"That there is a power of gravity tending to all bodies, proportional to the several quant.i.ties of matter which they contain.

"That all the planets mutually gravitate one towards another we have proved before; as well as that the force of gravity towards every one of them considered apart, is reciprocally as the square of the distance of places from the centre of the planet. And thence it follows, that the gravity tending towards all the planets is proportional to the matter which they contain.

"Moreover, since all the parts of any planet A gravitates towards any other planet B; and the gravity of every part is to the gravity of the whole as the matter of the part is to the matter of the whole; and to every action corresponds a reaction; therefore the planet B will, on the other hand, gravitate towards all the parts of planet A, and its gravity towards any one part will be to the gravity towards the whole as the matter of the part to the matter of the whole. Q.E.D.

"HENCE IT WOULD APPEAR THAT the force of the whole must arise from the force of the component parts."

Newton closes this remarkable Book iii. with the following words:

"Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity, but have not yet a.s.signed the cause of this power. This is certain, that it must proceed from a cause that penetrates to the very centre of the sun and planets, without suffering the least diminution of its force; that operates not according to the quant.i.ty of the surfaces of the particles upon which it acts (as mechanical causes used to do), but according to the quant.i.ty of solid matter which they contain, and propagates its virtue on all sides to immense distances, decreasing always in the duplicate proportions of the distances. Gravitation towards the sun is made up out of the gravitations towards the several particles of which the body of the sun is composed; and in receding from the sun decreases accurately in the duplicate proportion of the distances as far as the orb of Saturn, as evidently appears from the quiescence of the aphelions of the planets; nay, and even to the remotest aphelions of the comets, if those aphelions are also quiescent. But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypothesis; for whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.... And to us it is enough that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies and of our sea."(2)

The very magnitude of the importance of the theory of universal gravitation made its general acceptance a matter of considerable time after the actual discovery. This opposition had of course been foreseen by Newton, and, much as he dreaded controversy, he was prepared to face it and combat it to the bitter end. He knew that his theory was right; it remained for him to convince the world of its truth. He knew that some of his contemporary philosophers would accept it at once; others would at first doubt, question, and dispute, but finally accept; while still others would doubt and dispute until the end of their days. This had been the history of other great discoveries; and this will probably be the history of most great discoveries for all time. But in this case the discoverer lived to see his theory accepted by practically all the great minds of his time.

Delambre is authority for the following estimate of Newton by Lagrange.

"The celebrated Lagrange," he says, "who frequently a.s.serted that Newton was the greatest genius that ever existed, used to add--'and the most fortunate, for we cannot find MORE THAN ONCE a system of the world to establish.'" With pardonable exaggeration the admiring followers of the great generalizer p.r.o.nounced this epitaph:

"Nature and Nature's laws lay hid in night; G.o.d said 'Let Newton be!' and all was light."

XIII. INSTRUMENTS OF PRECISION IN THE AGE OF NEWTON

During the Newtonian epoch there were numerous important inventions of scientific instruments, as well as many improvements made upon the older ones. Some of these discoveries have been referred to briefly in other places, but their importance in promoting scientific investigation warrants a fuller treatment of some of the more significant.

Many of the errors that had arisen in various scientific calculations before the seventeenth century may be ascribed to the crudeness and inaccuracy in the construction of most scientific instruments.

Scientists had not as yet learned that an approach to absolute accuracy was necessary in every investigation in the field of science, and that such accuracy must be extended to the construction of the instruments used in these investigations and observations. In astronomy it is obvious that instruments of delicate exactness are most essential; yet Tycho Brahe, who lived in the sixteenth century, is credited with being the first astronomer whose instruments show extreme care in construction.

It seems practically settled that the first telescope was invented in Holland in 1608; but three men, Hans Lippershey, James Metius, and Zacharias Jansen, have been given the credit of the invention at different times. It would seem from certain papers, now in the library of the University of Leyden, and included in Huygens's papers, that Lippershey was probably the first to invent a telescope and to describe his invention. The story is told that Lippershey, who was a spectacle-maker, stumbled by accident upon the discovery that when two lenses are held at a certain distance apart, objects at a distance appear nearer and larger. Having made this discovery, he fitted two lenses with a tube so as to maintain them at the proper distance, and thus constructed the first telescope.

It was Galileo, however, as referred to in a preceding chapter, who first constructed a telescope based on his knowledge of the laws of refraction. In 1609, having heard that an instrument had been invented, consisting of two lenses fixed in a tube, whereby objects were made to appear larger and nearer, he set about constructing such an instrument that should follow out the known effects of refraction. His first telescope, made of two lenses fixed in a lead pipe, was soon followed by others of improved types, Galileo devoting much time and labor to perfecting lenses and correcting errors. In fact, his work in developing the instrument was so important that the telescope came gradually to be known as the "Galilean telescope."

In the construction of his telescope Galileo made use of a convex and a concave lens; but shortly after this Kepler invented an instrument in which both the lenses used were convex. This telescope gave a much larger field of view than the Galilean telescope, but did not give as clear an image, and in consequence did not come into general use until the middle of the seventeenth century. The first powerful telescope of this type was made by Huygens and his brother. It was of twelve feet focal length, and enabled Huygens to discover a new satellite of Saturn, and to determine also the true explanation of Saturn's ring.

It was Huygens, together with Malvasia and Auzout, who first applied the micrometer to the telescope, although the inventor of the first micrometer was William Gascoigne, of Yorkshire, about 1636. The micrometer as used in telescopes enables the observer to measure accurately small angular distances. Before the invention of the telescope such measurements were limited to the angle that could be distinguished by the naked eye, and were, of course, only approximately accurate. Even very careful observers, such as Tycho Brahe, were able to obtain only fairly accurate results. But by applying Gascoigne's invention to the telescope almost absolute accuracy became at once possible. The principle of Gascoigne's micrometer was that of two pointers lying parallel, and in this position pointing to zero. These were arranged so that the turning of a single screw separated or approximated them at will, and the angle thus formed could be determined with absolute accuracy.

Huygens's micrometer was a slip of metal of variable breadth inserted at the focus of the telescope. By observing at what point this exactly covered an object under examination, and knowing the focal length of the telescope and the width of the metal, he could then deduce the apparent angular breadth of the object. Huygens discovered also that an object placed in the common focus of the two lenses of a Kepler telescope appears distinct and clearly defined. The micrometers of Malvasia, and later of Auzout and Picard, are the development of this discovery.

Malvasia's micrometer, which he described in 1662, consisted of fine silver wires placed at right-angles at the focus of his telescope.

As telescopes increased in power, however, it was found that even the finest wire, or silk filaments, were much too thick for astronomical observations, as they obliterated the image, and so, finally, the spider-web came into use and is still used in micrometers and other similar instruments. Before that time, however, the fine crossed wires had revolutionized astronomical observations. "We may judge how great was the improvement which these contrivances introduced into the art of observing," says Whewell, "by finding that Hevelius refused to adopt them because they would make all the old observations of no value.

He had spent a laborious and active life in the exercise of the old methods, and could not bear to think that all the treasures which he had acc.u.mulated had lost their worth by the discovery of a new mine of richer ones."(1)

Until the time of Newton, all the telescopes in use were either of the Galilean or Keplerian type, that is, refractors. But about the year 1670 Newton constructed his first reflecting telescope, which was greatly superior to, although much smaller than, the telescopes then in use. He was led to this invention by his experiments with light and colors.

In 1671 he presented to the Royal Society a second and somewhat larger telescope, which he had made; and this type of instrument was little improved upon until the introduction of the achromatic telescope, invented by Chester Moor Hall in 1733.

As is generally known, the element of accurate measurements of time plays an important part in the measurements of the movements of the heavenly bodies. In fact, one was scarcely possible without the other, and as it happened it was the same man, Huygens, who perfected Kepler's telescope and invented the pendulum clock. The general idea had been suggested by Galileo; or, better perhaps, the equal time occupied by the successive oscillations of the pendulum had been noted by him. He had not been able, however, to put this discovery to practical account. But in 1656 Huygens invented the necessary machinery for maintaining the motion of the pendulum and perfected several accurate clocks. These clocks were of invaluable a.s.sistance to the astronomers, affording as they did a means of keeping time "more accurate than the sun itself."

When Picard had corrected the variation caused by heat and cold acting upon the pendulum rod by combining metals of different degrees of expansibility, a high degree of accuracy was possible.

But while the pendulum clock was an unequalled stationary time-piece, it was useless in such unstable situations as, for example, on shipboard.

But here again Huygens played a prominent part by first applying the coiled balance-spring for regulating watches and marine clocks. The idea of applying a spring to the balance-wheel was not original with Huygens, however, as it had been first conceived by Robert Hooke; but Huygens's application made practical Hooke's idea. In England the importance of securing accurate watches or marine clocks was so fully appreciated that a reward of L20,000 sterling was offered by Parliament as a stimulus to the inventor of such a time-piece. The immediate incentive for this offer was the obvious fact that with such an instrument the determination of the longitude of places would be much simplified.

Encouraged by these offers, a certain carpenter named Harrison turned his attention to the subject of watch-making, and, after many years of labor, in 1758 produced a spring time-keeper which, during a sea-voyage occupying one hundred and sixty-one days, varied only one minute and five seconds. This gained for Harrison a reward Of L5000 sterling at once, and a little later L10,000 more, from Parliament.

While inventors were busy with the problem of accurate chronometers, however, another instrument for taking longitude at sea had been invented. This was the reflecting quadrant, or s.e.xtant, as the improved instrument is now called, invented by John Hadley in 1731, and independently by Thomas G.o.dfrey, a poor glazier of Philadelphia, in 1730. G.o.dfrey's invention, which was constructed on the same principle as that of the Hadley instrument, was not generally recognized until two years after Hadley's discovery, although the instrument was finished and actually in use on a sea-voyage some months before Hadley reported his invention. The principle of the s.e.xtant, however, seems to have been known to Newton, who constructed an instrument not very unlike that of Hadley; but this invention was lost sight of until several years after the philosopher's death and some time after Hadley's invention.

The introduction of the s.e.xtant greatly simplified taking reckonings at sea as well as facilitating taking the correct longitude of distant places. Before that time the mariner was obliged to depend upon his compa.s.s, a cross-staff, or an astrolabe, a table of the sun's declination and a correction for the alt.i.tude of the polestar, and very inadequate and incorrect charts. Such were the instruments used by Columbus and Vasco da Gama and their immediate successors.

During the Newtonian period the microscopes generally in use were those constructed of simple lenses, for although compound microscopes were known, the difficulties of correcting aberration had not been surmounted, and a much clearer field was given by the simple instrument.

The results obtained by the use of such instruments, however, were very satisfactory in many ways. By referring to certain plates in this volume, which reproduce ill.u.s.trations from Robert Hooke's work on the microscope, it will be seen that quite a high degree of effectiveness had been attained. And it should be recalled that Antony von Leeuwenhoek, whose death took place shortly before Newton's, had discovered such micro-organisms as bacteria, had seen the blood corpuscles in circulation, and examined and described other microscopic structures of the body.

XIV. PROGRESS IN ELECTRICITY FROM GILBERT AND VON GUERICKE TO FRANKLIN

We have seen how Gilbert, by his experiments with magnets, gave an impetus to the study of magnetism and electricity. Gilbert himself demonstrated some facts and advanced some theories, but the system of general laws was to come later. To this end the discovery of electrical repulsion, as well as attraction, by Von Guericke, with his sulphur ball, was a step forward; but something like a century pa.s.sed after Gilbert's beginning before anything of much importance was done in the field of electricity.

In 1705, however, Francis Hauksbee began a series of experiments that resulted in some startling demonstrations. For many years it had been observed that a peculiar light was seen sometimes in the mercurial barometer, but Hauksbee and the other scientific investigators supposed the radiance to be due to the mercury in a vacuum, brought about, perhaps, by some agitation. That this light might have any connection with electricity did not, at first, occur to Hauksbee any more than it had to his predecessors. The problem that interested him was whether the vacuum in the tube of the barometer was essential to the light; and in experimenting to determine this, he invented his "mercurial fountain."

Having exhausted the air in a receiver containing some mercury, he found that by allowing air to rush through the mercury the metal became a jet thrown in all directions against the sides of the vessel, making a great, flaming shower, "like flashes of lightning," as he said. But it seemed to him that there was a difference between this light and the glow noted in the barometer. This was a bright light, whereas the barometer light was only a glow. Pondering over this, Hauksbee tried various experiments, revolving pieces of amber, flint, steel, and other substances in his exhausted air-pump receiver, with negative, or unsatisfactory, results. Finally, it occurred to him to revolve an exhausted gla.s.s tube itself. Mounting such a globe of gla.s.s on an axis so that it could be revolved rapidly by a belt running on a large wheel, he found that by holding his fingers against the whirling globe a purplish glow appeared, giving sufficient light so that coa.r.s.e print could be read, and the walls of a dark room sensibly lightened several feet away. As air was admitted to the globe the light gradually diminished, and it seemed to him that this diminished glow was very similar in appearance to the pale light seen in the mercurial barometer.

Could it be that it was the gla.s.s, and not the mercury, that caused it?

Going to a barometer he proceeded to rub the gla.s.s above the column of mercury over the vacuum, without disturbing the mercury, when, to his astonishment, the same faint light, to all appearances identical with the glow seen in the whirling globe, was produced.

Turning these demonstrations over in his mind, he recalled the well-known fact that rubbed gla.s.s attracted bits of paper, leaf-bra.s.s, and other light substances, and that this phenomenon was supposed to be electrical. This led him finally to determine the hitherto unsuspected fact, that the glow in the barometer was electrical as was also the glow seen in his whirling globe. Continuing his investigations, he soon discovered that solid gla.s.s rods when rubbed produced the same effects as the tube. By mere chance, happening to hold a rubbed tube to his cheek, he felt the effect of electricity upon the skin like "a number of fine, limber hairs," and this suggested to him that, since the mysterious manifestation was so plain, it could be made to show its effects upon various substances. Suspending some woollen threads over the whirling gla.s.s cylinder, he found that as soon as he touched the gla.s.s with his hands the threads, which were waved about by the wind of the revolution, suddenly straightened themselves in a peculiar manner, and stood in a radical position, pointing to the axis of the cylinder.

Encouraged by these successes, he continued his experiments with breathless expectancy, and soon made another important discovery, that of "induction," although the real significance of this discovery was not appreciated by him or, for that matter, by any one else for several generations following. This discovery was made by placing two revolving cylinders within an inch of each other, one with the air exhausted and the other unexhausted. Placing his hand on the unexhausted tube caused the light to appear not only upon it, but on the other tube as well.

A little later he discovered that it is not necessary to whirl the exhausted tube to produce this effect, but simply to place it in close proximity to the other whirling cylinder.

These demonstrations of Hauksbee attracted wide attention and gave an impetus to investigators in the field of electricity; but still no great advance was made for something like a quarter of a century. Possibly the energies of the scientists were exhausted for the moment in exploring the new fields thrown open to investigation by the colossal work of Newton.

THE EXPERIMENTS OF STEPHEN GRAY

In 1729 Stephen Gray (died in 1736), an eccentric and irascible old pensioner of the Charter House in London, undertook some investigations along lines similar to those of Hauksbee. While experimenting with a gla.s.s tube for producing electricity, as Hauksbee had done, he noticed that the corks with which he had stopped the ends of the tube to exclude the dust, seemed to attract bits of paper and leaf-bra.s.s as well as the gla.s.s itself. He surmised at once that this mysterious electricity, or "virtue," as it was called, might be transmitted through other substances as it seemed to be through gla.s.s.

"Having by me an ivory ball of about one and three-tenths of an inch in diameter," he writes, "with a hole through it, this I fixed upon a fir-stick about four inches long, thrusting the other end into the cork, and upon rubbing the tube found that the ball attracted and repelled the feather with more vigor than the cork had done, repeating its attractions and repulsions for many times together. I then fixed the ball on longer sticks, first upon one of eight inches, and afterwards upon one of twenty-four inches long, and found the effect the same. Then I made use of iron, and then bra.s.s wire, to fix the ball on, inserting the other end of the wire in the cork, as before, and found that the attraction was the same as when the fir-sticks were made use of, and that when the feather was held over against any part of the wire it was attracted by it; but though it was then nearer the tube, yet its attraction was not so strong as that of the ball. When the wire of two or three feet long was used, its vibrations, caused by the rubbing of the tube, made it somewhat troublesome to be managed. This put me to thinking whether, if the ball was hung by a pack-thread and suspended by a loop on the tube, the electricity would not be carried down the line to the ball; I found it to succeed accordingly; for upon suspending the ball on the tube by a pack-thread about three feet long, when the tube had been excited by rubbing, the ivory ball attracted and repelled the leaf-bra.s.s over which it was held as freely as it had done when it was suspended on sticks or wire, as did also a ball of cork, and another of lead that weighed one pound and a quarter."

Gray next attempted to determine what other bodies would attract the bits of paper, and for this purpose he tried coins, pieces of metal, and even a tea-kettle, "both empty and filled with hot or cold water"; but he found that the attractive power appeared to be the same regardless of the substance used.

"I next proceeded," he continues, "to try at what greater distances the electric virtues might be carried, and having by me a hollow walking-cane, which I suppose was part of a fishing-rod, two feet seven inches long, I cut the great end of it to fit into the bore of the tube, into which it went about five inches; then when the cane was put into the end of the tube, and this excited, the cane drew the leaf-bra.s.s to the height of more than two inches, as did also the ivory ball, when by a cork and stick it had been fixed to the end of the cane.... With several pieces of Spanish cane and fir-sticks I afterwards made a rod, which, together with the tube, was somewhat more than eighteen feet long, which was the greatest length I could conveniently use in my chamber, and found the attraction very nearly, if not altogether, as strong as when the ball was placed on the shorter rods."

This experiment exhausted the capacity of his small room, but on going to the country a little later he was able to continue his experiments.

"To a pole of eighteen feet there was tied a line of thirty-four feet in length, so that the pole and line together were fifty-two feet. With the pole and tube I stood in the balcony, the a.s.sistant below in the court, where he held the board with the leaf-bra.s.s on it. Then the tube being excited, as usual, the electric virtue pa.s.sed from the tube up the pole and down the line to the ivory ball, which attracted the leaf-bra.s.s, and as the ball pa.s.sed over it in its vibrations the leaf-bra.s.s would follow it till it was carried off the board."

Gray next attempted to send the electricity over a line suspended horizontally. To do this he suspended the pack-thread by pieces of string looped over nails driven into beams for that purpose. But when thus suspended he found that the ivory ball no longer excited the leaf-bra.s.s, and he guessed correctly that the explanation of this lay in the fact that "when the electric virtue came to the loop that was suspended on the beam it went up the same to the beam," none of it reaching the ball. As we shall see from what follows, however, Gray had not as yet determined that certain substances will conduct electricity while others will not. But by a lucky accident he made the discovery that silk, for example, was a poor conductor, and could be turned to account in insulating the conducting-cord.

A certain Mr. Wheler had become much interested in the old pensioner and his work, and, as a guest at the Wheler house, Gray had been repeating some of his former experiments with the fishing-rod, line, and ivory ball. He had finally exhausted the heights from which these experiments could be made by climbing to the clock-tower and exciting bits of leaf-bra.s.s on the ground below.