• "A Letter of Mr. Isaac Newton ... containing his New Theory about Light and Colours ..." by Isaac Newton;

• "Critique of Newton's Theory of Light and Colors", by Robert Hooke;

• "Answer to some Considerations upon his Doctrine of Light and Colors" by Isaac Newton;

• "Mr. Newton's Doctrine of Colors" by Christiaan Huyghens;

• "Mr. Newtons Answer to the foregoing Letter ..." by Isaac Newton;

• "A Manuscript of Mr. Newton, touching his theory of light and colours" by Isaac Newton;

• Letter to J. Lelong, 13 December 1707 by Gottfried Willhelm von Leibniz;

• Letter to a friend, 1707 by Father Nicolas Malebranche;

• Letter to J. Lelong, 9 April 1708 by Gottfried Willhelm von Leibniz;

• Dissertation sur la cause de la lumiere des phosphores et des moctiluques (1717) by Jean-Jacques Dortous de Mairan;

• Experiences de physique (1709) by Pierre Poliniere;

• The Elogium of Sir Isaac Newton (1728) by Bernard le Bovier de Fontenelle;

• "An Account of some Experiments of Light and Colours ..." by John Theophilus Desaguliers; and

• Theory of Colours (1810) by Johann Wolfgang von Goethe.

SIR,
To perform my late promise to you, I shall without further ceremony acquaint you that in the beginning of the year 1666 (at which time I applied myself to the grinding of optic glasses of other figures than spherical) I procured me a triangular glass prism, to try therewith the celebrated phenomena of colors.  And in order thereto having darkened my chamber and made a small hole in my window shuts, to let in a convenient quantity of the sun's light, I placed my prism at his entrance, that it might be thereby refracted to the opposite wall.  It was at first a pleasing divertisement to view the vivid and intense colors produced thereby; but after a while applying myself to consider them more circumspectly, I became surprised to see them in an oblong form; which according to the received laws of refraction, I expected should have been circular.
 

They were terminated at the sides with straight lines, but at the ends the decay of light was so gradual that it was difficult to determine justly what was their figure; yet they seemed semi-circular.

Comparing the length of this colored spectrum with its breadth, I found it about five times greater, a disproportion so extravagant that it excited me to a more than ordinary curiosity of examining from whence it might proceed.  I could scarce think that the various thickness of the glass, or the termination with shadow or darkness, could have any influence on light to produce such an effect; yet I thought it not amiss first to examine those circumstances, and so tried what would happen by transmitting light through parts of the glass of divers thickness or through holes in the window of divers bignesses, or by setting the prism without so that the light might pass through it and be refracted before it was terminated by the hole; but I found none of those circumstances material.  The fashion of the colors was in all these cases the same.

Then I suspected whether, by any unevenness in the glass or other contingent irregularity, these colors might be thus dilated....

I then proceeded to examine more critically what might be effected by the difference of the incidence of rays coming from divers parts of the sun; and to that end measured the several lines and angles belonging to the image....

Then I began to suspect whether the rays, after their trajection through the prism, did not move in curved lines, and according to their more or less curvity tend to divers parts of the wall.  And it increased my suspicion when I remembered that I had often seen a tennis ball, struck with an oblique racket, describe such a curved line.  For a circular as well as a progressive motion being communicated to it by that stroke, its parts on that side where the motions conspire must press and beat the contiguous air more violently than on the other, and there excite a reluctancy and reaction of the air proportionably greater.  And for the same reason, if the rays of light be globular bodies, and by their oblique passage out of one medium into another acquire a circular motion, they ought to feel the greater resistance from the ambient ether on that side where the motions conspire, and thence be continually bowed to the other.  But notwithstanding this plausible ground of suspicion, when I came to examine it I could observe no such curvity in them.

The gradual removal of these suspicions at length led me to the Experimentum Crucis, which was this:  I took two boards and placed one of them close behind the prism at the window, so that the light might pass through a small hole, made in it for the purpose, and fall on the other board, which I placed at about 12 feet distance, having first made a small hole in it also for some of that incident light to pass through.  Then I placed another prism behind this second board, so that the light, trajected through both the boards, might pass through that also and be again refracted before it arrived at the wall.  This done, I took the first prism in my hand and turned it to and fro slowly about its axis, so much as to make the several parts of the image cast on the second board successively pass through the hole in it, that I might observe to what places on the wall the second prism would refract them.  And I saw by the variation of those places that the light, tending to that end of the image toward which the refraction of the first prism was made, did in the second prism suffer a refraction considerably greater than the light tending to the other end.  And so the true cause of the length of that image was detected to be no other than that light consists of rays differently refrangible, which without any respect to a difference in their incidence were, according to their degrees of refrangibility, transmitted toward divers parts of the wall.
 

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 optic authors (which all men have hitherto imagined), as because that light itself is a heterogeneous mixture of differently refrangible rays....

I shall now proceed to acquaint you with another more notable difformity in its rays, wherein the origin of colors 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 color.  Colors are not qualifications of light, derived from refractions or reflections of natural bodies (as is generally believed), but original and connate properties, which in divers rays are divers....

2. To the same degree of refrangibility ever belongs the same color, and to the same color ever belongs the same degree of refrangibility.  The least refrangible rays are all disposed to exhibit a red color...; so the most refrangible rays are all disposed to exhibit a deep violet color....

3. The species of color 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....

4. Yet seeming transmutations of colors may be made where there is any mixture of divers sorts of rays....  [I]f by refraction or any other of the aforesaid causes, the difform rays latent in such a mixture be separated, there shall emerge colors different from the color of the composition....

5. There are therefore two sorts of colors.  The one original and simple, the other compounded of these.  The original or primary colors are red, yellow, green, blue, and a violet-purple, together with orange, indigo, and an indefinite variety of intermediate gradations....

7. But the most surprising and wonderful composition was that of whiteness.  There is no one sort of rays which alone can exhibit this.  It is ever compounded, and to its composition are requisite all the aforesaid primary colors, mixed in a due proportion.  I have often with admiration beheld that, all the colors of the prism being made to converge and thereby to be again mixed as they were in the light before it was incident upon the prism, reproduced light entirely and perfectly white, and not at all sensibly differing from a direct light of the sun....

9. These things considered, the manner how colors are produced by the prism is evident.  For of the rays constituting the incident light, since those which differ in color proportionally differ in refrangibility, they by their unequal refractions must be severed and dispersed into an oblong form in an orderly succession, from the least refracted scarlet to the most refracted violet....

10. Why the colors of the rainbow appear in falling drops of rain is also from hence evident....

These things being so, it can be no longer disputed whether there be colors in the dark, nor whether they be the qualities of the object we see, nor perhaps whether light be a body.  For since colors are the qualities of light, having its rays for their entire and immediate subject, how can we think those rays qualities also unless one quality may be the subject of and sustain another, which in effect is to call it substance.

...[A]ll the experiments and observations I have hitherto made, nay, and even those very experiments, which he alledgeth, do seem to me to prove, that white is nothing but a pulse or motion, propagated through an homogeneous, uniform, and transparent medium:  and that colour is nothing but the disturbance of that light, by the communication of that pulse to other transparent mediums, that is, by the refraction thereof:  that whiteness and blackness are nothing but the plenty or scarcity of the undisturbed rays of light....

But why there is a necessity, that all those motions, or whatever else it be that makes colours, should be originally in the simple rays of light, I do not yet understand the necessity of, no more than that all those sounds must be in the air of the bellows, which are afterwards heard to issue from the organpipes; or the string, which are afterwards, by different stoppings and strikings produced; which string (by the way) is a pretty representation of the shape of a refracted ray to the eye; and the manner of it may be somewhat imagined by the similitude thereof:  for the ray is like the string, strained between the luminous object and the eye, and the stop or fingers is like the refracting surface, on the one side of which the string hath no motion, on the other a vibrating one.  Now we may say indeed and imagine, that the rest or streightness of the string is caused by the cessation of motions, or coalition of all vibrations; and that all the vibrations are dormant in it:  but yet it seems more natural to me to imagine it the other way....

Mr. Newton alledgeth, that as the rays of light differ in refrangibility, so they differ in their disposition to exibit this or that colour:  with which I do in the main agree; that is, that the ray by refraction is, as it were, split or rarified, and that the one side, namely that which is most refracted, gives a blue, and that which is least a red:  the intermediate are the dilutings and intermixtures of those two, which I thus explain.  The motion of light in an uniform medium, in which it is generated, is propagated by simple and uniform pulses or waves, which are at right angles with the line of direction; but falling obliquely on the refracting medium, it receives another impression or motion, which disturbs the former motion, somewhat like the vibration of a string:  and that, which was before a line, now becomes a triangular superficies, in which the pulse is not propagated at right angles with its line of direction, but ascew, as I have more at large explained in my Micrographia; and that, which makes excursions on the one side, impresses  a compound motion on the bottom of the eye, of which we have the imagination of red; and that, which makes excursions on the other, causes a sensation, which we imagine a blue; and so of all the intermediate dilutings of those colours.  Now, that the intermediate are nothing but the dilutings of those two primary, I hope I have sufficiently proved by [earlier] experiment....

I believe Mr. Newton will think it no difficult matter, by my hypothesis, to solve all the phenomena, not only of the prism, tinged liquors, and solid bodies, but of the colours of plated bodies, which seem to have the greatest difficulty....  If Mr. Newton hath any argument, that he supposes an absolute demonstration of his theory, I should be very glad to be convinced by it....

... Tis true, that from my Theory I argue the Corporeity of Light; but I do it without any absolute positiveness, as the word perhaps intimates; and make it at most but a very plausible consequence of the Doctrine, and not a fundamental supposition, nor so much as any part of it; which was wholly comprehended in the precedent Propositions....  Had I intended any such Hypothesis, I should somewhere have explain'd it.  But I knew, that the Properties, which I declar'd of Light, were in some measure capable of being explicated not only by that, but by many other Mechanical Hypotheses.  And therefore I chose to decline them all, and to speak of Light in general terms, considering it abstractly, as something or other propagated every way in streight lines from luminous bodies, without determining, what that Thing is; whether a confused Mixture of difform qualities, or Modes of bodies, or of Bodies themselves, or of any Virtues, Powers, or Beings whatsoever.  And for the same reason I chose to speak of Colours according to the information of our Senses, as if they were Qualities of Light without us.

I have seen, how Mr. Newton endeavours to maintain his new Theory concerning Colours.  Me thinks, that the most important Objection, which is made against him by way of Quere, is that, Whether there be more than two sorts of Colours.  For my part, I believe, that an Hypothesis, that should explain mechanically and by the nature of the motion the Colors Yellow and Blew, would be sufficient for all the rest, in regard that those others, being only more deeply charged (as appears by the Prismes of Mr. Hook) do produce the dark or deep-Red and Blew; and that of these four all the other colors may be compounded.  Neither do I see, why Mr. Newton doth not content himself with the two Colors, Yellow and Blew; for it will be much more easy to find an Hypothesis by Motion, that may explicate these two differences, than for so many diversities as there are of others Colors.  And till he hath found this Hypothesis, he hath not taught us, what it is wherein consists the nature and difference of Colours, but only this accident (which certainly is very considerable) of their different Refrangibility.

Concerning the business of Colors; in my saying that when Monsieur N. hath shewn how White may be produced out of two uncompounded colors, I will tell him, why he can conclude nothing from that; my meaning was, that such a White, (were there any such,) would have different properties from the White, which I had respect to, when I described my Theory, that is, from the White of the Sun's immediate light, of the ordinary objects of our senses, and of all white Phenomena that have hitherto faln under my observation.  And those different properties would evince it to be of a different constitution:  Insomuch that such a production of white would be so far from contradicting, that it would rather illustrate and confirm my Theory; because by the difference of that from other whites it would appear, that other Whites are not compounded of only two colours like that.  And therefore if Monsieur N. would prove anything, it is requisite that he do not only produce out of two primitive Colors a white which to the naked eye shall appear like other whites, but also shall agree with them in all other properties.

First, it is to be supposed therein, that there is an aethereal medium much of the same constitution with air, but far rarer, subtler, and more strongly elastic....

In the second place, it is to be supposed, that the aether is a vibrating medium like air, only the vibrations far more swift and minute; those of air, made by a man's ordinary voice succeeding one another at more than half a foot or a foot distance; but those of aether at a less distance than the hundred thousandth part of an inch.  And, as in air the vibrations are some larger than others, but yet all equally swift ... so, I suppose, the aethereal vibrations differ in bigness, but not in swiftness....

Third'y, as the air can pervade the bores of small glass pipes, but yet not so easily as if they were wider; and therefore stands at a greater degree of rarity than in the free aereal spaces, and at so much a greater degree of rarity as the pipe is smaller, as is known by the rising of water in such pipes to a much greater hight than the surface of the stagnating water, into which they are dipped; so I suppose aether, though it pervades the pores of crystal, glass, water, and other natural bodies, yet it stands at a greater degree of rarity in those pores, than in the free aethereal spaces, and at so much a greater degree of rarity, as the pores of the body are smaller.  Whence it may be, that the spirit of wine, for instance, though a lighter body, yet having subtiler parts, and consequently smaller pores, than water, is the more strongly refracting liquor....

In the fourth place therefore, I suppose light is neither aether, nor its vibrating motion, but something of a different kind propagated from lucid bodies.  They, that will, may suppose it an aggregate of various peripatetic qualities.  Others may suppose it multitudes of unimaginable small and swift corpuscles of various sizes, springing from shining bodies at great distances one after another; but yet without any sensible interval of time, and continually urged forward by a principle of motion, which in the beginning accelerates them, till the resistence of the aethereal medium equal the force of that principle....  To avoid dispute, and make this hypothesis general, let every man here take his fancy:  only, whatever light be, I suppose, it consists of rays differing from one another in contingent circumstances, as bigness, form, or vigour; like as the sands on the shore, the waves of the sea, the faces of men, and all other natural things of the same kind differ; it being almost impossible for any sort of things to be found without some contingent variety....

Fifthly, it is to be supposed, that light and aether mutually act upon one another, aether in refracting light, and light in warming aether; and that the densest aether acts most strongly.  When a ray therefore moves through aether of uneven density, I suppose it most pressed, urged, or acted upon by the medium on that side towards the denser aether, and receives a continual impulse or ply from that side to recede towards the rarer, and so is accelerated, if it move that way, or retarded, if the contrary....  And this may be the ground of all refraction and reflexion....

Now for the cause of these and such like colours made by refraction, the biggest or strongest rays must penetrate the refracting superficies more freely and easily than the weaker, and so be less turned awry by it, that is, less refracted; which is as much as to say, the rays, which make red, are least refrangible, those, which make blue and violet, most refrangible, and others otherwise refrangible according to their colour:  whence, if the rays, which come promiscuously from the sun, be refracted by a prism ... must go to several places on an opposite paper or wall, and so parted, exhibit every one their own colours which they could not do while blended together....

On this ground may all the phenomena of refractions be understood:  but to explain the colours made by reflections, I must further suppose, that, though light be unimaginably swift, yet the aethereal vibrations, excited by a ray, move faster than the ray itself, and so overtake and outrun it one after another.  And this, I suppose, they will think an allowable supposition, who have been inclined to suspect, that these vibrations themselves might be light....  This celerity of the vibrations therefore supposed, if light be incident on a thin skin or plate of any transparent body, the waves, excited by its passage through the first superficies, overtaking it one after another, till it arrive at the second superficies, will cause it to be there reflected or refracted accordingly as the condensed or expanded part of the wave overtakes it there.  If the plate be of such a thickness, that the condensed part of the first wave overtake the ray at the second superficies, it must be reflected there; if double that thickness, that the following rarified part of the wave, that is the space between that and the next wave overtake it, there it must be transmitted; if triple the thickness,  that the condensed part of the second wave overtake it, there it must be reflected, and so where the plate is five, seven, or nine times that thickness, it must be reflected by reason of the third, fourth, or fifth wave, overtaking it at the second superficies; but when it is four, six, or eight times that thickness, so that the ray may be overtaken there by the dilated interval of those waves, it shall be transmitted, and so on...

I should here conclude, but that there is another strange phenomenon of colours, which may deserve to be taken notice of[:]  an odd straying of light, caused in its passage near the edge of a razor, knife, or other opake body in a dark room; the rays which pass very near the edge, being thereby made to stray at all angles into the shadow of the knife.

I should be curious to learn what the Reverend Father Malebranche may have observed about colors.  The subject is important.  There is an experiment of M. Newton which M. Mariotte has challenged, and which should be examined above all.  For M. Newton claims that one can separate the colored rays from one another, so that after this separation refraction does not make them change color any further.

Although M. Newton is not a physicist, his book is very curious and very useful to those who have the right principles in physics, and he is moreover an excellent mathematician.  Everything I believe concerning the properties of light fits all his experiments.

 I fear that M. de La Hire may have tried the experiments of M. Newton on colors with some preconceptions, and may not have used all of the care that could be given to them.  For, since M. Newton has worked at them for so many years, and since one cannot doubt his ability, it is not credible that he has recounted imaginary experiments.  So I should wish that persons with all the necessary leisure, and who are willing to apply themselves sufficiently ... might be entrusted with this inquiry....

Every kind of light has its definite refraction, that is to say, each color in passing from one medium to another, from air, for example, into crystal, is bent by an angle different from that of the other colors.  That is what Mr. Newton, author of this discovery, calls the 'different refrangibility of the colors of light.'  It was principally by this property that he found out all the others; and the ingenious experiments which he used to prove it, could serve by themselves to immortalize a name less celebrated than his.

One of the English scientists ... claims to have demonstrated that light is composed of a multitude of rays with different properties.  Among these rays are those that produce the sensation of red, others the sensation of yellow, still others the sensation of other colors....

We learn, further, that the colors we perceive after the refraction or reflection of light are not produced by some new modifications this light receives, and even that the whiteness of the sun's light is composed of all the principal colors, mingled together in some fashion....Furthermore it is also to be noted that all light of the same kind has its characteristic color and refrangibility, and that this color cannot be altered by any reflections or refractions....

For the rest I do not claim that these new ideas are incontestable and without difficulty.  I only hope that they will contribute to extending further that investigation to which we are invited every day by the objects we see around us.

While Sir Isaac was composing his great work, the Principia, he had also another in hand, as much an original and as new; which, tho' by the title it did not seem so gene[r]al, is yet as extensive by the manner in which he has treated that particular subject.  This work was his Opticks, or treatise of Light and Colours, which first appeared in the year 1704, after he had been making the necessary experiments for thirty years together.

It is no small art to make experiments exactly.  Every matter of fact which offers it self to our consideration is complicated with so many others, which either compound or modify it, that without abundance of skill they cannot be separated; nay without an extraordinary sagacity, the different elements that enter into the composition can hardly be guessed at.  The fact therefore to be considered must be resolved into the different ones of which it is composed; and they themselves are perhaps composed of others; so that if we have not chosen the right road, we may sometimes be engaged in endless Labyrinths.  The Principles and Elements of things seem to have been conceal'd from us by Nature, with as much care as the Causes, and when we attain to the discovery of them, it is a sight entirely new and unexpected.

What Sir Isaac Newton aims at quite through his Opticks, is the Anatomy of Light;  this expression is not too bold since it is no more than the thing it self.  By his experiments, the smallest ray of Light that is convey'd into a dark room, and which cannot be so small, but that it is yet compounded of an infinite number of other rays, is divided and dissected in such manner, that the Elementary rays of which it is composed, are separated from each other, and discover themselves every one tinged with its particular colour, which after this separation can no more be altered.  The first total ray before the dissection, is white, and this whiteness arose from all the particular colours of the Primitive rays.  The separating these rays is so difficult, that when Mariotte undertook it upon the first news of Sir Isaac's experiments, he miscarried in the attempt, even he who had such a genius for experiments, and had been so successful on many other subjects.

No primitive coloured rays could be separated, unless they were such by their nature, that in passing through the same medium, or through the same glass prism, they are refracted at different angles, and by that means separate when they are received at proper distances.  This different Refrangibility of rays, red, yellow, green, blue, purple, and all other colours infinite in number, a property which was never before suspected, and to which we could hardly be led by conjecture, is the fundamental discovery of Sir Isaac Newton's treatise.  The different Refrangibility leads us to the different Reflexibility.  But there is something more; for the rays which fall at the same angle upon a surface are refracted and reflected alternately, with a kind of play only distinguishable to a quick eye, and well assisted by the judgment of the Observer.  The only point, the first idea of which does not entirely belong to Sir Isaac Newton, is, that the rays which pass near the extremities of a body without touching it, do somewhat turn from strait line, which is called Inflection.  But the whole together forms a body of Opticks so perfectly new, that we may henceforward look upon that science as almost wholly owing to this Author....

One advantage of this book, equal perhaps to that of the many new discoveries with which it abounds, is that it furnishes us with an excellent model of proceeding in Experimental Philosophy.  When we are for prying into Nature, we ought to examine her like Sir Isaac, that is, in as accurate and importunate a manner.  Things that almost hide themselves from our enquiries, as being of too abstracted a nature, he knows how to reduce to calculation, tho' such calculations might elude the skill of the best Geometricians, without that Dexterity which was peculiar to himself; and the use which he makes of his geometry, is as artful as the Geometry it self is sublime.

He did not finish his Opticks, because several necessary experiments had been interrupted, and he could not begin them again.  The parts of this building, which he left unfinished, could by no means be carried on but by as able hands as those of the first Architect:  However he hath put such who are inclined to carry on this work in a proper method, and even chalks out to them a way to proceed from Opticks, to a compleat body of Physicks, under the form of Doubts, or Queries proposing a great many designs which will help future Philosophers, or which at least will make a curious history of the Conjectures of a great Philosopher.

The manner of separating the primitive Colours of Light to such a Degree that if any one of the separated Lights be taken apart, its Colour shall be found unchangeable, was not published before Sir Is. Newton's Opticks came abroad.  For want of knowing how this was to be done, some Gentlemen of the English College at Liege, and Monsieur Mariotte in France, and some others took those for primitive Colours, which are made by immitting a Beam of Sun's Light into a dark Room through a small round Hole, and refracting the Beam by a triangular Prism of Glass placed at the Hole.  And by trying the Experiment in this manner, they found that the Colours thus made were capable of change, and thereupon reported that the Experiment did not succeed.  And lately the Editor of the Acta Eruditorum ... desired that Sir Is. Newton would remove this Difficulty....

The Colours in this Case were very vivid and well separated, only the Violet had some pale Light darting from its End, upon account of some Veins in the Prism A, and the Light not coming directly from the Sun, but reflected; which ought not to have been, if the Sun had been low enough to have thrown the Rays a good way into the Room without the Help of a Looking Glass....
The Lens ought to be very good, without Veins or Blebs, and ground to no less a Radius than I mentioned in the Experiment; tho' a Radius of a Foot or two longer is not amiss.  The Prism ought to be of the same Glass as the Object-Glasses of Telescopes, the white Glass, of which Prisms are usually made, being commonly full of Veins.  And the Room in these last Experiments ought to be very dark....

A few Days after, having got very good Prisms made for the purpose of the above mention'd Glass, I made all the Experiments over again before several Members of the Royal Society with better Success; and had the Spectrum very regularly terminated, without any pale Light darting from the Ends of it....

[For further experiments, consult the Opticks] to which I might have referr'd the Reader altogether; but that I was willing to be particular in mentioning such things as ought to be avoided in making the Experiments above-mention'd; some Gentlemen abroad having complained that they had not found the Experiments answer, for want of sufficient Directions in Sir Isaac Newton's Opticks; tho' I had no other Directions than what I found there.

We compare the Newtonian theory of colours to an old castle, which was at first constructed by its architect with youthful precipitation; it was, however, gradually enlarged and equipped by him according to the exigencies of time and circumstances, and moreover was still further fortified and secured in consequence of feuds and hostile demonstrations.

The same system was pursued by his successors and heirs:  their increased wants within, the harassing vigilance of the opponents without, and various accidents compelled them in some places to build near, in others in connexion with the fabric, and thus to extend the original plan.

It became necessary to connect all these incongruous parts and additions by the strangest galleries, halls and passages.  All damages, whether inflicted by the hand of the enemy or the power of time, were quickly made good.  As occasion required, they deepened the moats, raised the walls, and took care there should be no lack of towers, battlements, and embrasures.  This care and these exertions gave rise to a prejudice in favour of the great importance of the fortress, and still upheld that prejudice, although the arts of building and fortification were by this time very much advanced, and people had learnt to construct much better dwellings and defences in other cases.  But the old castle was chiefly held in honour because it had never been taken, because it had repulsed so many assaults, had baffled so many hostile operations, and had always preserved its virgin renown.  This renown, this influence lasts even now:  it occurs to no one that the old castle is become uninhabitable.  Its great duration, its costly construction, are still constantly spoken of.  Pilgrims wend their way to it; hasty sketches of it are shown in all schools, and it is thus recommended to the reverence of susceptible youth.  Meanwhile, the building itself is already abandoned; its only inmates are a few invalids, who in simple seriousness imagine that they are prepared for war.

Thus there is no question here respecting a tedious siege or a doubtful war; so far from it we find this eighth wonder of the world already nodding to its fall as a deserted piece of antiquity, and begin at once, without further ceremony, to dismantle it from gable and roof downwards; that the sun may at last shine into the old nest of rats and owls, and exhibit to the eye of the wondering traveller that labyrinthine, incongruous style of building, with its scanty, make-shift contrivances, the result of accident and emergency, its intentional artifice and clumsy repairs.  Such an inspection will, however, only be possible when wall after wall, arch after arch, is demolished, the rubbish being at once cleared away as well as it can be.

To effect this, and to level the site where it is possible to do so, to arrange the materials thus acquired, so that they can be hereafter again employed for a new building, is the arduous duty we have undertaken in this Second Part.  Should we succeed, by a cheerful application of all possible ability and dexterity, in razing this Bastille, and in gaining a free space, it is thus by no means intended at once to cover the site again and to encumber it with a new structure; we propose rather to make use of this area for the purpose of passing in review a pleasing and varied series of illustrative figures.

670. But we have here chiefly to speak of colour, and observe that the colour of the human skin, in all its varieties, is never an elementary colour, but presents, by means of organic concoction, a highly complicated result....

716. The investigator of nature ... should form to himself a method in accordance with observation, but he should take heed not to reduce observation to mere notion, to substitute words for this notion, and to use and deal with these words as if they were things....

718. The worst that can happen to physical science as well as to many other kinds of knowledge is, that men should treat a secondary phenomenon as a primordial one, and ... seek to explain what is in reality the cause by an effect made to usurp its place....

719. While the observer, the investigator of nature, is thus dissatisfied in finding that the appearances he sees still contradict a received theory, the philosopher can calmly continue to operate in his abstract department on a false result, for no result is so false but that it can be made to appear valid, and form without substance, by some means or other.

720. If, on the other hand, the investigator of nature can attain to the knowledge of that which we have called a primordial phenomenon, he is safe; and the philosopher with him....

724. It will be universally allowed that mathematics, one of the noblest auxiliaries which can be employed by man, has, in one point of view, been of the greatest use to the physical sciences; but that, by false application of its methods, it has, in many respects been prejudicial to them, is also not to be denied; we find it here and there reluctantly admitted.

725. The theory of colours, in particular, has suffered much, and its progress has been incalculably retarded by having been mixed up with optics generally, a science which cannot dispense with mathematics; whereas the theory of colours, in strictness, may be investigated quite independently of optics.

726. But besides this there was an additional evil.  A great mathematician was possessed with an entirely false notion on the physical origin of colours; yet, owing to his great authority as a geometer, the mistakes which he committed as an experimentalist long became sanctioned in the eyes of a world ever fettered in prejudices.

727. The author of the present inquiry has endeavoured throughout to keep the theory of colours distinct from the mathematics, although there are evidently certain points where the assistance of geometry would be desirable.  Had not the unprejudiced mathematicians, with whom he has had, or still has, the good fortune to be acquainted, been prevented by other occupations from making common cause with him, his work would not have wanted some merit in this respect.  But this very want may be in the end advantageous, since it may now become the object of the enlightened mathematician to ascertain where the doctrine of colours is in need of his aid, and how he can contribute the means at his command with a view to the complete elucidation of this branch of physics....

735. If we may at all hope that natural history will gradually be modified by the principle of deducing the ordinary appearances of nature from higher phenomena, the author believes he may have given some hints and introductory views bearing on this object also.  As colour, in its infinite variety, exhibits itself on the surface of living beings, it becomes an important part of the outward indications, by means of which we can discover what passes underneath....

739. True observers of nature, however they may differ in opinion in other respects, will agree that all which presents itself as appearance, all that we meet with as phenomenon, must either indicate an original division which is capable of union, or an original unity which admits of division, and that the phenomenon will present itself accordingly.  To divide the united, to unite the divided, is the life of nature; this is the eternal systole and diastole, the eternal collapsion and expansion, the inspiration and expiration of the world in which we live and move.