We left 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...o...b..t. 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 cakes and 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 it _could_ not 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 elongated oval and was coloured at its extremities. Evidently refraction was not a simple geometrical deflection of a ray, there was a spreading out as well.
[Ill.u.s.tration: FIG. 63.--A prism not only _deviates_ a beam of sunlight, but also spreads it out or _disperses_ it.]
Why did the image thus spread out? If it were due to irregularities in the gla.s.s 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 pa.s.sing through the prism travelled in variously curved lines, as spinning racquet b.a.l.l.s 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 const.i.tuents, and that its different const.i.tuents were differently bent?
No sooner thought than tried. Pierce the screen to let one of the const.i.tuents 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 const.i.tuent 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 a.n.a.lysed into const.i.tuents. 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 const.i.tuent parts which were differently refracted, and the most striking of which Newton named violet, indigo, blue, green, yellow, orange, and red.
[Ill.u.s.tration: FIG. 64.--A single const.i.tuent 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 gla.s.s for instance adds nothing to sunlight. The light does not get dyed red by pa.s.sing through the gla.s.s; all that the red gla.s.s 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 out the 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 his _Farbenlehre_, endeavoured to controvert Newton, and to reinstate something more like the old views; but his failure was complete.
Refraction a.n.a.lysed out the various const.i.tuents 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 a.n.a.lysis. 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 const.i.tuents have different foci; every bright object is fringed with colour, and nothing like a clear image can be obtained.
[Ill.u.s.tration: FIG. 65.--Showing the boundary rays of a parallel beam pa.s.sing through a lens.]
A parallel beam pa.s.sing 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 the place 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 was 1/50th the diameter of the lens. To overcome this difficulty (called chromatic aberration) telescope gla.s.ses were made small and of very long focus: some of them so long that they had no tube, all of them egregiously c.u.mbrous. 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 "gla.s.s 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 s.e.xtant, 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:--
[Ill.u.s.tration: 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 a.n.a.lysis.
[Ill.u.s.tration: FIG. 67.--The s.e.xtant, 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 was accordingly 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 a.s.sistant, 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 a.s.suring 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 his _Optics_. 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, s.e.xtant, 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_, _Oth.e.l.lo_,--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 his contemporaries--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...o...b..t, 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 the _Principia_ was 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 the _work_, it was a severe tax upon the powers of the _man_. 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 the _Principia_ must 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 is that 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 the _Principia_ in 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.