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Isaac Newton/The first 15 years as Lucasian professor
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Newton was elected Lucasian professor on October 29, 1670. It was his duty as professor to lecture at least once a week in term time on some portion of geometry, arithmetic, astronomy, geography, optics, statics, or some other mathematical subject, and also for two hours in the week to allow an audience to any student who might come to consult with the professor on any difficulties he had met with. The subject which Newton chose for his lectures was optics. The success which attended his researches in optics must have been great, although the results were known only through his own oral lectures, until he presented an account of them to the Royal Society in the spring of 1672.
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The Composition of White Light
On December 21, 1671 he was proposed as a candidate for admission into the Royal Society by Dr Seth Ward[?], bishop of Salisbury, and on January 11, 1672 he was elected a fellow of the Society. At the meeting at which Newton was elected, he read a description of a reflecting telescope[?] which he had invented, and "it was ordered that a letter should be written by the secretary to Mr Newton to acquaint him of his election into the Society, and to thank him for the communication of his telescope, and to assure him that the Society would take care that all right should be done him with respect to this invention."In his reply to the secretary on January 18, 1672, Newton writes: "I desire that in your next letter you would inform me for what time the society continue their weekly meetings; because, if they continue them for any time, I am purposing them to be considered of and examined an account of a philosophical discovery, which induced me to the making of the said telescope, and which I doubt not but will prove much more grateful than the communication of that instrument being in my judgment the oddest if not the most considerable detection which hath hitherto been made into the operations of nature."
This promise was fulfilled in a communication which Newton addressed to Henry Oldenburg[?], the secretary of the Royal Society, on February 6, 1672, and which was read before the society two days afterwards. The whole is printed in No. 80 of the Philosophical Transactions[?].
Newton's "philosophical discovery" was the realisation that white light is composed of a spectrum of colours. He realised that objects are coloured only because they absorb some of these colours more than others.
After he explained this to the Society, he proceeded: "When I understood this, I left off my aforesaid glass works; for I saw, that the perfection of telescopes was hitherto limited, not so much for want of glasses truly figured according to the prescriptions of Optics Authors (which all men have hitherto imagined), as because that light itself is a heterogeneous mixture of differently refrangible rays. So that, were a glass so exactly figured as to collect any one sort of rays into one point, it could not collect those also into the same point, which having the same incidence upon the same medium are apt to suffer a different refraction. Nay, I wondered, that seeing the difference of refrangibility was so great, as I found it, telescopes should arrive to that perfection they are now at." This "difference in refrangibility" is now known as dispersion.
He then points out why "the object-glass of any telescope cannot collect all the rays which come from one point of an object, so as to make them convene at its focus in less room than in a circular space, whose diameter is the 50th part of the diameter of its aperture: which is an irregularity some hundreds of times greater, than a circularly figured lens, of so small a section as the object-glasses of long telescopes are, would cause by the unfitness of its figure, were light uniform." He adds: "This made me take reflections into consideration, and finding them regular, so that the Angle of Reflection of all sorts of Rays was equal to their Angle of Incidence; I understood, that by their mediation optic instruments might be brought to any degree of perfection imaginable, provided a reflecting substance could be found, which would polish as finely as glass, and reflect as much light, as glass transmits, and the art of communicating to it a parabolic figure be also attained. But these seemed very great difficulties, and I have almost thought them insuperable, when I further considered, that every irregularity in a reflecting superficies makes the rays stray 5 or 6 times more out of their due course, than the like irregularities in a refracting one; so that a much greater curiosity would be here requisite, than in figuring glasses for refraction.
"Amidst these thoughts I was forced from Cambridge by the intervening Plague, and it was more than two years before I proceeded further. But then having thought on a tender way of polishing, proper for metal, whereby, as I imagined, the figure also would be corrected to the last; I began to try, what might be effected in this kind, and by degrees so far perfected an instrument (in the essential parts of it like that I sent to London), by which I could discern Jupiter's 4 Concomitants, and showed them diverse times to two others of my acquaintance. I could also discern the Moon-like phase of Venus, but not very distinctly, nor without some niceness in disposing the instrument.
"From that time I was interrupted till this last autumn, when I made the other. And as that was sensibly better than the first (especially for day-objects), so I doubt not, but they will be still brought to a much greater perfection by their endeavours, who, as you inform me, are taking care about it at London."
After a remark that microscopes seem as capable of improvement as telescopes, he adds: "I shall now proceed to acquaint you with another more notable deformity in its Rays, wherein the origin of colour is unfolded: concerning which I shall lay down the doctrine first, and then, for its examination, give you an instance or two of the experiments, as a specimen of the rest. The doctrine you will find comprehended and illustrated in the following propositions:
"1. As the rays of light, differ in degrees of refrangibility, so they also differ in their disposition to exhibit this or that particular colour. Colours are not qualifications of light, derived from refractions, or reflections of natural bodies (as 'tis generally believed), but original and connate properties, which in diverse rays are diverse. Some rays are disposed to exhibit a red colour and no other; some a yellow and no other, some a green and no other, and so of the rest. Nor are there only rays proper and particular to the more eminent colours, but even to all their intermediate gradations.
"2. To the same degree of refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of refrangibility. The least refrangible rays are all disposed to exhibit a red colour, and contrarily those rays, which are disposed to exhibit a red colour, are all the least refrangible: so the most refrangible rays are all disposed to exhibit a deep violet colour, and contrarily those which are apt to exhibit such a violet colour are all the most refrangible.
"And so to all the intermediate colours in a continued series belong intermediate degrees of refrangibility. And this analogy 'twixt colours, and refrangibility is very precise and strict; the rays always either exactly agreeing in both, or proportionally disagreeing in both.
"3. The species of colour, and degree of refrangibility proper to any particular sort of rays, is not mutable by refraction, nor by reflection from natural bodies, nor by any other cause, that I could yet observe. When any one sort of rays hath been well parted from those of other kinds, it hath afterwards obstinately retained its colour, notwithstanding my utmost endeavours to change it. I have refracted it with prisms, and reflected it with bodies, which in daylight were of other colours; I have intercepted it with the coloured film of air interceding two compressed plates of glass, transmitted it through coloured mediums, and through mediums irradiated with other sorts of rays, and diversely terminated it; and yet could never produce any new colour out of it. It would by contracting or dilating become more brisk, or faint, and by the loss of many Rays, in some cases very obscure and dark; but I could never see it changed in specie.
"Yet seeming transmutations of colours may be made, where there is any mixture of diverse sorts of rays. For in such mixtures, the component colours appear not, but, by their mutual allaying each other constitute a middling colour."
Further on, after some remarks on the subject of compound colours, he says: "I might add more instances of this nature, but I shall conclude with this general one, that the colours of all natural bodies have no other origin than this, that they are variously qualified to reflect one sort of light in greater plenty then another. And this I have experimented in a dark room by illuminating those bodies with uncompounded light of diverse colours. For by that means any body may be made to appear of any colour. They have there no appropriate colour, but ever appear of the colour 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 colour. Minium appears there of any colour indifferently, with which 'tis illustrated, but yet most luminous in red, and so bise[?] appears indifferently of any colour with which 'tis illustrated, but yet most luminous in blue. And therefore minium reflects rays of any colour, but most copiously those endued 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 colour. 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 colours, is manifest, because they have no power to change or alter the colours of any sort of rays incident apart, but put on all colours indifferently, with which they are enlightened.
"Reviewing what I have written, I see the discourse itself will lead to diverse experiments sufficient for its examination: And therefore I shall not trouble you further, than to describe one of those, which I have already insinuated.
"In a darkened room make a hole in the shutter of a window whose diameter may conveniently be about a third part of an inch, to admit a convenient quantity of the Sun's light: And there place a clear and colourless prism, to refract the entering light towards the further part of the room, which, as I said, will thereby be diffused into an oblong coloured image. Then place a lens of about three foot radius (suppose a broad object-glass of a three foot telescope), at the distance of about four or five foot from thence, through which all those colours may at once be transmitted, and made by its refraction to convene at a further distance of about ten or twelve feet. If at that distance you intercept this light with a sheet of white paper, you will see the colours converted into whiteness again by being mingled.
"But it is requisite, that the prism and lens be placed steady, and that the paper, on which the colours are cast be moved to and fro; for, by such motion, you will not only find, at what distance the whiteness is most perfect but also see, how the colours gradually convene, and vanish into whiteness, and afterwards having crossed one another in that place where they compound whiteness, are again dissipated and severed, and in an inverted order retain the same colours, which they had before they entered the composition. You may also see, that, if any of the colours at the lens be intercepted, the whiteness will be changed into the other colours. And therefore, that the composition of whiteness be perfect, care must be taken, that none of the colours fall besides the lens."
He concludes his communication with the words: "This, I conceive, is enough for an introduction to experiments of this kind: which if any of the R. Society shall be so curious as to prosecute, I should be very glad to be informed with what success: That, if any thing seem to be defective, or to thwart this relation, I may have an opportunity of giving further direction about it, or of acknowledging my errors, if I have committed any."
The publication of these discoveries led to a series of controversies which lasted for several years, in which Newton had to contend with the eminent English physicist Robert Hooke, Lucas[?] (mathematical professor at Liege[?]) Linus[?] (a physician in Liege), and many others. Some of his opponents denied the truth of his experiments, refusing to believe in the existence of the spectrum. Others criticized the experiments, saying that the length of the spectrum was never more than three and a half times the breadth, whereas Newton found it to be five times the breadth. It appears that Newton made the mistake of supposing that all prisms would give a spectrum of exactly the same length; the objections of his opponents led him to measure carefully the lengths of spectra formed by prisms of different angles and of different refractive indices; and it seems strange that he was not led thereby to the discovery of the different dispersive powers of different refractive substances.
Newton carried on the discussion with the objectors with great courtesy and patience, but the amount of pain which these perpetual discussions gave to his sensitive mind may be estimated from the fact of his writing on November 18, 1676 to Oldenburg[?]: "I promised to send you an answer to Mr Lucas this next Tuesday, but I find I shall scarce finish what I have designed, so as to get a copy taken of it by that time, and therefore I beg your patience a week longer. I see I nave made myself a slave to philosophy, but if I get free of Mr Lucas's business, I will resolutely bid adieu to it eternally, excepting 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."
It was a fortunate circumstance that these disputes did not so thoroughly damp Newton's ardour as he at the time felt they would. He subsequently published many papers in the Philosophical Transactions on various parts of the science of optics, and, although some of his views have been found to be erroneous, and are now almost universally rejected, his investigations led to discoveries which are of permanent value. He succeeded in explaining the colour of thin and of thick plates, and the inflexion of light, and he wrote on double refraction, polarization and binocular vision. He also invented a reflecting sextant for observing the distance between the moon and the fixed stars—the same in every essential as the historically important navigational instrument more commonly known as Halley's quadrant[?]. This discovery was communicated by him to Edmund Halley in 1700, but was not published, or communicated to the Royal Society, till after Newton's death, when a description of it was found among his papers.
Conflict over oratorship elections
In March 1673 Newton took a prominent part in a dispute in the university. The public oratorship fell vacant, and a contest arose between the heads of the colleges and the members of the senate as to the mode of electing to the office. The heads claimed the right of nominating two persons, one of whom was to be elected by the senate. The senate insisted that the proper mode was by an open election. The duke of Buckingham, who was the chancellor of the university, endeavoured to effect a compromise which, he says, "I hope may for the present satisfy both sides. I propose that the heads may for this time nominate and the body comply, yet interposing (if they think fit) a protestation concerning their plea that this election may not hereafter pass for a decisive precedent in prejudice of their claim," and, "whereas I understand that the whole university has chiefly consideration for Dr Henry Paman[?] of St John's College and Mr Craven of Trinity College, I do recommend them both to be nominated." The heads, however, nominated Dr Paman and Ralph Sanderson[?] of St John's, and the next day one hundred and twenty-one members of the senate recorded their votes for Craven and ninety-eight for Paman. On the morning of the election a protest in which Newton's name appeared was read, and entered in the Regent House. But the vice-chancellor admitted Paman the same morning, and so ended the first contest of a non-scientific character in which Newton took part.
Newton's poverty
On March 8, 1673 Newton wrote to Oldenburg, the secretary of the Royal Society:
"Sir, I desire that you will procure that I may be put out from being any longer Fellow of the Royal Society: for though I honour that body, yet since I see I shall neither profit them, nor (by reason of this distance) can partake of the advantage of their assemblies, I desire to withdraw."
Oldenburg must have replied to this by an offer to apply to the Society to excuse Newton the weekly payments, as in a letter of Newton's to Oldenburg, dated June 23, 1673, be says, "For your proffer about my quarterly payments, I thank you, but I would not have you trouble yourself to get them excused, if you have not done it already." Nothing further seems to have been done in the matter until January 28, 1675, when Oldenburg informed" the Society that Mr Newton is now in such circumstances that he desires to be excused from the weekly payments." Upon this "it was agreed to by the council that he be dispensed with, as several others are." On February 18, 1675 Newton was formally admitted into the Society. The most probable explanation of the reason why Newton wished to be excused from these payments is to be found in the fact that, as he was not in holy orders, his fellowship at Trinity College would lapse in the autumn of 1675. It is true that the loss to his income which this would have caused was obviated by a patent from the crown in April 1675, allowing him as Lucasian professor to retain his fellowship without the obligation of taking holy orders. This must have relieved Newton's mind from a great deal of anxiety about financial matters, since in November 1676 he donated £40 towards the building of the new library of Trinity College.
Universal Law of Gravitation
It is supposed that it was at Woolsthorpe in the summer of 1666 that Newton's thoughts were directed to the subject of gravity. Voltaire is the authority for the well-known anecdote about the apple. He had his information from Newton's favourite niece Catharine Barton[?], who married Conduitt, a fellow of the Royal Society, and one of Newton's intimate friends. How much truth there is in what is a plausible and a favourite story can never be known, but it is certain that tradition marked a tree as that from which the apple fell, till 1860, when, owing to decay, the tree was cut down and its wood carefully preserved.
Johann Kepler[?] had proved by an elaborate series of measurements that each planet revolves in an elliptical orbit around the sun, whose centre occupies one of the foci of the orbit, that the radius vector of each planet drawn from the sun sweeps out equal areas in equal times, and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the sun. The fact that heavy bodies have always a tendency to fall to the earth, no matter at what height they are placed above the earth's surface, seems to have led Newton to conjecture that it was possible that the same tendency to fall to the earth was the cause by which the moon was retained in its orbit round the earth.
Newton, by calculating from Kepler's laws, and supposing the orbits of the planets to be circles round the sun in the centre, had already proved that the force of the sun acting upon the different planets must vary as the inverse square of the distances of the planets from the sun. He therefore was led to inquire whether, if the earth's attraction extended to the moon, the force at that distance would be of the exact magnitude necessary to retain the moon in its orbit. He found that the moon by her motion in her orbit was deflected from the tangent in every minute of time through a space of thirteen feet. But by observing the distance through which a body would fall in one second of time at the earth's surface, and by calculating from that on the supposition of the force diminishing in the ratio of the inverse square of the distance, he found that the earth's attraction at the distance of the moon would draw a body through 15 ft. in 1 min. Newton regarded the discrepancy between the results as a proof of the inaccuracy of his conjecture, and "laid aside at that time any further thoughts of this matter."
But in 1679 a controversy between Hooke and Newton, about the form of the path of a body falling from a height, taking the motion of the earth round its axis into consideration, led Newton again to revert to his former conjectures on the moon. The estimate Newton had used for the radius of the earth, which had been accepted by geographers and navigators, was based on the very rough estimate that the length of a degree of latitude of the earth's surface measured along a meridian was 60 miles. At a meeting of the Royal Society on January 11, 1672, Oldenburg the secretary read a letter from Paris describing the procedure followed by Jean Picard[?] in measuring a degree, and specifically stating the precise length that he calculated it to be. It is probable that Newton had become acquainted with this measurement of Picard's, and that he was therefore led to make use of it when his thoughts were redirected to the subject. This estimate of the earth's magnitude, giving 691 miles to 10°, made the two results, the discrepancy between which Newton had regarded as a disproof of his conjecture, to agree so exactly that he now regarded his conjecture as fully established.
In January 1684, Sir Christopher Wren, Halley and Hooke were led to discuss the law of gravity, and although probably they all agreed in the truth of the law of the inverse square, yet this truth was not looked upon as established. It appears that Hooke professed to have a solution of the problem of the path of a body moving round a centre of force attracting as the inverse square of the distance, but Halley declared after a delay of some months that Hooke "had not been so good as his word" in showing his solution to Wren, started in the month of August 1684 for Cambridge to consult Newton on the subject. Without mentioning the speculations which had been made, he asked Newton what would be the curve described by a planet round the sun on the assumption that the sun's force diminished as the square of the distance. Newton replied promptly, "an ellipse," and on being questioned by Halley as to the reason for his answer he replied, "Why, I have calculated it." He could not, however, put his hand upon his calculation, but he promised to send it to Halley. After the latter had left Cambridge, Newton set to work to reproduce the calculation. After making a mistake and producing a different result he corrected his work and obtained his former result.
In the following November Newton redeemed his promise to Halley by sending him, by the hand of Mr Paget, one of the fellows of his own college, and at that time mathematical master of Christ's Hospital, a copy of his demonstration; and very soon afterwards Halley paid another visit to Cambridge to confer with Newton about the problem. On his return to London on December 10, 1684, he informed the Royal Society "that he had lately seen Mr Newton at Cambridge, who had showed him a curious treatise De Motu," which at Halley's desire he promised to send to the Society to be entered upon their register. "Mr Halley was desired to put Mr Newton in mind of his promise for the securing this invention to himself, till such time as he could be at leisure to publish it," and Paget was desired to join with Halley in urging Newton to do so. By the middle of February Newton had sent his paper to Aston, one of the secretaries of the Society, and in a letter to Aston dated February 23, 1685, we find Newton thanking him for "having entered on the register his notions about motion." This treatise De Motu was the starting point of the Principia, and was obviously meant to be a short account of what that work was intended to embrace. It occupies twenty-four octavo[?] pages, and consists of four theorems and seven problems, some of which are identical with some of the most important propositions of the second and third sections of the first book of the Principia.
Next: Authoring Principia
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