Galileo, that giant in physical science of the early seventeenth century, died in 1642. On Christmas day of the same year there was born in England another intellectual giant who was destined to carry forward the work of Copernicus, Kepler, and Galileo to a marvellous consummation through the discovery of the great unifying law in accordance with which the planetary motions are performed. We refer, of course, to the greatest of English physical scientists, Isaac Newton, the Shakespeare of the scientific world. Born thus before the middle of the seventeenth century, Newton lived beyond the first quarter of the eighteenth (1727). For the last forty years of that period his was the dominating scientific personality of the world. With full propriety that time has been spoken of as the "Age of Newton."
Yet the man who was to achieve such distinction gave no early premonition of future greatness. He was a sickly child from birth, and a boy of little seeming promise. He was an indifferent student, yet, on the other hand, he cared little for the common amusements of boyhood. He early exhibited, however, a taste for mechanical contrivances, and spent much time in devising windmills, water-clocks, sun-dials, and kites. While other boys were interested only in having kites that would fly, Newton—at least so the stories of a later time would have us understand—cared more for the investigation of the seeming principles involved, or for testing the best methods of attaching the strings, or the best materials to be used in construction.
Meanwhile the future philosopher was acquiring a taste for reading and study, delving into old volumes whenever he found an opportunity. These habits convinced his relatives that it was useless to attempt to make a farmer of the youth, as had been their intention. He was therefore sent back to school, and in the summer of 1661 he matriculated at Trinity College, Cambridge. Even at college Newton seems to have shown no unusual mental capacity, and in 1664, when examined for a scholarship by Dr. Barrow, that gentleman is said to have formed a poor opinion of the applicant. It is said that the knowledge of the estimate placed upon his abilities by his instructor piqued Newton, and led him to take up in earnest the mathematical studies in which he afterwards attained such distinction. The study of Euclid and Descartes's "Geometry" roused in him a latent interest in mathematics, and from that time forward his investigations were carried on with enthusiasm. In 1667 he was elected Fellow of Trinity College, taking the degree of M.A. the following spring.
It will thus appear that Newton's boyhood and early manhood were passed during that troublous time in British political annals which saw the overthrow of Charles I., the autocracy of Cromwell, and the eventual restoration of the Stuarts. His maturer years witnessed the overthrow of the last Stuart and the reign of the Dutchman, William of Orange. In his old age he saw the first of the Hanoverians mount the throne of England. Within a decade of his death such scientific path-finders as Cavendish, Black, and Priestley were born—men who lived on to the close of the eighteenth century. In a full sense, then, the age of Newton bridges the gap from that early time of scientific awakening under Kepler and Galileo to the time which we of the twentieth century think of as essentially modern.
THE COMPOSITION OF WHITE LIGHT
In December, 1672, Newton was elected a Fellow of the Royal Society, and at this meeting a paper describing his invention of the refracting telescope was read. A few days later he wrote to the secretary, making some inquiries as to the weekly meetings of the society, and intimating that he had an account of an interesting discovery that he wished to lay before the society. When this communication was made public, it proved to be an explanation of the discovery of the composition of white light. We have seen that the question as to the nature of color had commanded the attention of such investigators as Huygens, but that no very satisfactory solution of the question had been attained. Newton proved by demonstrative experiments that white light is composed of the blending of the rays of diverse colors, and that the color that we ascribe to any object is merely due to the fact that the object in question reflects rays of that color, absorbing the rest. That white light is really made up of many colors blended would seem incredible had not the experiments by which this composition is demonstrated become familiar to every one. The experiments were absolutely novel when Newton brought them forward, and his demonstration of the composition of light was one of the most striking expositions ever brought to the attention of the Royal Society. It is hardly necessary to add that, notwithstanding the conclusive character of Newton's work, his explanations did not for a long time meet with general acceptance.
Newton was led to his discovery by some experiments made with an ordinary glass prism applied to a hole in the shutter of a darkened room, the refracted rays of the sunlight being received upon the opposite wall and forming there the familiar spectrum. "It was a very pleasing diversion," he wrote, "to view the vivid and intense colors produced thereby; and after a time, applying myself to consider them very circumspectly, I became surprised to see them in varying form, which, according to the received laws of refraction, I expected should have been circular. They were terminated at the sides with straight lines, but at the ends the decay of light was so gradual that it was difficult to determine justly what was their figure, yet they seemed semicircular.
"Comparing the length of this colored spectrum with its breadth, I found it almost five times greater; a disproportion so extravagant that it excited me to a more than ordinary curiosity of examining from whence it might proceed. I could scarce think that the various thicknesses of the glass, or the termination with shadow or darkness, could have any influence on light to produce such an effect; yet I thought it not amiss, first, to examine those circumstances, and so tried what would happen by transmitting light through parts of the glass of divers thickness, or through holes in the window of divers bigness, or by setting the prism without so that the light might pass through it and be refracted before it was transmitted through the hole; but I found none of those circumstances material. The fashion of the colors was in all these cases the same.
"Then I suspected whether by any unevenness of the glass or other contingent irregularity these colors might be thus dilated. And to try this I took another prism like the former, and so placed it that the light, passing through them both, might be refracted contrary ways, and so by the latter returned into that course from which the former diverted it. For, by this means, I thought, the regular effects of the first prism would be destroyed by the second prism, but the irregular ones more augmented by the multiplicity of refractions. The event was that the light, which by the first prism was diffused into an oblong form, was by the second reduced into an orbicular one with as much regularity as when it did not all pass through them. So that, whatever was the cause of that length, 'twas not any contingent irregularity.
"I then proceeded to examine more critically what might be effected by the difference of the incidence of rays coming from divers parts of the sun; and to that end measured the several lines and angles belonging to the image. Its distance from the hole or prism was 22 feet; its utmost length 13 1/4 inches; its breadth 2 5/8; the diameter of the hole 1/4 of an inch; the angle which the rays, tending towards the middle of the image, made with those lines, in which they would have proceeded without refraction, was 44 degrees 56'; and the vertical angle of the prism, 63 degrees 12'. Also the refractions on both sides of the prism—that is, of the incident and emergent rays—were, as near as I could make them, equal, and consequently about 54 degrees 4'; and the rays fell perpendicularly upon the wall. Now, subducting the diameter of the hole from the length and breadth of the image, there remains 13 inches the length, and 2 3/8 the breadth, comprehended by those rays, which, passing through the centre of the said hole, which that breadth subtended, was about 31', answerable to the sun's diameter; but the angle which its length subtended was more than five such diameters, namely 2 degrees 49'.
"Having made these observations, I first computed from them the refractive power of the glass, and found it measured by the ratio of the sines 20 to 31. And then, by that ratio, I computed the refractions of two rays flowing from opposite parts of the sun's discus, so as to differ 31' in their obliquity of incidence, and found that the emergent rays should have comprehended an angle of 31', as they did, before they were incident.
"But because this computation was founded on the hypothesis of the proportionality of the sines of incidence and refraction, which though by my own experience I could not imagine to be so erroneous as to make that angle but 31', which in reality was 2 degrees 49', yet my curiosity caused me again to make my prism. And having placed it at my window, as before, I observed that by turning it a little about its axis to and fro, so as to vary its obliquity to the light more than an angle of 4 degrees or 5 degrees, the colors were not thereby sensibly translated from their place on the wall, and consequently by that variation of incidence the quantity of refraction was not sensibly varied. By this experiment, therefore, as well as by the former computation, it was evident that the difference of the incidence of rays flowing from divers parts of the sun could not make them after decussation diverge at a sensibly greater angle than that at which they before converged; which being, at most, but about 31' or 32', there still remained some other cause to be found out, from whence it could be 2 degrees 49'."
All this caused Newton to suspect that the rays, after their trajection through the prism, moved in curved rather than in straight lines, thus tending to be cast upon the wall at different places according to the amount of this curve. His suspicions were increased, also, by happening to recall that a tennis-ball sometimes describes such a curve when "cut" by a tennis-racket striking the ball obliquely.
"For a circular as well as a progressive motion being communicated to it by the stroke," he says, "its parts on that side where the motions conspire must press and beat the contiguous air more violently than on the other, and there excite a reluctancy and reaction of the air proportionately greater. And for the same reason, if the rays of light should possibly be globular bodies, and by their oblique passage out of one medium into another acquire a circulating motion, they ought to feel the greater resistance from the ambient ether on that side where the motions conspire, and thence be continually bowed to the other. But notwithstanding this plausible ground of suspicion, when I came to examine it I could observe no such curvity in them. And, besides (which was enough for my purpose), I observed that the difference 'twixt the length of the image and diameter of the hole through which the light was transmitted was proportionable to their distance.
"The gradual removal of these suspicions at length led me to the experimentum crucis, which was this: I took two boards, and, placing one of them close behind the prism at the window, so that the light must pass through a small hole, made in it for the purpose, and fall on the other board, which I placed at about twelve feet distance, having first made a small hole in it also, for some of the incident light to pass through. Then I placed another prism behind this second board, so that the light trajected through both the boards might pass through that also, and be again refracted before it arrived at the wall. This done, I took the first prism in my hands and turned it to and fro slowly about its axis, so much as to make the several parts of the image, cast on the second board, successively pass through the hole in it, that I might observe to what places on the wall the second prism would refract them. And I saw by the variation of these places that the light, tending to that end of the image towards which the refraction of the first prism was made, did in the second prism suffer a refraction considerably greater than the light tending to the other end. And so the true cause of the length of that image was detected to be no other than that LIGHT consists of RAYS DIFFERENTLY REFRANGIBLE, which, without any respect to a difference in their incidence, were, according to their degrees of refrangibility, transmitted towards divers parts of the wall."(1)
THE NATURE OF COLOR
Having thus proved the composition of light, Newton took up an exhaustive discussion as to colors, which cannot be entered into at length here. Some of his remarks on the subject of compound colors, however, may be stated in part. Newton's views are of particular interest in this connection, since, as we have already pointed out, the question as to what constituted color could not be agreed upon by the philosophers. Some held that color was an integral part of the substance; others maintained that it was simply a reflection from the surface; and no scientific explanation had been generally accepted. Newton concludes his paper as follows:
"I might add more instances of this nature, but I shall conclude with the general one that the colors of all natural bodies have no other origin than this, that they are variously qualified to reflect one sort of light in greater plenty than another. And this I have experimented in a dark room by illuminating those bodies with uncompounded light of divers colors. For by that means any body may be made to appear of any color. They have there no appropriate color, but ever appear of the color of the light cast upon them, but yet with this difference, that they are most brisk and vivid in the light of their own daylight color. Minium appeareth there of any color indifferently with which 'tis illustrated, but yet most luminous in red; and so Bise appeareth indifferently of any color with which 'tis illustrated, but yet most luminous in blue. And therefore Minium reflecteth rays of any color, but most copiously those indued with red; and consequently, when illustrated with daylight—that is, with all sorts of rays promiscuously blended—those qualified with red shall abound most in the reflected light, and by their prevalence cause it to appear of that color. And for the same reason, Bise, reflecting blue most copiously, shall appear blue by the excess of those rays in its reflected light; and the like of other bodies. And that this is the entire and adequate cause of their colors is manifest, because they have no power to change or alter the colors of any sort of rays incident apart, but put on all colors indifferently with which they are enlightened."(2)
This epoch-making paper aroused a storm of opposition. Some of Newton's opponents criticised his methods, others even doubted the truth of his experiments. There was one slight mistake in Newton's belief that all prisms would give a spectrum of exactly the same length, and it was some time before he corrected this error. Meanwhile he patiently met and answered the arguments of his opponents until he began to feel that patience was no longer a virtue. At one time he even went so far as to declare that, once he was "free of this business," he would renounce scientific research forever, at least in a public way. Fortunately for the world, however, he did not adhere to this determination, but went on to even greater discoveries—which, it may be added, involved still greater controversies.
In commenting on Newton's discovery of the composition of light, Voltaire said: "Sir Isaac Newton has demonstrated to the eye, by the bare assistance of a prism, that light is a composition of colored rays, which, being united, form white color. A single ray is by him divided into seven, which all fall upon a piece of linen or a sheet of white paper, in their order one above the other, and at equal distances. The first is red, the second orange, the third yellow, the fourth green, the fifth blue, the sixth indigo, the seventh a violet purple. Each of these rays transmitted afterwards by a hundred other prisms will never change the color it bears; in like manner as gold, when completely purged from its dross, will never change afterwards in the crucible."(3)
We come now to the story of what is by common consent the greatest of scientific achievements. The law of universal gravitation is the most far-reaching principle as yet discovered. It has application equally to the minutest particle of matter and to the most distant suns in the universe, yet it is amazing in its very simplicity. As usually phrased, the law is this: That every particle of matter in the universe attracts every other particle with a force that varies directly with the mass of the particles and inversely as the squares of their mutual distance. Newton did not vault at once to the full expression of this law, though he had formulated it fully before he gave the results of his investigations to the world. We have now to follow the steps by which he reached this culminating achievement.
At the very beginning we must understand that the idea of universal gravitation was not absolutely original with Newton. Away back in the old Greek days, as we have seen, Anaxagoras conceived and clearly expressed the idea that the force which holds the heavenly bodies in their orbits may be the same that operates upon substances at the surface of the earth. With Anaxagoras this was scarcely more than a guess. After his day the idea seems not to have been expressed by any one until the seventeenth century's awakening of science. Then the consideration of Kepler's Third Law of planetary motion suggested to many minds perhaps independently the probability that the force hitherto mentioned merely as centripetal, through the operation of which the planets are held in their orbits is a force varying inversely as the square of the distance from the sun. This idea had come to Robert Hooke, to Wren, and perhaps to Halley, as well as to Newton; but as yet no one had conceived a method by which the validity of the suggestion might be tested. It was claimed later on by Hooke that he had discovered a method demonstrating the truth of the theory of inverse squares, and after the full announcement of Newton's discovery a heated controversy was precipitated in which Hooke put forward his claims with accustomed acrimony. Hooke, however, never produced his demonstration, and it may well be doubted whether he had found a method which did more than vaguely suggest the law which the observations of Kepler had partially revealed. Newton's great merit lay not so much in conceiving the law of inverse squares as in the demonstration of the law. He was led to this demonstration through considering the orbital motion of the moon. According to the familiar story, which has become one of the classic myths of science, Newton was led to take up the problem through observing the fall of an apple. Voltaire is responsible for the story, which serves as well as another; its truth or falsity need not in the least concern us. Suffice it that through pondering on the familiar fact of terrestrial gravitation, Newton was led to question whether this force which operates so tangibly here at the earth's surface may not extend its influence out into the depths of space, so as to include, for example, the moon. Obviously some force pulls the moon constantly towards the earth; otherwise that body would fly off at a tangent and never return. May not this so-called centripetal force be identical with terrestrial gravitation? Such was Newton's query. Probably many another man since Anaxagoras had asked the same question, but assuredly Newton was the first man to find an answer.
The thought that suggested itself to Newton's mind was this: If we make a diagram illustrating the orbital course of the moon for any given period, say one minute, we shall find that the course of the moon departs from a straight line during that period by a measurable distance—that: is to say, the moon has been virtually pulled towards the earth by an amount that is represented by the difference between its actual position at the end of the minute under observation and the position it would occupy had its course been tangential, as, according to the first law of motion, it must have been had not some force deflected it towards the earth. Measuring the deflection in question—which is equivalent to the so-called versed sine of the arc traversed—we have a basis for determining the strength of the deflecting force. Newton constructed such a diagram, and, measuring the amount of the moon's departure from a tangential rectilinear course in one minute, determined this to be, by his calculation, thirteen feet. Obviously, then, the force acting upon the moon is one that would cause that body to fall towards the earth to the distance of thirteen feet in the first minute of its fall. Would such be the force of gravitation acting at the distance of the moon if the power of gravitation varies inversely as the square of the distance? That was the tangible form in which the problem presented itself to Newton. The mathematical solution of the problem was simple enough. It is based on a comparison of the moon's distance with the length of the earth's radius. On making this calculation, Newton found that the pull of gravitation—if that were really the force that controls the moon—gives that body a fall of slightly over fifteen feet in the first minute, instead of thirteen feet. Here was surely a suggestive approximation, yet, on the other band, the discrepancy seemed to be too great to warrant him in the supposition that he had found the true solution. He therefore dismissed the matter from his mind for the time being, nor did he return to it definitely for some years.
{illustration caption = DIAGRAM TO ILLUSTRATE NEWTON'S LAW OF GRAVITATION (E represents the earth and A the moon. Were the earth's pull on the moon to cease, the moon's inertia would cause it to take the tangential course, AB. On the other hand, were the moon's motion to be stopped for an instant, the moon would fall directly towards the earth, along the line AD. The moon's actual orbit, resulting from these component forces, is AC. Let AC represent the actual flight of the moon in one minute. Then BC, which is obviously equal to AD, represents the distance which the moon virtually falls towards the earth in one minute. Actual computation, based on measurements of the moon's orbit, showed this distance to be about fifteen feet. Another computation showed that this is the distance that the moon would fall towards the earth under the influence of gravity, on the supposition that the force of gravity decreases inversely with the square of the distance; the basis of comparison being furnished by falling bodies at the surface of the earth. Theory and observations thus coinciding, Newton was justified in declaring that the force that pulls the moon towards the earth and keeps it in its orbit, is the familiar force of gravity, and that this varies inversely as the square of the distance.)}
It was to appear in due time that Newton's hypothesis was perfectly valid and that his method of attempted demonstration was equally so. The difficulty was that the earth's proper dimensions were not at that time known. A wrong estimate of the earth's size vitiated all the other calculations involved, since the measurement of the moon's distance depends upon the observation of the parallax, which cannot lead to a correct computation unless the length of the earth's radius is accurately known. Newton's first calculation was made as early as 1666, and it was not until 1682 that his attention was called to a new and apparently accurate measurement of a degree of the earth's meridian made by the French astronomer Picard. The new measurement made a degree of the earth's surface 69.10 miles, instead of sixty miles.
Learning of this materially altered calculation as to the earth's size, Newton was led to take up again his problem of the falling moon. As he proceeded with his computation, it became more and more certain that this time the result was to harmonize with the observed facts. As the story goes, he was so completely overwhelmed with emotion that he was forced to ask a friend to complete the simple calculation. That story may well be true, for, simple though the computation was, its result was perhaps the most wonderful demonstration hitherto achieved in the entire field of science. Now at last it was known that the force of gravitation operates at the distance of the moon, and holds that body in its elliptical orbit, and it required but a slight effort of the imagination to assume that the force which operates through such a reach of space extends its influence yet more widely. That such is really the case was demonstrated presently through calculations as to the moons of Jupiter and by similar computations regarding the orbital motions of the various planets. All results harmonizing, Newton was justified in reaching the conclusion that gravitation is a universal property of matter. It remained, as we shall see, for nineteenth-century scientists to prove that the same force actually operates upon the stars, though it should be added that this demonstration merely fortified a belief that had already found full acceptance.
Having thus epitomized Newton's discovery, we must now take up the steps of his progress somewhat in detail, and state his theories and their demonstration in his own words. Proposition IV., theorem 4, of his Principia is as follows:
"That the moon gravitates towards the earth and by the force of gravity is continually drawn off from a rectilinear motion and retained in its orbit.
"The mean distance of the moon from the earth, in the syzygies in semi-diameters of the earth, is, according to Ptolemy and most astronomers, 59; according to Vendelin and Huygens, 60; to Copernicus, 60 1/3; to Street, 60 2/3; and to Tycho, 56 1/2. But Tycho, and all that follow his tables of refractions, making the refractions of the sun and moon (altogether against the nature of light) to exceed the refractions of the fixed stars, and that by four or five minutes NEAR THE HORIZON, did thereby increase the moon's HORIZONTAL parallax by a like number of minutes, that is, by a twelfth or fifteenth part of the whole parallax. Correct this error and the distance will become about 60 1/2 semi-diameters of the earth, near to what others have assigned. Let us assume the mean distance of 60 diameters in the syzygies; and suppose one revolution of the moon, in respect to the fixed stars, to be completed in 27d. 7h. 43', as astronomers have determined; and the circumference of the earth to amount to 123,249,600 Paris feet, as the French have found by mensuration. And now, if we imagine the moon, deprived of all motion, to be let go, so as to descend towards the earth with the impulse of all that force by which (by Cor. Prop. iii.) it is retained in its orb, it will in the space of one minute of time describe in its fall 15 1/12 Paris feet. For the versed sine of that arc which the moon, in the space of one minute of time, would by its mean motion describe at the distance of sixty semi-diameters of the earth, is nearly 15 1/12 Paris feet, or more accurately 15 feet, 1 inch, 1 line 4/9. Wherefore, since that force, in approaching the earth, increases in the reciprocal-duplicate proportion of the distance, and upon that account, at the surface of the earth, is 60 x 60 times greater than at the moon, a body in our regions, falling with that force, ought in the space of one minute of time to describe 60 x 60 x 15 1/12 Paris feet; and in the space of one second of time, to describe 15 1/12 of those feet, or more accurately, 15 feet, 1 inch, 1 line 4/9. And with this very force we actually find that bodies here upon earth do really descend; for a pendulum oscillating seconds in the latitude of Paris will be 3 Paris feet, and 8 lines 1/2 in length, as Mr. Huygens has observed. And the space which a heavy body describes by falling in one second of time is to half the length of the pendulum in the duplicate ratio of the circumference of a circle to its diameter (as Mr. Huygens has also shown), and is therefore 15 Paris feet, 1 inch, 1 line 4/9. And therefore the force by which the moon is retained in its orbit is that very same force which we commonly call gravity; for, were gravity another force different from that, then bodies descending to the earth with the joint impulse of both forces would fall with a double velocity, and in the space of one second of time would describe 30 1/6 Paris feet; altogether against experience."(1)
All this is beautifully clear, and its validity has never in recent generations been called in question; yet it should be explained that the argument does not amount to an actually indisputable demonstration. It is at least possible that the coincidence between the observed and computed motion of the moon may be a mere coincidence and nothing more. This probability, however, is so remote that Newton is fully justified in disregarding it, and, as has been said, all subsequent generations have accepted the computation as demonstrative.
Let us produce now Newton's further computations as to the other planetary bodies, passing on to his final conclusion that gravity is a universal force.
"That the circumjovial planets gravitate towards Jupiter; the circumsaturnal towards Saturn; the circumsolar towards the sun; and by the forces of their gravity are drawn off from rectilinear motions, and retained in curvilinear orbits.
"For the revolutions of the circumjovial planets about Jupiter, of the circumsaturnal about Saturn, and of Mercury and Venus and the other circumsolar planets about the sun, are appearances of the same sort with the revolution of the moon about the earth; and therefore, by Rule ii., must be owing to the same sort of causes; especially since it has been demonstrated that the forces upon which those revolutions depend tend to the centres of Jupiter, of Saturn, and of the sun; and that those forces, in receding from Jupiter, from Saturn, and from the sun, decrease in the same proportion, and according to the same law, as the force of gravity does in receding from the earth.
"COR. 1.—There is, therefore, a power of gravity tending to all the planets; for doubtless Venus, Mercury, and the rest are bodies of the same sort with Jupiter and Saturn. And since all attraction (by Law iii.) is mutual, Jupiter will therefore gravitate towards all his own satellites, Saturn towards his, the earth towards the moon, and the sun towards all the primary planets.
"COR. 2.—The force of gravity which tends to any one planet is reciprocally as the square of the distance of places from the planet's centre.
"COR. 3.—All the planets do mutually gravitate towards one another, by Cor. 1 and 2, and hence it is that Jupiter and Saturn, when near their conjunction, by their mutual attractions sensibly disturb each other's motions. So the sun disturbs the motions of the moon; and both sun and moon disturb our sea, as we shall hereafter explain.
"The force which retains the celestial bodies in their orbits has been hitherto called centripetal force; but it being now made plain that it can be no other than a gravitating force, we shall hereafter call it gravity. For the cause of the centripetal force which retains the moon in its orbit will extend itself to all the planets by Rules i., ii., and iii.
"That all bodies gravitate towards every planet; and that the weights of the bodies towards any the same planet, at equal distances from the centre of the planet, are proportional to the quantities of matter which they severally contain.
"It has been now a long time observed by others that all sorts of heavy bodies (allowance being made for the inability of retardation which they suffer from a small power of resistance in the air) descend to the earth FROM EQUAL HEIGHTS in equal times; and that equality of times we may distinguish to a great accuracy by help of pendulums. I tried the thing in gold, silver, lead, glass, sand, common salt, wood, water, and wheat. I provided two wooden boxes, round and equal: I filled the one with wood, and suspended an equal weight of gold (as exactly as I could) in the centre of oscillation of the other. The boxes hanging by eleven feet, made a couple of pendulums exactly equal in weight and figure, and equally receiving the resistance of the air. And, placing the one by the other, I observed them to play together forward and backward, for a long time, with equal vibrations. And therefore the quantity of matter in gold was to the quantity of matter in the wood as the action of the motive force (or vis motrix) upon all the gold to the action of the same upon all the wood—that is, as the weight of the one to the weight of the other: and the like happened in the other bodies. By these experiments, in bodies of the same weight, I could manifestly have discovered a difference of matter less than the thousandth part of the whole, had any such been. But, without all doubt, the nature of gravity towards the planets is the same as towards the earth. For, should we imagine our terrestrial bodies removed to the orb of the moon, and there, together with the moon, deprived of all motion, to be let go, so as to fall together towards the earth, it is certain, from what we have demonstrated before, that, in equal times, they would describe equal spaces with the moon, and of consequence are to the moon, in quantity and matter, as their weights to its weight.
"Moreover, since the satellites of Jupiter perform their revolutions in times which observe the sesquiplicate proportion of their distances from Jupiter's centre, their accelerative gravities towards Jupiter will be reciprocally as the square of their distances from Jupiter's centre—that is, equal, at equal distances. And, therefore, these satellites, if supposed to fall TOWARDS JUPITER from equal heights, would describe equal spaces in equal times, in like manner as heavy bodies do on our earth. And, by the same argument, if the circumsolar planets were supposed to be let fall at equal distances from the sun, they would, in their descent towards the sun, describe equal spaces in equal times. But forces which equally accelerate unequal bodies must be as those bodies—that is to say, the weights of the planets (TOWARDS THE SUN) must be as their quantities of matter. Further, that the weights of Jupiter and his satellites towards the sun are proportional to the several quantities of their matter, appears from the exceedingly regular motions of the satellites. For if some of these bodies were more strongly attracted to the sun in proportion to their quantity of matter than others, the motions of the satellites would be disturbed by that inequality of attraction. If at equal distances from the sun any satellite, in proportion to the quantity of its matter, did gravitate towards the sun with a force greater than Jupiter in proportion to his, according to any given proportion, suppose d to e; then the distance between the centres of the sun and of the satellite's orbit would be always greater than the distance between the centres of the sun and of Jupiter nearly in the subduplicate of that proportion: as by some computations I have found. And if the satellite did gravitate towards the sun with a force, lesser in the proportion of e to d, the distance of the centre of the satellite's orb from the sun would be less than the distance of the centre of Jupiter from the sun in the subduplicate of the same proportion. Therefore, if at equal distances from the sun, the accelerative gravity of any satellite towards the sun were greater or less than the accelerative gravity of Jupiter towards the sun by one-one-thousandth part of the whole gravity, the distance of the centre of the satellite's orbit from the sun would be greater or less than the distance of Jupiter from the sun by one one-two-thousandth part of the whole distance—that is, by a fifth part of the distance of the utmost satellite from the centre of Jupiter; an eccentricity of the orbit which would be very sensible. But the orbits of the satellites are concentric to Jupiter, and therefore the accelerative gravities of Jupiter and of all its satellites towards the sun, at equal distances from the sun, are as their several quantities of matter; and the weights of the moon and of the earth towards the sun are either none, or accurately proportional to the masses of matter which they contain.
"COR. 5.—The power of gravity is of a different nature from the power of magnetism; for the magnetic attraction is not as the matter attracted. Some bodies are attracted more by the magnet; others less; most bodies not at all. The power of magnetism in one and the same body may be increased and diminished; and is sometimes far stronger, for the quantity of matter, than the power of gravity; and in receding from the magnet decreases not in the duplicate, but almost in the triplicate proportion of the distance, as nearly as I could judge from some rude observations.
"That there is a power of gravity tending to all bodies, proportional to the several quantities 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 assigned 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 quantity of the surfaces of the particles upon which it acts (as mechanical causes used to do), but according to the quantity 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 asserted 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 pronounced this epitaph:
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 accumulated 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 assistance 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 sextant, as the improved instrument is now called, invented by John Hadley in 1731, and independently by Thomas Godfrey, a poor glazier of Philadelphia, in 1730. Godfrey'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 sextant, 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 sextant 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 compass, a cross-staff, or an astrolabe, a table of the sun's declination and a correction for the altitude 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 illustrations 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.