and non-conductors (which he called “electrics per se”), and found that the latter could be changed into conductors by being moistened with water. Charles Du Fay carried on researches which he reported to the Académie des Sciences in 1733–37; and in a modest letter to the Royal Society of London (1734) he formulated his most important conclusion:
Chance has thrown in my way another Principle: … that there are two distinct electricities, very different from each other; one of which I call vitreous electricity, and the other resinous electricity. The first is that of glass, rock crystal, precious stones, hair of animals, wool, and many other bodies. The second is that of amber, copal, gum-lack, silk, thread, paper, and a vast number of other substances. The character of these two electricities is that a body of the vitreous electricity … repels all such as are of the same electricity, and, on the contrary, attracts all those of the resinous electricity.17
So, Du Fay found, two bodies electrified by contact with the same electrified body repel each other; every schoolboy can recall his astonishment at seeing two pith balls, suspended by non-conductors from the same point and lying in contact with each other, suddenly spring apart when touched by the same electrified glass rod. Later experiments showed that “vitreous” bodies may develop “resinous” electricity, and “resinous” bodies may develop “vitreous” electricity. Franklin therefore replaced Du Fay’s terms withpositive and negative. Du Fay amused his contemporaries by suspending a man by non-conductive cords, charging him with electricity by contact with an electrified body, and then drawing sparks from his body, with no harm to the hanging man.II
The scene moved to Germany. About 1742 Georg Bose in some part anticipated Franklin by suggesting that the aurora borealis is of electrical origin. In 1744 Christian Ludolff, at the Berlin Academy, showed that an electric spark can ignite an inflammable fluid. Bose exploded gunpowder in this way, inaugurating the use of electricity in blasting, firing cannon, and a hundred other ways. In the same year Gottlieb Kratzenstein began the employment of electricity in dealing with diseases. In October, 1745, E. G. von Kleist, a Pomeranian clergyman, discovered that an electrical charge could be stored in a glass tube by filling this with a liquid into which he had inserted a nail connected with a machine producing frictional electricity; when the connection was severed, the liquid retained its charge for several hours. A few months later Pieter van Musschenbroek, professor at Leiden, without any knowledge of Kleist’s experiments, made the same discovery, and received from a charged but disconnected bowl a shock that for a moment seemed mortal; he took two days to recover. Further experiments at Leiden showed that a heavier charge could be stored in an empty bottle if its lower interior and exterior surfaces had been coated with tinfoil. Daniel Gralath conceived the idea of binding several such “Leiden jars” together, and found that their discharge would kill small animals.
In 1746 Louis Guillaume in Paris and in 1747 William Watson in London demonstrated what Watson was the first to call a “circuit.” Watson laid a wire some twelve hundred feet long across Westminster Bridge; on one side of the Thames a man held one end of the wire and touched the water; on the other side a second man held the wire and a Leiden jar; when a third man touched the jar with one hand and with the other grasped a wire that extended into the river, the “circuit” was closed, and all three men received a shock. In 1747 Grummert of Dresden noted that sparks could be made for some distance through a partial vacuum, giving out considerable light.
This year 1747 brings us to Benjamin Franklin, who then began the electrical experiments that made his name and honor oscillate between science and politics. Here was one of the great minds and hearts of history, whose creative curiosity ranged from such proposals as daylight-saving time, rocking chairs and bifocal glasses to lightning rods and the one-fluid theory of electricity. A leading scientist of our century, Sir Joseph Thomson, confessed that he was “struck by the similarity between some of the views which we are led to take by the results of the most recent researches with those enunciated by Franklin in the very infancy of the subject.”19
One of Franklin’s first discoveries was the effect of pointed bodies in “drawing off and throwing off the electrical fire.”20 He found that “a long, slender shaft-bodkin” could attract a flow of electricity from an electrified ball six or eight inches distant, whereas a blunt body had to be brought within an inch of the ball to produce the same effect. Franklin spoke of electricity as fire, but this fire, he thought, was the result of a disturbance between the equilibrium of the “positive” and “negative” fiery fluids which he conceived electricity to be. All bodies, in his view, contained such electrical fluid: a “plus” body, containing more than its normal amount, is positively electrified, and tends to discharge its surplus into a body containing a normal amount or less; a “minus” body, containing less than its normal amount, is negatively electrified, and will draw electricity from a body containing a normal amount or more. On this basis Franklin developed a battery composed of eleven large glass plates covered with sheets of lead, which were electrified to a high excess; when this structure was brought into contact with bodies less heavily charged, it released part of its charge with a force that (said Franklin) “knew no bounds,” sometimes exceeding “the greatest known effects of common lightning.”21
Several investigators—Wall, Newton, Hauksbee, Gray, and others—had noted the resemblance between electric sparks and lightning; Franklin proved their identity. In 1750 he sent to the Royal Society of London a letter reading in part:
May not the knowledge of this power of points be of use to mankind in preserving houses, churches, ships, etc., from the stroke of lightning, by directing us to fix on the highest parts of the edifices upright rods of iron made sharp as a needle, and gilt to prevent rusting, and from the foot of these rods a wire drawn down the outside of the building into the grounds, or round one of the shrouds of a ship down her side till it reaches the water? Would not these pointed rods probably draw the electrical fire silently out of a cloud before it came nigh enough to strike, and thereby secure us from that most sudden and terrible mischief?22
He went on to describe an experiment by which this could be tested. The Royal Society rejected the proposal as visionary, and refused to publish Franklin’s letter. Two French scientists, de Lor and d’Alibard, put Franklin’s theory to trial by erecting in a garden at Marly (1752) a pointed iron rod fifty feet high; they instructed a guard to touch the rod with an insulated brass wire if, in their absence, thunder clouds should pass overhead. The clouds came, the guard touched the rod not only with wire but also with his hand; sparks flew and crackled, and the guard was severely shocked. De Lor and d’Alibard confirmed the guard’s report by further tests, and informed the Académie des Sciences, “Franklin’s idea is no longer a conjecture but a reality.”
Franklin himself was not satisfied; he wished to make the identity of lightning and electricity evident by “extracting” lightning with something sent up into the storm cloud itself. In June, 1752, as a thunderstorm began, he sent up, on strong twine, a kite made of silk (as better fitted than paper to bear wind and moisture without tearing); a sharply pointed wire projected some twelve inches from the top of the kite; and at the observer’s end of the twine a key was fastened with a silk ribbon. In sending to England (October 19) directions for repeating the experiment, Franklin indicated the results:
When the rain has wet the kite twine so that it can conduct the electric fire freely, you will find it stream out plentifully from the key at the approach of your knuckle, and with this key a phial [or Leiden jar) may be charged; and from electric fire thus obtained spirits may be kindled, and all other electric experiments [may be] performed which are usually done by the help of a rubbed glass globe or tube; and therefore the sameness of the electrical matter with that of lightning completely demonstrated.23
The experiment was repeated in France (1753) with a larger kite and a 780-foot cord twisted around an iron wire, ending at the observer in a metal tube which, in action, emitted sparks eight inches long. Professor G. W. Richman of St. Petersburg, making a similar test, was killed by the shock (1753). Franklin’s publications, sent to England in 1751–54, won him election to the repentant Royal Society, and its Copley Medal. Their translation into French evoked a complimentary letter from Louis XV, and enthusiastic praise from Diderot, who called them models of scientific reporting. Those translations prepared for the favorable reception given to Franklin when he came to France to seek aid for the American colonies in their revolution. When, with the help of France, that revolution succeeded, d’Alembert (or Turgot) summed up Franklin’s achievement in a compact line worthy of Virgil or Lucretius:
Eripuit coelo fulmen sceptrumque tyrannis
—“he snatched the lightning from the sky, and the scepter from the tyrants.”
All Europe was alive, after 1750, with electrical theories and experiments. John Canton (1753) and the versatile Wilcke (1757) led the way in studying electrostatic induction, by which an uncharged conductor becomes electrified when placed near a charged body. Wilcke proved that most substances can be charged with positive (or negative) electricity if rubbed with a body less (or more) highly charged than themselves. Working with Wilcke at Berlin, Aepinus (Franz Ulrich Hoch) showed that two metal plates separated only by a layer of air acted like a Leiden jar. Joseph Priestley sought to measure the strength of an electric charge, and the maximum width across which the spark of a given charge would pass. He reported that when a spark crossed a gap even as wide as two inches between two metal rods in a vacuum, a “thin blue or purple light” appeared in the gap. But Priestley’s most brilliant contribution to electrical theory was the suggestion that the laws of electricity might be like those of gravitation, and that the force exerted upon each other by separate electric charges would vary inversely as the square of the distance between their source. Henry Cavendish (who, like Priestley, is remembered chiefly for his work in chemistry) tested Priestley’s suggestion in a series of patient experiments; he arrived at a slight but important modification, which James Clerk Maxwell further refined in 1878; as such the law is received today. Charles Augustin de Coulomb, after valuable work on the tension of beams and the resistance of metals to torsion, submitted to the Académie des Sciences reports of experiments (1785–89) which applied the torsion balance (a needle supported on a fine fiber) to the measurement of magnetic influences and electrical charges; in both cases he substantially verified the law of inverse squares.
Two Italians, like Coulomb, left their names in the terminology of electricity. Luigi Galvani, professor of anatomy at Bologna, discovered not only that muscular contractions could be produced in dead animals by direct electrical contact (this had long been known), but that such contractions occurred when the leg of a dead frog, connected with the earth, was brought near a machine that was discharging an electric spark. Similar convulsions were produced in frogs’ legs—likewise grounded, and tied to long iron wires—when lightning flashed into the room. Galvani was surprised to find that he could make a frog’s leg contract without any use or presence of electrical apparatus, merely by bringing the nerve and muscle of the leg into contact with two different metals. He concluded that there was a natural electricity in the animal organism.
Alessandro Volta, professor of physics at Pavia, repeated these experiments, and at first agreed with his countryman’s theory of animal electricity. But his further researches modified his views. Repeating an experience reported by J. G. Sulzer about 1750, Volta found that if he placed a piece of tin on the tip of his tongue, and a piece of silver on the back of his tongue, he felt a strong sour taste whenever he connected the two metals with a wire. By connecting his forehead and his palate with these two different metals he obtained a sensation of light. In 1792 he announced his conclusion that the metals themselves, and not the animal tissue, produced the electricity merely by their interaction with each other and their contact with a moist substance, preferably a solution of salt. Further experiments proved that the contact of two different metals caused them to be electrically charged—one positively, the other negatively—without the mediation of any moist substance, animal or not; but such direct contact produced only an interchange of charges, not an outflow of current. To produce a current Volta made a “Voltaic pile” by superimposing several layers, each composed of two connected plates of different metal and one plate of moist paper or wood. So was formed, in the last year of the eighteenth century, the first electrical-current battery. The way was opened for electricity to remake the face and night of the world.