V Mmr2
whereVis a constant, called the gravitation constant, to be determined by experiment.
If this is the centripetal force pulling a planet or satellite in, it must be equal to the centrifugal force of this latter, viz. (see above).
4π2mrT2
Equate the two together, and at once we get
r3=VM ;T24π2
or, in words, the cube of the distance divided by the square of the periodic time for every planet or satellite of the system under consideration, will be constant and proportional to the mass of the central body.
This is Kepler's third law, with a notable addition. It is stated above for circular motion only, so as to avoid geometrical difficulties, but even so it is very instructive. The reason of the proportion betweenr3andT2is at once manifest; and as soon as the constantVbecame known,the mass of the central body, the sun in the case of a planet, the earth in the case of the moon, Jupiter in the case of his satellites, was at once determined.
Newton's reasoning at this time might, however, be better displayed perhaps by altering the order of the steps a little, as thus:—
The centrifugal force of a body is proportional tor3/T2, but by Kepler's third lawr3/T2is constant for all the planets, reckoningrfrom the sun. Hence the centripetal force needed to hold in all the planets will be a single force emanating from the sun and varying inversely with the square of the distance from that body.
Such a force is at once necessary and sufficient. Such a force would explain the motion of the planets.
But then all this proceeds on a wrong assumption—thatthe planetary motion is circular. Will it hold for elliptic orbits? Will an inverse square law of force keep a body moving in an elliptic orbit about the sun in one focus? This is a far more difficult question. Newton solved it, but I do not believe that even he could have solved it, except that he had at his disposal two mathematical engines of great power—the Cartesian method of treating geometry, and his own method of Fluxions. One can explain the elliptic motion now mathematically, but hardly otherwise; and I must be content to state that the double fact is true—viz., that an inverse square law will move the body in an ellipse or other conic section with the sun in one focus, and that if a body so moves itmustbe acted on by an inverse square law.
Fig. 59.Fig. 59.
This then is the meaning of the first and third laws of Kepler. What about the second? What is the meaning of the equable description of areas? Well, that rigorously proves that a planet is acted on by a force directed to the centre about which the rate of description of areas is equable. It proves, in fact, that the sun is the attracting body, and that no other force acts.
For first of all if the first law of motion is obeyed,i.e.if no force acts, and if the path be equally subdivided to represent equal times, and straight lines be drawn from the divisions to any point whatever, all these areas thus enclosed will be equal, because they are triangles on equal base and of the same height (Euclid, I). SeeFig. 59;Sbeing any point whatever, andA,B,C, successive positions of a body.Now at each of the successive instants let the body receive a sudden blow in the direction of that same pointS, sufficient to carry it fromAtoDin the same time as it would have got toBif left alone. The result will be that there will be a compromise, and it will really arrive atP, travelling along the diagonal of the parallelogramAP. The area its radius vector sweeps out is thereforeSAP, instead of what it would have been,SAB. But then these two areas are equal, because they are triangles on the same baseAS, and between the same parallelsBP,AS; for by the parallelogram lawBPis parallel toAD. Hence the area that would have been described is described, and as all the areas were equal in the case of no force, they remain equal when the body receives a blow at the end of every equal interval of time,providedthat every blow is actually directed toS, the point to which radii vectores are drawn.
For first of all if the first law of motion is obeyed,i.e.if no force acts, and if the path be equally subdivided to represent equal times, and straight lines be drawn from the divisions to any point whatever, all these areas thus enclosed will be equal, because they are triangles on equal base and of the same height (Euclid, I). SeeFig. 59;Sbeing any point whatever, andA,B,C, successive positions of a body.
Now at each of the successive instants let the body receive a sudden blow in the direction of that same pointS, sufficient to carry it fromAtoDin the same time as it would have got toBif left alone. The result will be that there will be a compromise, and it will really arrive atP, travelling along the diagonal of the parallelogramAP. The area its radius vector sweeps out is thereforeSAP, instead of what it would have been,SAB. But then these two areas are equal, because they are triangles on the same baseAS, and between the same parallelsBP,AS; for by the parallelogram lawBPis parallel toAD. Hence the area that would have been described is described, and as all the areas were equal in the case of no force, they remain equal when the body receives a blow at the end of every equal interval of time,providedthat every blow is actually directed toS, the point to which radii vectores are drawn.
Fig. 60.Fig. 60.
Fig. 61.Fig. 61.
It is instructive to see that it does not hold if the blow is any otherwise directed; for instance, as inFig. 61, when the blow is alongAE, the body finds itself atPat the end of the secondinterval, but the areaSAPis by no means equal toSAB, and therefore not equal toSOA, the area swept out in the first interval.In order to modifyFig. 60so as to represent continuous motion and steady forces, we have to take the sides of the polygonOAPQ, &c., very numerous and very small; in the limit, infinitely numerous and infinitely small. The path then becomes a curve, and the series of blows becomes a steady force directed towardsS. About whatever point therefore the rate of description of areas is uniform, that point and no other must be the centre of all the force there is. If there be no force, as inFig. 59, well and good, but if there be any force however small not directed towardsS, then the rate of description of areas aboutScannot be uniform. Kepler, however, says that the rate of description of areas of each planet about the sun is, by Tycho's observations, uniform; hence the sun is the centre of all the force that acts on them, and there is no other force, not even friction. That is the moral of Kepler's second law.We may also see from it that gravity does not travel like light, so as to take time on its journey from sun to planet; for, if it did, there would be a sort of aberration, and the force on its arrival could no longer be accurately directed to the centre of the sun. (SeeNature, vol. xlvi., p. 497.) It is a matter for accuracy of observation, therefore, to decide whether the minutest trace of such deviation can be detected,i.e.within what limits of accuracy Kepler's second law is now known to be obeyed.I will content myself by saying that the limits are extremely narrow. [Reference may be made also top. 208.]
It is instructive to see that it does not hold if the blow is any otherwise directed; for instance, as inFig. 61, when the blow is alongAE, the body finds itself atPat the end of the secondinterval, but the areaSAPis by no means equal toSAB, and therefore not equal toSOA, the area swept out in the first interval.
In order to modifyFig. 60so as to represent continuous motion and steady forces, we have to take the sides of the polygonOAPQ, &c., very numerous and very small; in the limit, infinitely numerous and infinitely small. The path then becomes a curve, and the series of blows becomes a steady force directed towardsS. About whatever point therefore the rate of description of areas is uniform, that point and no other must be the centre of all the force there is. If there be no force, as inFig. 59, well and good, but if there be any force however small not directed towardsS, then the rate of description of areas aboutScannot be uniform. Kepler, however, says that the rate of description of areas of each planet about the sun is, by Tycho's observations, uniform; hence the sun is the centre of all the force that acts on them, and there is no other force, not even friction. That is the moral of Kepler's second law.
We may also see from it that gravity does not travel like light, so as to take time on its journey from sun to planet; for, if it did, there would be a sort of aberration, and the force on its arrival could no longer be accurately directed to the centre of the sun. (SeeNature, vol. xlvi., p. 497.) It is a matter for accuracy of observation, therefore, to decide whether the minutest trace of such deviation can be detected,i.e.within what limits of accuracy Kepler's second law is now known to be obeyed.
I will content myself by saying that the limits are extremely narrow. [Reference may be made also top. 208.]
Thus then it became clear to Newton that the whole solar system depended on a central force emanating from the sun, and varying inversely with the square of the distance from him: for by that hypothesis all the laws of Kepler concerning these motions were completely accounted for; and, in fact, the laws necessitated the hypothesis and established it as a theory.
Similarly the satellites of Jupiter were controlled by a force emanating from Jupiter and varying according to the same law. And again our moon must be controlled by a force from the earth, decreasing with the distance according to the same law.
Grant this hypothetical attracting force pulling theplanets towards the sun, pulling the moon towards the earth, and the whole mechanism of the solar system is beautifully explained.
If only one could be sure there was such a force! It was one thing to calculate out what the effects of such a force would be: it was another to be able to put one's finger upon it and say, this is the force that actually exists and is known to exist. We must picture him meditating in his garden on this want—an attractive force towards the earth.
If only such an attractive force pulling down bodies to the earth existed. An apple falls from a tree. Why, it does exist! There is gravitation, common gravity that makes bodies fall and gives them their weight.
Wanted, a force tending towards the centre of the earth. It is to hand!
It is common old gravity that had been known so long, that was perfectly familiar to Galileo, and probably to Archimedes. Gravity that regulates the motion of projectiles. Why should it only pull stones and apples? Why should it not reach as high as the moon? Why should it not be the gravitation of the sun that is the central force acting on all the planets?
Surely the secret of the universe is discovered! But, wait a bit; is it discovered? Is this force of gravity sufficient for the purpose? It must vary inversely with the square of the distance from the centre of the earth. How far is the moon away? Sixty earth's radii. Hence the force of gravity at the moon's distance can only be1⁄3600of what it is on the earth's surface. So, instead of pulling it 16 ft. per second, it should pull it16⁄3600ft. per second, or 16 ft. a minute.[17]How can one decide whether such a force is able to pull the moon the actual amount required? To Newton this would seem only like a sum in arithmetic. Out with a pencil and paper and reckon how much the moon falls toward the earth in every second ofits motion. Is it16⁄3600? That is what it ought to be: but is it? The size of the earth comes into the calculation. Sixty miles make a degree, 360 degrees a circumference. This gives as the earth's diameter 6,873 miles; work it out.
The answer is not 16 feet a minute, it is 13·9 feet.
Surely a mistake of calculation?
No, it is no mistake: there is something wrong in the theory, gravity is too strong.
Instead of falling toward the earth 5⅓ hundredths of an inch every second, as it would under gravity, the moon only falls 4⅔ hundredths of an inch per second.
With such a discovery in his grasp at the age of twenty-three he is disappointed—the figures do not agree, and he cannot make them agree. Either gravity is not the force in action, or else something interferes with it. Possibly, gravity does part of the work, and the vortices of Descartes interfere with it.
He must abandon the fascinating idea for the time. In his own words, "he laid aside at that time any further thought of the matter."
So far as is known, he never mentioned his disappointment to a soul. He might, perhaps, if he had been at Cambridge, but he was a shy and solitary youth, and just as likely he might not. Up in Lincolnshire, in the seventeenth century, who was there for him to consult?
True, he might have rushed into premature publication, after our nineteenth century fashion, but that was not his method. Publication never seemed to have occurred to him.
His reticence now is noteworthy, but later on it is perfectly astonishing. He is so absorbed in making discoveries that he actually has to be reminded to tell any one about them, and some one else always has to see to the printing and publishing for him.
I have entered thus fully into what I conjecture to be the stages of this early discovery of the law of gravitation, as applicable to the heavenly bodies, because it is frequently and commonly misunderstood. It is sometimes thought that he discovered the force of gravity; I hope I have made it clear that he did no such thing. Every educated man long before his time, if asked why bodies fell, would reply just as glibly as they do now, "Because the earth attracts them," or "because of the force of gravity."
His discovery was that the motions of the solar system were due to the action of a central force, directed to the body at the centre of the system, and varying inversely with the square of the distance from it. This discovery was based upon Kepler's laws, and was clear and certain. It might have been published had he so chosen.
But he did not like hypothetical and unknown forces; he tried to see whether the known force of gravity would serve. This discovery at that time he failed to make, owing to a wrong numerical datum. The size of the earth he only knew from the common doctrine of sailors that 60 miles make a degree; and that threw him out. Instead of falling 16 feet a minute, as it ought under gravity, it only fell 13·9 feet, so he abandoned the idea. We do not find that he returned to it for sixteen years.
Weleft Newton at the age of twenty-three on the verge of discovering the mechanism of the solar system, deterred therefrom only by an error in the then imagined size of the earth. He had proved from Kepler's laws that a centripetal force directed to the sun, and varying as the inverse square of the distance from that body, would account for the observed planetary motions, and that a similar force directed to the earth would account for the lunar motion; and it had struck him that this force might be the very same as the familiar force of gravitation which gave to bodies their weight: but in attempting a numerical verification of this idea in the case of the moon he was led by the then received notion that sixty miles made a degree on the earth's surface into an erroneous estimate of the size of the moon's orbit. Being thus baffled in obtaining such verification, he laid the matter aside for a time.
The anecdote of the apple we learn from Voltaire, who had it from Newton's favourite niece, who with her husband lived and kept house for him all his later life. It is very like one of those anecdotes which are easily invented and believed in, and very often turn out on scrutiny to have no foundation. Fortunately this anecdote is well authenticated, and moreover is intrinsically probable; I say fortunately, because it is always painful to have to give up these child-learnt anecdotes, like Alfred and the cakesand so on. This anecdote of the apple we need not resign. The tree was blown down in 1820 and part of its wood is preserved.
I have mentioned Voltaire in connection with Newton's philosophy. This acute critic at a later stage did a good deal to popularise it throughout Europe and to overturn that of his own countryman Descartes. Cambridge rapidly became Newtonian, but Oxford remained Cartesian for fifty years or more. It is curious what little hold science and mathematics have ever secured in the older and more ecclesiastical University. The pride of possessing Newton has however no doubt been the main stimulus to the special pursuits of Cambridge.
He now began to turn his attention to optics, and, as was usual with him, his whole mind became absorbed in this subject as if nothing else had ever occupied him. His cash-book for this time has been discovered, and the entries show that he is buying prisms and lenses and polishing powder at the beginning of 1667. He was anxious to improve telescopes by making more perfect lenses than had ever been used before. Accordingly he calculated out their proper curves, just as Descartes had also done, and then proceeded to grind them as near as he could to those figures. But the images did not please him; they were always blurred and rather indistinct.
At length, it struck him that perhaps it was not the lenses but the light which was at fault. Perhaps light was so composed that itcouldnot be focused accurately to a sharp and definite point. Perhaps the law of refraction was not quite accurate, but only an approximation. So he bought a prism to try the law. He let in sunlight through a small round hole in a window shutter, inserted the prism in the light, and received the deflected beam on a white screen; turning the prism about till it was deviated as little as possible. The patch on the screen was not a round disk, as it would have been without the prism, but was an elongatedoval and was coloured at its extremities. Evidently refraction was not a simple geometrical deflection of a ray, there was a spreading out as well.
Fig. 63.Fig. 63.—A prism not onlydeviatesa beam of sunlight, but also spreads it out ordispersesit.
Why did the image thus spread out? If it were due to irregularities in the glass a second prism should rather increase them, but a second prism when held in appropriate position was able to neutralise the dispersion and to reproduce the simple round white spot without deviation. Evidently the spreading out of the beam was connected in some definite way with its refraction. Could it be that the light particles after passing through the prism travelled in variously curved lines, as spinning racquet balls do? To examine this he measured the length of the oval patch when the screen was at different distances from the prism, and found that the two things were directly proportional to each other. Doubling the distance of the screen doubled the length of the patch. Hence the rays travelled in straight lines from the prism, and the spreading out was due to something that occurred within its substance. Could it be that white light was compound, was a mixture of several constituents, and that its different constituents were differently bent? No sooner thought than tried. Pierce the screen to let one ofthe constituents through and interpose a second prism in its path. If the spreading out depended on the prism only it should spread out just as much as before, but if it depended on the complex character of white light, this isolated simple constituent should be able to spread out no more. It did not spread out any more: a prism had no more dispersive power over it; it was deflected by the appropriate amount, but it was not analysed into constituents. It differed from sunlight in being simple. With many ingenious and beautifully simple experiments, which are quoted in full in several books on optics, he clinched the argument and established his discovery. White light was not simple but compound. It could be sorted out by a prism into an infinite number of constituent parts which were differently refracted, and the most striking of which Newton named violet, indigo, blue, green, yellow, orange, and red.
Fig. 64.Fig. 64.—A single constituent of white light, obtained by the use of perforated screens is capable of no more dispersion.
At once the true nature of colour became manifest. Colour resided not in the coloured object as had till now been thought, but in the light which illuminated it. Red glass for instance adds nothing to sunlight. The light does not get dyed red by passing through the glass; all that the red glass does is to stop and absorb a large part of the sunlight; it is opaque to the larger portion, but it is transparent to that particular portion which affects our eyes with the sensation of red. The prism acts like a sieve sorting outthe different kinds of light. Coloured media act like filters, stopping certain kinds but allowing the rest to go through. Leonardo's and all the ancient doctrines of colour had been singularly wrong; colour is not in the object but in the light.
Goethe, in hisFarbenlehre, endeavoured to controvert Newton, and to reinstate something more like the old views; but his failure was complete.
Refraction analysed out the various constituents of white light and displayed them in the form of a series of overlapping images of the aperture, each of a different colour; this series of images we call a spectrum, and the operation we now call spectrum analysis. The reason of the defect of lenses was now plain: it was not so much a defect of the lens as a defect of light. A lens acts by refraction and brings rays to a focus. If light be simple it acts well, but if ordinary white light fall upon a lens, its different constituents have different foci; every bright object is fringed with colour, and nothing like a clear image can be obtained.
Fig. 65.Fig. 65.—Showing the boundary rays of a parallel beam passing through a lens.
A parallel beam passing through a lens becomes conical; but instead of a single cone it is a sheaf or nest of cones, all having the edge of the lens as base, but each having a different vertex. The violet cone is innermost, near the lens, the red cone outermost, while the others lie between. Beyond the crossing point or focus the order of cones is reversed, as the above figure shows. Only the two marginal rays of the beam are depicted.
If a screen be held anywhere nearer the lens than theplace marked 1 there will be a whitish centre to the patch of light and a red and orange fringe or border. Held anywhere beyond the region 2, the border of the patch will be blue and violet. Held about 3 the colour will be less marked than elsewhere, but nowhere can it be got rid of. Each point of an object will be represented in the image not by a point but by a coloured patch: a fact which amply explains the observed blurring and indistinctness.
Newton measured and calculated the distance between the violet and red foci—VR in the diagram—and showed that it was1⁄50th the diameter of the lens. To overcome this difficulty (called chromatic aberration) telescope glasses were made small and of very long focus: some of them so long that they had no tube, all of them egregiously cumbrous. Yet it was with such instruments that all the early discoveries were made. With such an instrument, for instance, Huyghens discovered the real shape of Saturn's ring.
The defects of refractors seemed irremediable, being founded in the nature of light itself. So he gave up his "glass works"; and proceeded to think of reflexion from metal specula. A concave mirror forms an image just as a lens does, but since it does so without refraction or transmission through any substance, there is no accompanying dispersion or chromatic aberration.
The first reflecting telescope he made was 1 in. diameter and 6 in. long, and magnified forty times. It acted as well as a three or four feet refractor of that day, and showed Jupiter's moons. So he made a larger one, now in the library of the Royal Society, London, with an inscription:
"The first reflecting telescope, invented by Sir Isaac Newton, and made with his own hands."
This has been the parent of most of the gigantic telescopes of the present day. Fifty years elapsed before it was much improved on, and then, first by Hadley and afterwards by Herschel and others, large and good reflectors were constructed.
The largest telescope ever made, that of Lord Rosse, is a Newtonian reflector, fifty feet long, six feet diameter, with a mirror weighing four tons. The sextant, as used by navigators, was also invented by Newton.
The year after the plague, in 1667, Newton returned to Trinity College, and there continued his experiments on optics. It is specially to be noted that at this time, at the age of twenty-four, Newton had laid the foundations of all his greatest discoveries:—
Fig. 66.Fig. 66.—Newton's telescope.
The Theory of Fluxions; or, the Differential Calculus.
The Law of Gravitation; or, the complete theory of astronomy.
The compound nature of white light; or, the beginning of Spectrum Analysis.
Fig. 67.Fig. 67.—The sextant, as now made.
His later life was to be occupied in working these incipient discoveries out. But the most remarkable thing is that no one knew about any one of them. However, he was known as an accomplished young mathematician, and was made a fellow of his college. You remember that he had a friend there in the person of Dr. Isaac Barrow, first Lucasian Professor of Mathematics in the University. It happened, about 1669, that a mathematical discovery of some interest was being much discussed, and Dr. Barrow happened to mention it to Newton, who said yes, he had worked out that and a few other similar things some time ago. He accordingly went and fetched some papers to Dr. Barrow, who forwarded them to other distinguished mathematicians, and it thus appeared that Newton had discovered theorems much more general than this special case that was exciting so much interest. Dr. Barrow, being anxious to devote his time more particularly to theology, resigned his chair the same year in favour of Newton, who wasaccordingly elected to the Lucasian Professorship, which he held for thirty years. This chair is now the most famous in the University, and it is commonly referred to as the chair of Newton.
Still, however, his method of fluxions was unknown, and still he did not publish it. He lectured first on optics, giving an account of his experiments. His lectures were afterwards published both in Latin and English, and are highly valued to this day.
The fame of his mathematical genius came to the ears of the Royal Society, and a motion was made to get him elected a fellow of that body. The Royal Society, the oldest and most famous of all scientific societies with a continuous existence, took its origin in some private meetings, got up in London by the Hon. Robert Boyle and a few scientific friends, during all the trouble of the Commonwealth.
After the restoration, Charles II. in 1662 incorporated it under Royal Charter; among the original members being Boyle, Hooke, Christopher Wren, and other less famous names. Boyle was a great experimenter, a worthy follower of Dr. Gilbert. Hooke began as his assistant, but being of a most extraordinary ingenuity he rapidly rose so as to exceed his master in importance. Fate has been a little unkind to Hooke in placing him so near to Newton; had he lived in an ordinary age he would undoubtedly have shone as a star of the first magnitude. With great ingenuity, remarkable scientific insight, and consummate experimental skill, he stands in many respects almost on a level with Galileo. But it is difficult to see stars even of the first magnitude when the sun is up, and thus it happens that the name and fame of this brilliant man are almost lost in the blaze of Newton. Of Christopher Wren I need not say much. He is well known as an architect, but he was a most accomplished all-round man, and had a considerable taste and faculty for science.
These then were the luminaries of the Royal Society at the time we are speaking of, and to them Newton's first scientific publication was submitted. He communicated to them an account of his reflecting telescope, and presented them with the instrument.
Their reception of it surprised him; they were greatly delighted with it, and wrote specially thanking him for the communication, and assuring him that all right should be done him in the matter of the invention. The Bishop of Salisbury (Bishop Burnet) proposed him for election as a fellow, and elected he was.
In reply, he expressed his surprise at the value they set on the telescope, and offered, if they cared for it, to send them an account of a discovery which he doubts not will prove much more grateful than the communication of that instrument, "being in my judgment the oddest, if not the most considerable detection that has recently been made into the operations of Nature."
So he tells them about his optical researches and his discovery of the nature of white light, writing them a series of papers which were long afterwards incorporated and published as hisOptics. A magnificent work, which of itself suffices to place its author in the first rank of the world's men of science.
The nature of white light, the true doctrine of colour, and the differential calculus! besides a good number of minor results—binomial theorem, reflecting telescope, sextant, and the like; one would think it enough for one man's life-work, but the masterpiece remains still to be mentioned. It is as when one is considering Shakspeare:King Lear,Macbeth,Othello,—surely a sufficient achievement,—but the masterpiece remains.
Comparisons in different departments are but little help perhaps, nevertheless it seems to me that in his own department, and considered simply as a man of science, Newton towers head and shoulders over, not only hiscontemporaries—that is a small matter—but over every other scientific man who has ever lived, in a way that we can find no parallel for in other departments. Other nations admit his scientific pre-eminence with as much alacrity as we do.
Well, we have arrived at the year 1672 and his election to the Royal Society. During the first year of his membership there was read at one of the meetings a paper giving an account of a very careful determination of the length of a degree (i.e.of the size of the earth), which had been made by Picard near Paris. The length of the degree turned out to be not sixty miles, but nearly seventy miles. How soon Newton heard of this we do not learn—probably not for some years,—Cambridge was not so near London then as it is now, but ultimately it was brought to his notice. Armed with this new datum, his old speculation concerning gravity occurred to him. He had worked out the mechanics of the solar system on a certain hypothesis, but it had remained a hypothesis somewhat out of harmony with apparent fact. What if it should turn out to be true after all!
He took out his old papers and began again the calculation. If gravity were the force keeping the moon in its orbit, it would fall toward the earth sixteen feet every minute. How far did it fall? The newly known size of the earth would modify the figures: with intense excitement he runs through the working, his mind leaps before his hand, and as he perceives the answer to be coming out right, all the infinite meaning and scope of his mighty discovery flashes upon him, and he can no longer see the paper. He throws down the pen; and the secret of the universe is, to one man, known.
But of course it had to be worked out. The meaning might flash upon him, but its full detail required years of elaboration; and deeper and deeper consequences revealed themselves to him as he proceeded.
For two years he devoted himself solely to this one object. During those years he lived but to calculate and think, and the most ludicrous stories are told concerning his entire absorption and inattention to ordinary affairs of life. Thus, for instance, when getting up in a morning he would sit on the side of the bed half-dressed, and remain like that till dinner time. Often he would stay at home for days together, eating what was taken to him, but without apparently noticing what he was doing.
One day an intimate friend, Dr. Stukely, called on him and found on the table a cover laid for his solitary dinner. After waiting a long time, Dr. Stukely removed the cover and ate the chicken underneath it, replacing and covering up the bones again. At length Newton appeared, and after greeting his friend, sat down to dinner, but on lifting the cover he said in surprise, "Dear me, I thought I had not dined, but I see I have."
It was by this continuous application that thePrincipiawas accomplished. Probably nothing of the first magnitude can be accomplished without something of the same absorbed unconsciousness and freedom from interruption. But though desirable and essential for thework, it was a severe tax upon the powers of theman. There is, in fact, no doubt that Newton's brain suffered temporary aberration after this effort for a short time. The attack was slight, and it has been denied; but there are letters extant which are inexplicable otherwise, and moreover after a year or two he writes to his friends apologizing for strange and disjointed epistles, which he believed he had written without understanding clearly what he wrote. The derangement was, however, both slight and temporary: and it is only instructive to us as showing at what cost such a work as thePrincipiamust be produced, even by so mighty a mind as that of Newton.
The first part of the work having been done, any ordinary mortal would have proceeded to publish it; but the fact isthat after he had sent to the Royal Society his papers on optics, there had arisen controversies and objections; most of them rather paltry, to which he felt compelled to find answers. Many men would have enjoyed this part of the work, and taken it as evidence of interest and success. But to Newton's shy and retiring disposition these discussions were merely painful. He writes, indeed, his answers with great patience and ability, and ultimately converts the more reasonable of his opponents, but he relieves his mind in the following letter to the secretary of the Royal Society: "I see I have made myself a slave to philosophy, but if I get free of this present business I will resolutely bid adieu to it eternally, except what I do for my private satisfaction or leave to come out after me; for I see a man must either resolve to put out nothing new, or to become a slave to defend it." And again in a letter to Leibnitz: "I have been so persecuted with discussions arising out of my theory of light that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow." This shows how much he cared for contemporary fame.
So he locked up the first part of thePrincipiain his desk, doubtless intending it to be published after his death. But fortunately this was not so to be.
In 1683, among the leading lights of the Royal Society, the same sort of notions about gravity and the solar system began independently to be bruited. The theory of gravitation seemed to be in the air, and Wren, Hooke, and Halley had many a talk about it.
Hooke showed an experiment with a pendulum, which he likened to a planet going round the sun. The analogy is more superficial than real. It does not obey Kepler's laws; still it was a striking experiment. They had guessed at a law of inverse squares, and their difficulty was to prove what curve a body subject to it would describe. They knew it ought to be an ellipse if it was to serve to explain the planetary motion, and Hooke said he could prove that anellipse it was; but he was nothing of a mathematician, and the others scarcely believed him. Undoubtedly he had shrewd inklings of the truth, though his guesses were based on little else than a most sagacious intuition. He surmised also that gravity was the force concerned, and asserted that the path of an ordinary projectile was an ellipse, like the path of a planet—which is quite right. In fact the beginnings of the discovery were beginning to dawn upon him in the well-known way in which things do dawn upon ordinary men of genius: and had Newton not lived we should doubtless, by the labours of a long chain of distinguished men, beginning with Hooke, Wren, and Halley, have been now in possession of all the truths revealed by thePrincipia. We should never have had them stated in the same form, nor proved with the same marvellous lucidity and simplicity, but the facts themselves we should by this time have arrived at. Their developments and completions, due to such men as Clairaut, Euler, D'Alembert, Lagrange, Laplace, Airy, Leverrier, Adams, we should of course not have had to the same extent; because the lives and energies of these great men would have been partially consumed in obtaining the main facts themselves.
The youngest of the three questioners at the time we are speaking of was Edmund Halley, an able and remarkable man. He had been at Cambridge, doubtless had heard Newton lecture, and had acquired a great veneration for him.
In January, 1684, we find Wren offering Hooke and Halley a prize, in the shape of a book worth forty shillings, if they would either of them bring him within two months a demonstration that the path of a planet subject to an inverse square law would be an ellipse. Not in two months, nor yet in seven, was there any proof forthcoming. So at last, in August, Halley went over to Cambridge to speak to Newton about the difficult problem and secure his aid. Arriving at his rooms he went straight to the point.He said, "What path will a body describe if it be attracted by a centre with a force varying as the inverse square of the distance." To which Newton at once replied, "An ellipse." "How on earth do you know?" said Halley in amazement. "Why, I have calculated it," and began hunting about for the paper. He actually couldn't find it just then, but sent it him shortly by post, and with it much more—in fact, what appeared to be a complete treatise on motion in general.
With his valuable burden Halley hastened to the Royal Society and told them what he had discovered. The Society at his representation wrote to Mr. Newton asking leave that it might be printed. To this he consented; but the Royal Society wisely appointed Mr. Halley to see after him and jog his memory, in case he forgot about it. However, he set to work to polish it up and finish it, and added to it a great number of later developments and embellishments, especially the part concerning the lunar theory, which gave him a deal of trouble—and no wonder; for in the way he has put it there never was a man yet living who could have done the same thing. Mathematicians regard the achievement now as men might stare at the work of some demigod of a bygone age, wondering what manner of man this was, able to wield such ponderous implements with such apparent ease.
To Halley the world owes a great debt of gratitude—first, for discovering thePrincipia; second, for seeing it through the press; and third, for defraying the cost of its publication out of his own scanty purse. For though he ultimately suffered no pecuniary loss, rather the contrary, yet there was considerable risk in bringing out a book which not a dozen men living could at the time comprehend. It is no small part of the merit of Halley that he recognized the transcendent value of the yet unfinished work, that he brought it to light, and assisted in its becoming understood to the best of his ability.
Though Halley afterwards became Astronomer-Royal, lived to the ripe old age of eighty-six, and made many striking observations, yet he would be the first to admit that nothing he ever did was at all comparable in importance with his discovery of thePrincipia; and he always used to regard his part in it with peculiar pride and pleasure.
And how was thePrincipiareceived? Considering the abstruse nature of its subject, it was received with great interest and enthusiasm. In less than twenty years the edition was sold out, and copies fetched large sums. We hear of poor students copying out the whole in manuscript in order to possess a copy—not by any means a bad thing to do, however many copies one may possess. The only useful way really to read a book like that is to pore over every sentence: it is no book to be skimmed.
While thePrincipiawas preparing for the press a curious incident of contact between English history and the University occurred. It seems that James II., in his policy of Catholicising the country, ordered both Universities to elect certain priests to degrees without the ordinary oaths. Oxford had given way, and the Dean of Christ Church was a creature of James's choosing. Cambridge rebelled, and sent eight of its members, among them Mr. Newton, to plead their cause before the Court of High Commission. Judge Jeffreys presided over the Court, and threatened and bullied with his usual insolence. The Vice-Chancellor of Cambridge was deprived of office, the other deputies were silenced and ordered away. From the precincts of this court of justice Newton returned to Trinity College to complete thePrincipia.
By this time Newton was only forty-five years old, but his main work was done. His method of fluxions was still unpublished; his optics was published only imperfectly; a second edition of thePrincipia, with additions and improvements, had yet to appear; but fame had now come upon him, and with fame worries of all kinds.
By some fatality, principally no doubt because of the interest they excited, every discovery he published was the signal for an outburst of criticism and sometimes of attack. I shall not go into these matters: they are now trivial enough, but it is necessary to mention them, because to Newton they evidently loomed large and terrible, and occasioned him acute torment.
Fig. 68.Fig. 68.—Newton when young.(From an engraving by B. Reading after Sir Peter Lely.)
No sooner was thePrincipiaput than Hooke put in his claims for priority. And indeed his claims were notaltogether negligible; for vague ideas of the same sort had been floating in his comprehensive mind, and he doubtless felt indistinctly conscious of a great deal more than he could really state or prove.
By indiscreet friends these two great men were set somewhat at loggerheads, and worse might have happened had they not managed to come to close quarters, and correspond privately in a quite friendly manner, instead of acting through the mischievous medium of third parties. In the next edition Newton liberally recognizes the claims of both Hooke and Wren. However, he takes warning betimes of what he has to expect, and writes to Halley that he will only publish the first two books, those containing general theorems on motion. The third book—concerning the system of the world,i.e.the application to the solar system—he says "I now design to suppress. Philosophy is such an impertinently litigious lady that a man had as good be engaged in law-suits as have to do with her. I found it so formerly, and now I am no sooner come near her again but she gives me warning. The two books without the third will not so well bear the title 'Mathematical Principles of Natural Philosophy,' and therefore I had altered it to this, 'On the Free Motion of Two Bodies'; but on second thoughts I retain the former title: 'twill help the sale of the book—which I ought not to diminish now 'tis yours."
However, fortunately, Halley was able to prevail upon him to publish the third book also. It is, indeed, the most interesting and popular of the three, as it contains all the direct applications to astronomy of the truths established in the other two.
Some years later, when his method of fluxions was published, another and a worse controversy arose—this time with Leibnitz, who had also independently invented the differential calculus. It was not so well recognized then how frequently it happens that two men independently andunknowingly work at the very same thing at the same time. The history of science is now full of such instances; but then the friends of each accused the other of plagiarism.
I will not go into the controversy: it is painful and useless. It only served to embitter the later years of two great men, and it continued long after Newton's death—long after both their deaths. It can hardly be called ancient history even now.
But fame brought other and less unpleasant distractions than controversies. We are a curious, practical, and rather stupid people, and our one idea of honouring a man is tovotefor him in some way or other; so they sent Newton to Parliament. He went, I believe, as a Whig, but it is not recorded that he spoke. It is, in fact, recorded that he was once expected to speak when on a Royal Commission about some question of chronometers, but that he would not. However, I dare say he made a good average member.
Then a little later it was realized that Newton was poor, that he still had to teach for his livelihood, and that though the Crown had continued his fellowship to him as Lucasian Professor without the necessity of taking orders, yet it was rather disgraceful that he should not be better off. So an appeal was made to the Government on his behalf, and Lord Halifax, who exerted himself strongly in the matter, succeeding to office on the accession of William III., was able to make him ultimately Master of the Mint, with a salary of some £1,200 a year. I believe he made rather a good Master, and turned out excellent coins: certainly he devoted his attention to his work there in a most exemplary manner.
But what a pitiful business it all is! Here is a man sent by Heaven to do certain things which no man else could do, and so long as he is comparatively unknown he does them; but so soon as he is found out, he is clapped into a routine office with a big salary: and there is, comparatively speaking, an end of him. It is not to be supposed that hehad lost his power, for he frequently solved problems very quickly which had been given out by great Continental mathematicians as a challenge to the world.
We may ask why Newton allowed himself to be thus bandied about instead of settling himself down to the work in which he was so pre-eminently great. Well, I expect your truly great man never realizes how great he is, and seldom knows where his real strength lies. Certainly Newton did not know it. He several times talks of giving up philosophy altogether; and though he never really does it, and perhaps the feeling is one only born of some temporary overwork, yet he does not sacrifice everything else to it as he surely must had he been conscious of his own greatness. No; self-consciousness was the last thing that affected him. It is for a great man's contemporaries to discover him, to make much of him, and to put him in surroundings where he may flourish luxuriantly in his own heaven-intended way.
However, it is difficult for us to judge of these things. Perhaps if he had been maintained at the national expense to do that for which he was preternaturally fitted, he might have worn himself out prematurely; whereas by giving him routine work the scientific world got the benefit of his matured wisdom and experience. It was no small matter to the young Royal Society to be able to have him as their President for twenty-four years. His portrait has hung over the President's chair ever since, and there I suppose it will continue to hang until the Royal Society becomes extinct.
The events of his later life I shall pass over lightly. He lived a calm, benevolent life, universally respected and beloved. His silver-white hair when he removed his peruke was a venerable spectacle. A lock of it is still preserved, with many other relics, in the library of Trinity College. He died quietly, after a painful illness, at the ripe age of eighty-five. His body lay in state in the Jerusalem Chamber, and he was buried in Westminster Abbey, six peers bearing the pall. These things are to be mentionedto the credit of the time and the country; for after we have seen the calamitous spectacle of the way Tycho and Kepler and Galileo were treated by their ungrateful and unworthy countries, it is pleasant to reflect that England, with all its mistakes, yet recognizedhergreat man when she received him, and honoured him with the best she knew how to give.