Goethe's Theory of Colours

PART II.

PHYSICAL COLOURS.

136.

We give this designation to colours which are produced by certain material mediums: these mediums, however, have no colour themselves, and may be either transparent, semi-transparent yet transmitting light, or altogether opaque.The colours in question are thus produced in the eye through such external given causes, or are merely reflected to the eye when by whatever means they are already produced without us.Although we thus ascribe to them a certain objective character, their distinctive quality still consists in their being transient, and not to be arrested.

137.

They are called by former investigators colores apparentes, fluxi, fugitivi, phantastici, falsi, variantes. They are also called speciosi and emphatici, on account of their striking splendour.They are immediately connected with the physiological colours, and appear to have but little more reality: for, while in the production of the physiological colours the eye itself was chiefly efficient, and we could only perceive the phenomena thus evoked within ourselves, but not without us, we have now to consider the fact that colours are produced in the eye by means of colourless objects; that we thus too have a colourless surface before us which is acted upon as the retina itself is, and that we can perceive the appearance produced upon it without us. In such a process, however, every observation will convince us that we have to do with colours in a progressive and mutable, but not in a final or complete, state.

138.

Hence, in directing our attention to these physical colours, we find it quite possible to place an objective phenomenon beside a subjective one, and often by means of the union of the two successfully to penetrate farther into the nature of the appearance.

139.

Thus, in the observations by which we become acquainted with the physical colours, the eye is not to be considered as acting alone; nor is the light ever to be considered in immediate relation with the eye: but we direct our attention especially to the various effects produced by mediums, those mediums being themselves colourless.

140.

Light under these circumstances may be affected by three conditions. First, when it flashes back from the surface of a medium; in considering which catoptrical experiments invite our attention. Secondly, when it passes by the edge of a medium: the phenomena thus produced were formerly called perioptical; we prefer the term paroptical. Thirdly, when it passes through either a merely light-transmitting or an actually transparent body; thus constituting a class of appearances on which dioptrical experiments are founded. We have called a fourth class of physical colours epoptical, as the phenomena exhibit themselves on the colourless surface of bodies under various conditions, without previous or actual dye (βαφή).—Note K

141.

In examining these categories with reference to our three leading divisions, according to which we consider the phenomena of colours in a physiological, physical, or chemical view, we find that the catoptrical colours are closely connected with the physiological; the paroptical are already somewhat more distinct and independent; the dioptrical exhibit themselves as entirely and strictly physical, and as having a decidedly objective character; the epoptical, although still only apparent, may be considered as the transition to the chemical colours.

142.

If we were desirous of prosecuting our investigation strictly in the order of nature, we ought to proceed according to the classification which has just been made; but in didactic treatises it is not of so much consequence to connect as to duly distinguish the various divisions of a subject, in order that at last, when every single class and case has been presented to the mind, the whole may be embraced in one comprehensive view.We therefore turn our attention forthwith to the dioptrical class, in order at once to give the reader the full impression of the physical colours, and to exhibit their characteristics the more strikingly.

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IX.

DIOPTRICAL COLOURS.

143.

Colours are called dioptrical when a colourless medium is necessary to produce them; the medium must be such that light and darkness can act through it either on the eye or on opposite surfaces.It is thus required that the medium should be transparent, or at least capable, to a certain degree, of transmitting light.

144.

According to these conditions we divide the dioptrical phenomena into two classes, placing in the first those which are produced by means of imperfectly transparent, yet light-transmitting mediums; and in the second such as are exhibited when the medium is in the highest degree transparent.

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X.

DIOPTRICAL COLOURS OF THE FIRST CLASS.

145.

Space, if we assume it to be empty, would have the quality of absolute transparency to our vision.If this space is filled so that the eye cannot perceive that it is so, there exists a more or less material transparent medium, which may be of the nature of air and gas, may be fluid or even solid.

146.

The pure and light-transmitting semi-transparent medium is only an accumulated form of the transparent medium.It may therefore be presented to us in three modes.

147.

The extreme degree of this accumulation is white; the simplest, brightest, first, opaque occupation of space.

148.

Transparency itself, empirically considered, is already the first degree of the opposite state.The intermediate degrees from this point to opaque white are infinite.

149.

At whatever point short of opacity we arrest the thickening medium, it exhibits simple and remarkable phenomena when placed in relation with light and darkness.

150.

The highest degree of light, such as that of the sun, of phosphorus burning in oxygen, is dazzling and colourless: so the light of the fixed stars is for the most part colourless.This light, however, seen through a medium but very slightly thickened, appears to us yellow.If the density of such a medium be increased, or if its volume become greater, we shall see the light gradually assume a yellow-red hue, which at last deepens to a ruby-colour.—Note L

151.

If on the other hand darkness is seen through a semi-transparent medium, which is itself illumined by a light striking on it, a blue colour appears: this becomes lighter and paler as the density of the medium is increased, but on the contrary appears darker and deeper the more transparent the medium becomes: in the least degree of dimness short of absolute transparence, always supposing a perfectly colourless medium, this deep blue approaches the most beautiful violet.

152.

If this effect takes place in the eye as here described, and may thus be pronounced to be subjective, it remains further to convince ourselves of this by objective phenomena.For a light thus mitigated and subdued illumines all objects in like manner with a yellow, yellow-red, or red hue; and, although the effect of darkness through the non-transparent medium does not exhibit itself so powerfully, yet the blue sky displays itself in the camera obscura very distinctly on white paper, as well as every other material colour.

153.

In examining the cases in which this important leading phenomenon appears, we naturally mention the atmospheric colours first: most of these may be here introduced in order.

154.

The sun seen through a certain degree of vapour appears with a yellow disk; the centre is often dazzlingly yellow when the edges are already red.The orb seen through a thick yellow mist appears ruby-red (as was the case in 1794, even in the north); the same appearance is still more decided, owing to the state of the atmosphere, when the scirocco prevails in southern climates: the clouds generally surrounding the sun in the latter case are of the same colour, which is reflected again on all objects.

The red hues of morning and evening are owing to the same cause.The sun is announced by a red light, in shining through a greater mass of vapours.The higher he rises, the yellower and brighter the light becomes.

155.

If the darkness of infinite space is seen through atmospheric vapours illumined by the day-light, the blue colour appears.On high mountains the sky appears by day intensely blue, owing to the few thin vapours that float before the endless dark space: as soon as we descend in the valleys, the blue becomes lighter; till at last, in certain regions, and in consequence of increasing vapours, it altogether changes to a very pale blue.

156.

The mountains, in like manner, appear to us blue; for, as we see them at so great a distance that we no longer distinguish the local tints, and as no light reflected from their surface acts on our vision, they are equivalent to mere dark objects, which, owing to the interposed vapours, appear blue.

157.

So we find the shadowed parts of nearer objects are blue when the air is charged with thin vapours.

158.

The snow-mountains, on the other hand, at a great distance, still appear white, or approaching to a yellowish hue, because they act on our eyes as brightness seen through atmospheric vapour.

159.

The blue appearance at the lower part of the flame of a candle belongs to the same class of phenomena.If the flame be held before a white ground, no blue will be seen, but this colour will immediately appear if the flame is opposed to a black ground. This phenomenon may be exhibited most strikingly with a spoonful of lighted spirits of wine. We may thus consider the lower part of the flame as equivalent to the vapour which, although infinitely thin, is still apparent before the dark surface; it is so thin, that one may easily see to read through it: on the other hand, the point of the flame which conceals objects from our sight is to be considered as a self-illuminating body.

160.

Lastly, smoke is also to be considered as a semi-transparent medium, which appears to us yellow or reddish before a light ground, but blue before a dark one.

161.

If we now turn our attention to fluid mediums, we find that water, deprived in a very slight degree of its transparency, produces the same effects.

162.

The infusion of the lignum nephriticum (guilandina Linnæi), which formerly excited so much attention, is only a semi-transparent liquor, which in dark wooden cups must appear blue, but held towards the sun in a transparent glass must exhibit a yellow appearance.

163.

A drop of scented water, of spirit varnish, of several metallic solutions, may be employed to give various degrees of opacity to water for such experiments.Spirit of soap perhaps answers best.

164.

The bottom of the sea appears to divers of a red colour in bright sunshine: in this case the water, owing to its depth, acts as a semi-transparent medium.Under these circumstances, they find the shadows green, which is the complemental colour.

165.

Among solid mediums the opal attracts our attention first: its colours are, at least, partly to be explained by the circumstance that it is, in fact, a semi-transparent medium, through which sometimes light, sometimes dark, substrata are visible.

166.

For these experiments, however, the opal-glass (vitrum astroides, girasole) is the most desirable material.It is prepared in various ways, and its semi-opacity is produced by metallic oxydes.The same effect is produced also by melting pulverised and calcined bones together with the glass, on which account it is also known by the name of beinglas; but, prepared in this mode, it easily becomes too opaque.

167.

This glass may be adapted for experiments in various ways: it may either be made in a very slight degree non-transparent, in which case the light seen through various layers placed one upon the other may be deepened from the lightest yellow to the deepest red, or, if made originally more opaque, it may be employed in thinner or thicker laminæ.The experiments may be successfully made in both ways: in order, however, to see the bright blue colour, the glass should neither be too opaque nor too thick.For, as it is quite natural that darkness must act weakly through the semi-transparent medium, so this medium, if too thick, soon approaches whiteness.

168.

Panes of glass throw a yellow light on objects through those parts where they happen to be semi-opaque, and these same parts appear blue if we look at a dark object through them.

169.

Smoked glass may be also mentioned here, and is, in like manner, to be considered as a semi-opaque medium.It exhibits the sun more or less ruby-coloured; and, although this appearance may be attributed to the black-brown colour of the soot, we may still convince ourselves that a semi-transparent medium here acts if we hold such a glass moderately smoked, and lit by the sun on the unsmoked side, before a dark object, for we shall then perceive a bluish appearance.

170.

A striking experiment may be made in a dark room with sheets of parchment.If we fasten a piece of parchment before the opening in the window-shutter when the sun shines, it will appear nearly white; by adding a second, a yellowish colour appears, which still increases as more leaves are added, till at last it changes to red.

171.

A similar effect, owing to the state of the crystalline lens in milky cataract, has been already adverted to (131).

172.

Having now, in tracing these phenomena, arrived at the effect of a degree of opacity scarcely capable of transmitting light, we may here mention a singular appearance which was owing to a momentary state of this kind.

A portrait of a celebrated theologian had been painted some years before the circumstance to which we allude, by an artist who was known to have considerable skill in the management of his materials.The very reverend individual was represented in a rich velvet dress, which was not a little admired, and which attracted the eye of the spectator almost more than the face.The picture, however, from the effect of the smoke of lamps and dust, had lost much of its original vivacity.It was, therefore, placed in the hands of a painter, who was to clean it, and give it a fresh coat of varnish.This person began his operations by carefully washing the picture with a sponge: no sooner, however, had he gone over the surface once or twice, and wiped away the first dirt, than to his amazement the black velvet dress changed suddenly to a light blue plush, which gave the ecclesiastic a very secular, though somewhat old-fashioned, appearance.The painter did not venture to go on with his washing: he could not comprehend how a light blue should be the ground of the deepest black, still less how he could so suddenly have removed a glazing colour capable of converting the one tint to the other.

At all events, he was not a little disconcerted at having spoilt the picture to such an extent.Nothing to characterize the ecclesiastic remained but the richly-curled round wig, which made the exchange of a faded plush for a handsome new velvet dress far from desirable. Meanwhile, the mischief appeared irreparable, and the good artist, having turned the picture to the wall, retired to rest with a mind ill at ease. But what was his joy the next morning, when, on examining the picture, he beheld the black velvet dress again in its full splendour. He could not refrain from again wetting a corner, upon which the blue colour again appeared, and after a time vanished. On hearing of this phenomenon, I went at once to see the miraculous picture. A wet sponge was passed over it in my presence, and the change quickly took place. I saw a somewhat faded, but decidedly light blue plush dress, the folds under the arm being indicated by some brown strokes.

I explained this appearance to myself by the doctrine of the semi-opaque medium.The painter, in order to give additional depth to his black, may have passed some particular varnish over it: on being washed, this varnish imbibed some moisture, and hence became semi-opaque, in consequence of which the black underneath immediately appeared blue.Perhaps those who are practically acquainted with the effect of varnishes may, through accident or contrivance, arrive at some means of exhibiting this singular appearance, as an experiment, to those who are fond of investigating natural phenomena. Notwithstanding many attempts, I could not myself succeed in re-producing it.

173.

Having now traced the most splendid instances of atmospheric appearances, as well as other less striking yet sufficiently remarkable cases, to the leading examples of semi-transparent mediums, we have no doubt that attentive observers of nature will carry such researches further, and accustom themselves to trace and explain the various appearances which present themselves in every-day experience on the same principle: we may also hope that such investigators will provide themselves with an adequate apparatus in order to place remarkable facts before the eyes of others who may be desirous of information.

174.

We venture, once for all, to call the leading appearance in question, as generally described in the foregoing pages, a primordial and elementary phenomenon; and we may here be permitted at once to state what we understand by the term.

175.

The circumstances which come under our notice in ordinary observation are, for the most part, insulated cases, which, with some attention, admit of being classed under general leading facts. These again range themselves under theoretical rubrics which are more comprehensive, and through which we become better acquainted with certain indispensable conditions of appearances in detail. From henceforth everything is gradually arranged under higher rules and laws, which, however, are not to be made intelligible by words and hypotheses to the understanding merely, but, at the same time, by real phenomena to the senses. We call these primordial phenomena, because nothing appreciable by the senses lies beyond them, on the contrary, they are perfectly fit to be considered as a fixed point to which we first ascended, step by step, and from which we may, in like manner, descend to the commonest case of every-day experience. Such an original phenomenon is that which has lately engaged our attention. We see on the one side light, brightness; on the other darkness, obscurity: we bring the semi-transparent medium between the two, and from these contrasts and this medium the colours develop themselves, contrasted, in like manner, but soon, through a reciprocal relation, directly tending again to a point of union.[1]

176.

With this conviction we look upon the mistake that has been committed in the investigation of this subject to be a very serious one, inasmuch as a secondary phenomenon has been thus placed higher in order—the primordial phenomenon has been degraded to an inferior place; nay, the secondary phenomenon has been placed at the head, a compound effect has been treated as simple, a simple appearance as compound: owing to this contradiction, the most capricious complication and perplexity have been introduced into physical inquiries, the effects of which are still apparent.

177.

But when even such a primordial phenomenon is arrived at, the evil still is that we refuse to recognise it as such, that we still aim at something beyond, although it would become us to confess that we are arrived at the limits of experimental knowledge.Let the observer of nature suffer the primordial phenomenon to remain undisturbed in its beauty; let the philosopher admit it into his department, and he will find that important elementary facts are a worthier basis for further operations than insulated cases, opinions, and hypotheses.—Note M

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XI.

DIOPTRICAL COLOURS OF THE SECOND CLASS.—REFRACTION.

178.

Dioptrical colours of both classes are closely connected, as will presently appear on a little examination.Those of the first class appeared through semi-transparent mediums, those of the second class will now appear through transparent mediums. But since every substance, however transparent, may be already considered to partake of the opposite quality (as every accumulation of a medium called transparent proves), so the near affinity of the two classes is sufficiently manifest.

179.

We will, however, first consider transparent mediums abstractedly as such, as entirely free from any degree of opacity, and direct our whole attention to a phenomenon which here presents itself, and which is known by the name of refraction.

180.

In treating of the physiological colours, we have already had occasion to vindicate what were formerly called illusions of sight, as the active energies of the healthy and duly efficient eye (2), and we are now again invited to consider similar instances confirming the constancy of the laws of vision.

181.

Throughout nature, as presented to the senses, everything depends on the relation which things bear to each other, but especially on the relation which man, the most important of these, bears to the rest. Hence the world divides itself into two parts, and the human being as subject, stands opposed to the objectThus the practical man exhausts himself in the accumulation of facts, the thinker in speculation; each being called upon to sustain a conflict which admits of no peace and no decision.

182.

But still the main point always is, whether the relations are truly seen.As our senses, if healthy, are the surest witnesses of external relations, so we may be convinced that, in all instances where they appear to contradict reality, they lay the greater and surer stress on true relations.Thus a distant object appears to us smaller; and precisely by this means we are aware of distance.We produced coloured appearances on colourless objects, through colourless mediums, and at the same moment our attention was called to the degree of opacity in the medium.

183.

Thus the different degrees of opacity in so-called transparent mediums, nay, even other physical and chemical properties belonging to them, are known to our vision by means of refraction, and invite us to make further trials in order to penetrate more completely by physical and chemical means into those secrets which are already opened to our view on one side.

184.

Objects seen through mediums more or less transparent do not appear to us in the place which they should occupy according to the laws of perspective.On this fact the dioptrical colours of the second class depend.

185.

Those laws of vision which admit of being expressed in mathematical formulæ are based on the principle that, as light proceeds in straight lines, it must be possible to draw a straight line from the eye to any given object in order that it be seen.If, therefore, a case arises in which the light arrives to us in a bent or broken line, that we see the object by means of a bent or broken line, we are at once informed that the medium between the eye and the object is denser, or that it has assumed this or that foreign nature.

186.

This deviation from the law of right-lined vision is known by the general term of refraction; and, although we may take it for granted that our readers are sufficiently acquainted with its effects, yet we will here once more briefly exhibit it in its objective and subjective point of view.

187.

Let the sun shine diagonally into an empty cubical vessel, so that the opposite side be illumined, but not the bottom: let water be then poured into this vessel, and the direction of the light will be immediately altered; for a part of the bottom is shone upon.At the point where the light enters the thicker medium it deviates from its rectilinear direction, and appears broken: hence the phenomenon is called the breaking (brechung) or refraction.Thus much of the objective experiment.

188.

We arrive at the subjective fact in the following mode:—Let the eye be substituted for the sun: let the sight be directed in like manner diagonally over one side, so that the opposite inner side be entirely seen, while no part of the bottom is visible. On pouring in water the eye will perceive a part of the bottom; and this takes place without our being aware that we do not see in a straight line; for the bottom appears to us raised, and hence we give the term elevation (hebung) to the subjective phenomenon.Some points, which are particularly remarkable with reference to this, will be adverted to hereafter.

189.

Were we now to express this phenomenon generally, we might here repeat, in conformity with the view lately taken, that the relation of the objects is changed or deranged.

190.

But as it is our intention at present to separate the objective from the subjective appearances, we first express the phenomenon in a subjective form, and say,—a derangement or displacement of the object seen, or to be seen, takes place.

191.

But that which is seen without a limiting outline may be thus affected without our perceiving the change.On the other hand, if what we look at has a visible termination, we have an evident indication that a displacement occurs.If, therefore, we wish to ascertain the relation or degree of such a displacement, we must chiefly confine ourselves to the alteration of surfaces with visible boundaries; in other words, to the displacement of circumscribed objects.

192.

The general effect may take place through parallel mediums, for every parallel medium displaces the object by bringing it perpendicularly towards the eye.The apparent change of position is, however, more observable through mediums that are not parallel.

193.

These latter may be perfectly spherical, or may be employed in the form of convex or concave lenses.We shall make use of all these as occasion may require in our experiments.But as they not only displace the object from its position, but alter it in various ways, we shall, in most cases, prefer employing mediums with surfaces, not, indeed, parallel with reference to each other, but still altogether plane, namely, prisms. These have a triangle for their base, and may, it is true, be considered as portions of a lens, but they are particularly available for our experiments, inasmuch as they very perceptibly displace the object from its position, without producing a remarkable distortion.

194.

And now, in order to conduct our observations with as much exactness as possible, and to avoid all confusion and ambiguity, we confine ourselves at first to

SUBJECTIVE EXPERIMENTS,

in which, namely, the object is seen by the observer through a refracting medium.As soon as we have treated these in due series, the objective experiments will follow in similar order.

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XII.

REFRACTION WITHOUT THE APPEARANCE OF COLOUR.

195.

Refraction can visibly take place without our perceiving an appearance of colour.To whatever extent a colourless or uniformly coloured surface may be altered as to its position by refraction, no colour consequent upon refraction appears within it, provided it has no outline or boundary.We may convince ourselves of this in various ways.

196.

Place a glass cube on any larger surface, and look through the glass perpendicularly or obliquely, the unbroken surface opposite the eye appears altogether raised, but no colour exhibits itself.If we look at a pure grey or blue sky or a uniformly white or coloured wall through a prism, the portion of the surface which the eye thus embraces will be altogether changed as to its position, without our therefore observing the smallest appearance of colour.

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XIII.

CONDITIONS OF THE APPEARANCE OF COLOUR.

197.

Although in the foregoing experiments we have found all unbroken surfaces, large or small, colourless, yet at the outlines or boundaries, where the surface is relieved upon a darker or lighter object, we observe a coloured appearance.

198.

Outline, as well as surface, is necessary to constitute a figure or circumscribed object.We therefore express the leading fact thus: circumscribed objects must be displaced by refraction in order to the exhibition of an appearance of colour.

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199.

We place before us the simplest object, a light disk on a dark ground (A).[1] A displacement occurs with regard to this object, if we apparently extend its outline from the centre by magnifying it. This may be done with any convex glass, and in this case we see a blue edge (B).

200.

We can, to appearance, contract the circumference of the same light disk towards the centre by diminishing the object; the edge will then appear yellow (C).This may be done with a concave glass, which, however, should not be ground thin like common eye-glasses, but must have some substance.In order, however, to make this experiment at once with the convex glass, let a smaller black disk be inserted within the light disk on a black ground.If we magnify the black disk on a white ground with a convex glass, the same result takes place as if we diminished the white disk; for we extend the black outline upon the white, and we thus perceive the yellow edge together with the blue edge (D).

201.

These two appearances, the blue and yellow, exhibit themselves in and upon the white: they both assume a reddish hue, in proportion as they mingle with the black.[2]

202.

In this short statement we have described the primordial phenomena of all appearance of colour occasioned by refraction.These undoubtedly may be repeated, varied, and rendered more striking; may be combined, complicated, confused; but, after all, may be still restored to their original simplicity.

203.

In examining the process of the experiment just given, we find that in the one case we have, to appearance, extended the white edge upon the dark surface; in the other we have extended the dark edge upon the white surface, supplanting one by the other, pushing one over the other.We will now endeavour, step by step, to analyse these and similar cases.

204.

If we cause the white disk to move, in appearance, entirely from its place, which can be done effectually by prisms, it will be coloured according to the direction in which it apparently moves, in conformity with the above laws. If we look at the disk a[3] through a prism, so that it appear moved to b, the outer edge will appear blue and blue-red, according to the law of the figure B (fig. 1), the other edge being yellow, and yellow-red, according to the law of the figure C (fig. 1). For in the first case the white figure is, as it were, extended over the dark boundary, and in the other case the dark boundary is passed over the white figure. The same happens if the disk is, to appearance, moved from a to c, from a to d, and so throughout the circle.

205.

As it is with the simple effect, so it is with more complicated appearances.If we look through a horizontal prism (a b[4]) at a white disk placed at some distance behind it at e, the disk will be raised to f, and coloured according to the above law.If we remove this prism, and look through a vertical one (c d) at the same disk, it will appear at h, and coloured according to the same law.If we place the two prisms one upon the other, the disk will appear displaced diagonally, in conformity with a general law of nature, and will be coloured as before; that is, according to its movement in the direction, e.g.:[5]

206.

If we attentively examine these opposite coloured edges, we find that they only appear in the direction of the apparent change of place.A round figure leaves us in some degree uncertain as to this: a quadrangular figure removes all doubt.

207.

The quadrangular figure a,[6] moved in the direction a b or a d exhibits no colour on the sides which are parallel with the direction in which it moves: on the other hand, if moved in the direction a c, parallel with its diagonal, all the edges of the figure appear coloured.[7]

208.

Thus, a former position (203) is here confirmed; viz.to produce colour, an object must be so displaced that the light edges be apparently carried over a dark surface, the dark edges over a light surface, the figure over its boundary, the boundary over the figure.But if the rectilinear boundaries of a figure could be indefinitely extended by refraction, so that figure and background might only pursue their course next, but not over each other, no colour would appear, not even if they were prolonged to infinity.

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XIV.

CONDITIONS UNDER WHICH THE APPEARANCE OF COLOUR INCREASES.

209.

We have seen in the foregoing experiments that all appearance of colour occasioned by refraction depends on the condition that the boundary or edge be moved in upon the object itself, or the object itself over the ground, that the figure should be, as it were, carried over itself, or over the ground.And we shall now find that, by increased displacement of the object, the appearance of colour exhibits itself in a greater degree.This takes place in subjective experiments, to which, for the present, we confine ourselves, under the following conditions.

210.

First, if, in looking through parallel mediums, the eye is directed more obliquely.

Secondly, if the surfaces of the medium are no longer parallel, but form a more or less acute angle.

Thirdly, owing to the increased proportion of the medium, whether parallel mediums be increased in size, or whether the angle be increased, provided it does not attain a right angle.

Fourthly, owing to the distance of the eye armed with a refracting medium from the object to be displaced.

Fifthly, owing to a chemical property that may be communicated to the glass, and which may be afterwards increased in effect.

211.

The greatest change of place, short of considerable distortion of the object, is produced by means of prisms, and this is the reason why the appearance of colour can be exhibited most powerfully through glasses of this form.Yet we will not, in employing them, suffer ourselves to be dazzled by the splendid appearances they exhibit, but keep the above well-established, simple principles calmly in view.

212.

The colour which is outside, or foremost, in the apparent change of an object by refraction, is always the broader, and we will henceforth call this a border: the colour that remains next the outline is the narrower, and this we will call an edge

213.

If we move a dark boundary towards a light surface, the yellow broader border is foremost, and the narrower yellow-red edge follows close to the outline.If we move a light boundary towards a dark surface, the broader violet border is foremost, and the narrower blue edge follows.

214.

If the object is large, its centre remains uncoloured.Its inner surface is then to be considered as unlimited (195): it is displaced, but not otherwise altered: but if the object is so narrow, that under the above conditions the yellow border can reach the blue edge, the space between the outlines will be entirely covered with colour.If we make this experiment with a white stripe on a black ground,[1] the two extremes will presently meet, and thus produce green. We shall then see the following series of colours:—

Yellow-red.
Yellow.
Green.
Blue.
Blue-red.

215.

If we place a black band, or stripe, on white paper,[2] the violet border will spread till it meets the yellow-red edge. In this case the intermediate black is effaced (as the intermediate white was in the last experiment), and in its stead a splendid pure red will appear.[3] The series of colours will now be as follows:—

Blue.
Blue-red.
Red.
Yellow-red.
Yellow.

216.

The yellow and blue, in the first case (214), can by degrees meet so fully, that the two colours blend entirely in green, and the order will then be,

Yellow-red.
Green.
Blue-red.

In the second case (215), under similar circumstances, we see only

Blue.
Red.
Yellow.

This appearance is best exhibited by refracting the bars of a window when they are relieved on a grey sky.[4]

217.

In all this we are never to forget that this appearance is not to be considered as a complete or final state, but always as a progressive, increasing, and, in many senses, controllable appearance.Thus we find that, by the negation of the above five conditions, it gradually decreases, and at last disappears altogether.

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XV.

EXPLANATION OF THE FOREGOING PHENOMENA.

218.

Before we proceed further, it is incumbent on us to explain the first tolerably simple phenomenon, and to show its connexion with the principles first laid down, in order that the observer of nature may be enabled clearly to comprehend the more complicated appearances that follow.

219.

In the first place, it is necessary to remember that we have to do with circumscribed objects.In the act of seeing, generally, it is the circumscribed visible which chiefly invites our observation; and in the present instance, in speaking of the appearance of colour, as occasioned by refraction, the circumscribed visible, the detached object solely occupies our attention.

220.

For our chromatic exhibitions we can, however, divide objects generally into primary and secondaryThe expressions of themselves denote what we understand by them, but our meaning will be rendered still more plain by what follows.

221.

Primary objects may be considered firstly as original, as images which are impressed on the eye by things before it, and which assure us of their reality. To these the secondary images may be opposed as derived images, which remain in the organ when the object itself is taken away; those apparent after-images, which have been circumstantially treated of in the doctrine of physiological colours.

222.

The primary images, again, may be considered as direct images, which, like the original impressions, are conveyed immediately from the object to the eye. In contradistinction to these, the secondary images may be considered as indirect, being only conveyed to us, as it were, at second-hand from a reflecting surface.These are the mirrored, or catoptrical, images, which in certain cases can also become double images:

223.

When, namely, the reflecting body is transparent, and has two parallel surfaces, one behind the other: in such a case, an image may be reflected to the eye from both surfaces, and thus arise double images, inasmuch as the upper image does not quite cover the under one: this may take place in various ways.

Let a playing-card be held before a mirror.We shall at first see the distinct image of the card, but the edge of the whole card, as well as that of every spot upon it, will be bounded on one side with a border, which is the beginning of the second reflection.This effect varies in different mirrors, according to the different thickness of the glass, and the accidents of polishing.If a person wearing a white waistcoat, with the remaining part of his dress dark, stands before certain mirrors, the border appears very distinctly, and in like manner the metal buttons on dark cloth exhibit the double reflection very evidently.

224.

The reader who has made himself acquainted with our former descriptions of experiments (80) will the more readily follow the present statement.The window-bars reflected by plates of glass appear double, and by increased thickness of the glass, and a due adaptation of the angle of reflection, the two reflections may be entirely separated from each other.So a vase full of water, with a plane mirror-like bottom, reflects any object twice, the two reflections being more or less separated under the same conditions. In these cases it is to be observed that, where the two reflections cover each other, the perfect vivid image is reflected, but where they are separated they exhibit only weak, transparent, and shadowy images.

225.

If we wish to know which is the under and which the upper image, we have only to take a coloured medium, for then a light object reflected from the under surface is of the colour of the medium, while that reflected from the upper surface presents the complemental colour.With dark objects it is the reverse; hence black and white surfaces may be here also conveniently employed.How easily the double images assume and evoke colours will here again be striking.

226.

Thirdly, the primary images may be considered as principal images, while the secondary can be, as it were, annexed to these as accessory images. Such an accessory image produces a sort of double form; except that it does not separate itself from the principal object, although it may be said to be always endeavouring to do so. It is with secondary images of this last description that we have to do in prismatic appearances.

227.

A surface without a boundary exhibits no appearance of colour when refracted (195).Whatever is seen must be circumscribed by an outline to produce this effect.In other words a figure, an object, is required; this object undergoes an apparent change of place by refraction: the change is however not complete, not clean, not sharp; but incomplete, inasmuch as an accessory image only is produced.

228.

In examining every appearance of nature, but especially in examining an important and striking one, we should not remain in one spot, we should not confine ourselves to the insulated fact, nor dwell on it exclusively, but look round through all nature to see where something similar, something that has affinity to it, appears: for it is only by combining analogies that we gradually arrive at a whole which speaks for itself, and requires no further explanation.

229.

Thus we here call to mind that in certain cases refraction unquestionably produces double images, as is the case in Iceland spar: similar double images are also apparent in cases of refraction through large rock crystals, and in other instances; phenomena which have not hitherto been sufficiently observed.[1]

230.

But since in the case under consideration (227) the question relates not to double but to accessory images, we refer to a phenomenon already adverted to, but not yet thoroughly investigated.We allude to an earlier experiment, in which it appeared that a sort of conflict took place in regard to the retina between a light object and its dark ground, and between a dark object and its light ground (16).The light object in this case appeared larger, the dark one smaller.

231.

By a more exact observation of this phenomenon we may remark that the forms are not sharply distinguished from the ground, but that they appear with a kind of grey, in some degree, coloured edge; in short, with an accessory image.If, then, objects seen only with the naked eye produce such effects, what may not take place when a dense medium is interposed?It is not that alone which presents itself to us in obvious operation which produces and suffers effects, but likewise all principles that have a mutual relation only of some sort are efficient accordingly, and indeed often in a very high degree.

232.

Thus when refraction produces its effect on an object there appears an accessory image next the object itself: the real form thus refracted seems even to linger behind, as if resisting the change of place; but the accessory image seems to advance, and extends itself more or less in the mode already shown (212-216).

233.

We also remarked (224) that in double images the fainter appear only half substantial, having a kind of transparent, evanescent character, just as the fainter shades of double shadows must always appear as half-shadows.These latter assume colours easily, and produce them readily (69), the former also (80); and the same takes place in the instance of accessory images, which, it is true, do not altogether quit the real object, but still advance or extend from it as half-substantial images, and hence can appear coloured so quickly and so powerfully.

234.

That the prismatic appearance is in fact an accessory image we may convince ourselves in more than one mode. It corresponds exactly with the form of the object itself. Whether the object be bounded by a straight line or a curve, indented or waving, the form of the accessory image corresponds throughout exactly with the form of the object.[2]

235.

Again, not only the form but other qualities of the object are communicated to the accessory image.If the object is sharply relieved from its ground, like white on black, the coloured accessory image in like manner appears in its greatest force.It is vivid, distinct, and powerful; but it is most especially powerful when a luminous object is shown on a dark ground, which may be contrived in various ways.

236.

But if the object is but faintly distinguished from the ground, like grey objects on black or white, or even on each other, the accessory image is also faint, and, when the original difference of tint or force is slight, becomes hardly discernible.

237.

The appearances which are observable when coloured objects are relieved on light, dark, or coloured grounds are, moreover, well worthy of attention.In this case a union takes place between the apparent colour of the accessory image and the real colour of the object; a compound colour is the result, which is either assisted and enhanced by the accordance, or neutralised by the opposition of its ingredients.

238.

But the common and general characteristic both of the double and accessory image is semi-transparence.The tendency of a transparent medium to become only half transparent, or merely light-transmitting, has been before adverted to (147, 148).Let the reader assume that he sees within or through such a medium a visionary image, and he will at once pronounce this latter to be a semi-transparent image.

239.

Thus the colours produced by refraction may be fitly explained by the doctrine of the semi-transparent mediums. For where dark passes over light, as the border of the semi-transparent accessory image advances, yellow appears; and, on the other hand, where a light outline passes over the dark background, blue appears (150, 151).

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240.

The advancing foremost colour is always the broader.Thus the yellow spreads over the light with a broad border, but the yellow-red appears as a narrower stripe and is next the dark, according to the doctrine of augmentation, as an effect of shade.[3]

241.

On the opposite side the condensed blue is next the edge, while the advancing border, spreading as a thinner veil over the black, produces the violet colour, precisely on the principles before explained in treating of semi-transparent mediums, principles which will hereafter be found equally efficient in many other cases.

242.

Since an analysis like the present requires to be confirmed by ocular demonstration, we beg every reader to make himself acquainted with the experiments hitherto adduced, not in a superficial manner, but fairly and thoroughly.We have not placed arbitrary signs before him instead of the appearances themselves; no modes of expression are here proposed for his adoption which may be repeated for ever without the exercise of thought and without leading any one to think; but we invite him to examine intelligible appearances, which must be present to the eye and mind, in order to enable him clearly to trace these appearances to their origin, and to explain them to himself and to others.

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XVI.

DECREASE OF THE APPEARANCE OF COLOUR.

243.

We need only take the five conditions (210) under which the appearance of colour increases in the contrary order, to produce the contrary or decreasing state; it may be as well, however, briefly to describe and review the corresponding modifications which are presented to the eye.

244.

At the highest point of complete junction of the opposite edges, the colours appear as follows (216):—

Yellow-red.	Blue.
Green.	Red.
Blue-red.	Yellow.

245.

Where the junction is less complete, the appearance is as follows (214, 215):—

Yellow-red.	Blue.
Yellow.	Blue-red.
Green.	Red.
Blue.	Yellow-red.
Blue-red.	Yellow.

Here, therefore, the surface still appears completely coloured, but neither series is to be considered as an elementary series, always developing itself in the same manner and in the same degrees; on the contrary, they can and should be resolved into their elements; and, in doing this, we become better acquainted with their nature and character.

246.

These elements then are (199, 200, 201)—

Yellow-red.	Blue.
Yellow.	Blue-red.
White.	Black.
Blue.	Yellow-red.
Blue-red.	Yellow.

Here the surface itself, the original object, which has been hitherto completely covered, and as it were lost, again appears in the centre of the colours, asserts its right, and enables us fully to recognise the secondary nature of the accessory images which exhibit themselves as "edges" and "borders." —Note N.

247.

We can make these edges and borders as narrow as we please; nay, we can still have refraction in reserve after having done away with all appearance of colour at the boundary of the object.

Having now sufficiently investigated the exhibition of colour in this phenomenon, we repeat that we cannot admit it to be an elementary phenomenon.On the contrary, we have traced it to an antecedent and a simpler one; we have derived it, in connexion with the theory of secondary images, from the primordial phenomenon of light and darkness, as affected or acted upon by semi-transparent mediums. Thus prepared, we proceed to describe the appearances which refraction produces on grey and coloured objects, and this will complete the section of subjective phenomena.

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XVII.

GREY OBJECTS DISPLACED BY REFRACTION.

248.

Hitherto we have confined our attention to black and white objects relieved on respectively opposite grounds, as seen through the prism, because the coloured edges and borders are most clearly displayed in such cases.We now repeat these experiments with grey objects, and again find similar results.

249.

As we called black the equivalent of darkness, and white the representative of light (18), so we now venture to say that grey represents half-shadow, which partakes more or less of light and darkness, and thus stands between the two.We invite the reader to call to mind the following facts as bearing on our present view.

250.

Grey objects appear lighter on a black than on a white ground (33); they appear as a light on a black ground, and larger; as a dark on the white ground, and smaller.(16.)

251.

The darker the grey the more it appears as a faint light on black, as a strong dark on white, and vice versâ; hence the accessory images of dark-grey on black are faint, on white strong: so the accessory images of light-grey on white are faint, on black strong.

252.

Grey on black, seen through the prism, will exhibit the same appearances as white on black; the edges are coloured according to the same law, only the borders appear fainter.If we relieve grey on white, we have the same edges and borders which would be produced if we saw black on white through the prism.—Note O.

253.

Various shades of grey placed next each other in gradation will exhibit at their edges, either blue and violet only, or red and yellow only, according as the darker grey is placed over or under.

254.

A series of such shades of grey placed horizontally next each other will be coloured conformably to the same law according as the whole series is relieved, on a black or white ground above or below.

255.

The observer may see the phenomena exhibited by the prism at one glance, by enlarging the plate intended to illustrate this section.[1]

256.

It is of great importance duly to examine and consider another experiment in which a grey object is placed partly on a black and partly on a white surface, so that the line of division passes vertically through the object.

257.

The colours will appear on this grey object in conformity with the usual law, but according to the opposite relation of the light to the dark, and will be contrasted in a line.For as the grey is as a light to the black, so it exhibits the red and yellow above the blue and violet below: again, as the grey is as a dark to the white, the blue and violet appear above the red and yellow below.This experiment will be found of great importance with reference to the next chapter.

XVIII.

COLOURED OBJECTS DISPLACED BY REFRACTION.

258.

An unlimited coloured surface exhibits no prismatic colour in addition to its own hue, thus not at all differing from a black, white, or grey surface. To produce the appearance of colour, light and dark boundaries must act on it either accidentally or by contrivance. Hence experiments and observations on coloured surfaces, as seen through the prism, can only be made when such surfaces are separated by an outline from another differently tinted surface, in short when circumscribed objects are coloured.

259.

All colours, whatever they may be, correspond so far with grey, that they appear darker than white and lighter than black.This shade-like quality of colour (σκιέρον) has been already alluded to (69), and will become more and more evident.If then we begin by placing coloured objects on black and white surfaces, and examine them through the prism, we shall again have all that we have seen exhibited with grey surfaces.

260.

If we displace a coloured object by refraction, there appears, as in the case of colourless objects and according to the same laws, an accessory image.This accessory image retains, as far as colour is concerned, its usual nature, and acts on one side as a blue and blue-red, on the opposite side as a yellow and yellow-red.Hence the apparent colour of the edge and border will be either homogeneous with the real colour of the object, or not so.In the first case the apparent image identifies itself with the real one, and appears to increase it, while, in the second case, the real image may be vitiated, rendered indistinct, and reduced in size by the apparent image.We proceed to review the cases in which these effects are most strikingly exhibited.

261.

If we take a coloured drawing enlarged from the plate, which illustrates this experiment[1], and examine the red and blue squares placed next each other on a black ground, through the prism as usual, we shall find that as both colours are lighter than the ground, similarly coloured edges and borders will appear above and below, at the outlines of both, only they will not appear equally distinct to the eye.

262.

Red is proportionally much lighter on black than blue is.The colours of the edges will therefore appear stronger on the red than on the blue, which here acts as a dark-grey, but little different from black.(251.)

263.

The extreme red edge will identify itself with the vermilion colour of the square, which will thus appear a little elongated in this direction; while the yellow border immediately underneath it only gives the red surface a more brilliant appearance, and is not distinguished without attentive observation.

264.

On the other hand the red edge and yellow border are heterogeneous with the blue square; a dull red appears at the edge, and a dull green mingles with the figure, and thus the blue square seems, at a hasty glance, to be comparatively diminished on this side.

265.

At the lower outline of the two squares a blue edge and a violet border will appear, and will produce the contrary effect; for the blue edge, which is heterogeneous with the warm red surface, will vitiate it and produce a neutral colour, so that the red on this side appears comparatively reduced and driven upwards, and the violet border on the black is scarcely perceptible.

266.

On the other hand, the blue apparent edge will identify itself with the blue square, and not only not reduce, but extend it.The blue edge and even the violet border next it have the apparent effect of increasing the surface, and elongating it in that direction.

267.

The effect of homogeneous and heterogeneous edges, as I have now minutely described it, is so powerful and singular that the two squares at the first glance seem pushed out of their relative horizontal position and moved in opposite directions, the red upwards, the blue downwards.But no one who is accustomed to observe experiments in a certain succession, and respectively to connect and trace them, will suffer himself to be deceived by such an unreal effect.

268.

A just impression with regard to this important phenomenon will, however, much depend on some nice and even troublesome conditions, which are necessary to produce the illusion in question. Paper should be tinged with vermilion or the best minium for the red square, and with deep indigo for the blue square. The blue and red prismatic edges will then unite imperceptibly with the real surfaces where they are respectively homogeneous; where they are not, they vitiate the colours of the squares without producing a very distinct middle tint. The real red should not incline too much to yellow, otherwise the apparent deep red edge above will be too distinct; at the same time it should be somewhat yellow, otherwise the transition to the yellow border will be too observable. The blue must not be light, otherwise the red edge will be visible, and the yellow border will produce a too decided green, while the violet border underneath would not give us the impression of being part of an elongated light blue square.

269.

All this will be treated more circumstantially hereafter, when we speak of the apparatus intended to facilitate the experiments connected with this part of our subject.[2] Every inquirer should prepare the figures himself, in order fairly to exhibit this specimen of ocular deception, and at the same time to convince himself that the coloured edges, even in this case, cannot escape accurate examination.

270.

Meanwhile various other combinations, as exhibited in the plate, are fully calculated to remove all doubt on this point in the mind of every attentive observer.

271.

If, for instance, we look at a white square, next the blue one, on a black ground, the prismatic hues of the opposite edges of the white, which here occupies the place of the red in the former experiment, will exhibit themselves in their utmost force.The red edge extends itself above the level of the blue almost in a greater degree than was the case with the red square itself in the former experiment.The lower blue edge, again, is visible in its full force next the white, while, on the other hand, it cannot be distinguished next the blue square.The violet border underneath is also much more apparent on the white than on the blue.

272.

If the observer now compares these double squares, carefully prepared and arranged one above the other, the red with the white, the two blue squares together, the blue with the red, the blue with the white, he will clearly perceive the relations of these surfaces to their coloured edges and borders.

273.

The edges and their relations to the coloured surfaces appear still more striking if we look at the coloured squares and a black square on a white ground; for in this case the illusion before mentioned ceases altogether, and the effect of the edges is as visible as in any case that has come under our observation.Let the blue and red squares be first examined through the prism.In both the blue edge now appears above; this edge, homogeneous with the blue surface, unites with it, and appears to extend it upwards, only the blue edge, owing to its lightness, is somewhat too distinct in its upper portion; the violet border underneath it is also sufficiently evident on the blue.The apparent blue edge is, on the other hand, heterogeneous with the red square; it is neutralised by contrast, and is scarcely visible; meanwhile the violet border, uniting with the real red, produces a hue resembling that of the peach-blossom.

274.

If thus, owing to the above causes, the upper outlines of these squares do not appear level with each other, the correspondence of the under outlines is the more observable; for since both colours, the red and the blue, are darks compared with the white (as in the former case they were light compared with the black), the red edge with its yellow border appears very distinctly under both. It exhibits itself under the warm red surface in its full force, and under the dark blue nearly as it appears under the black: as may be seen if we compare the edges and borders of the figures placed one above the other on the white ground.

275.

In order to present these experiments with the greatest variety and perspicuity, squares of various colours are so arranged[3] that the boundary of the black and white passes through them vertically. According to the laws now known to us, especially in their application to coloured objects, we shall find the squares as usual doubly coloured at each edge; each square will appear to be split in two, and to be elongated upwards or downwards. We may here call to mind the experiment with the grey figure seen in like manner on the line of division between black and white (257).[4]

276.

A phenomenon was before exhibited, even to illusion, in the instance of a red and blue square on a black ground; in the present experiment the elongation upwards and downwards of two differently coloured figures is apparent in the two halves of one and the same figure of one and the same colour.Thus we are still referred to the coloured edges and borders, and to the effects of their homogeneous and heterogeneous relations with respect to the real colours of the objects.

277.

I leave it to observers themselves to compare the various gradations of coloured squares, placed half on black half on white, only inviting their attention to the apparent alteration which takes place in contrary directions; for red and yellow appear elongated upwards if on a black ground, downwards if on a white; blue, downwards if on a black ground, upwards if on a white.All which, however, is quite in accordance with the diffusely detailed examples above given.

278.

Let the observer now turn the figures so that the before-mentioned squares placed on the line of division between black and white may be in a horizontal series; the black above, the white underneath.On looking at these squares through the prism, he will observe that the red square gains by the addition of two red edges; on more accurate examination he will observe the yellow border on the red figure, and the lower yellow border upon the white will be perfectly apparent.

279.

The upper red edge on the blue square is on the other hand hardly visible; the yellow border next it produces a dull green by mingling with the figure; the lower red edge and the yellow border are displayed in lively colours.

280.

After observing that the red figure in these cases appears to gain by an addition on both sides, while the dark blue, on one side at least, loses something; we shall see the contrary effect produced by turning the same figures upside down, so that the white ground be above, the black below.

281.

For as the homogeneous edges and borders now appear above and below the blue square, this appears elongated, and a portion of the surface itself seems even more brilliantly coloured: it is only by attentive observation that we can distinguish the edges and borders from the colour of the figure itself.

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282.

The yellow and red squares, on the other hand, are comparatively reduced by the heterogeneous edges in this position of the figures, and their colours are, to a certain extent, vitiated.The blue edge in both is almost invisible.The violet border appears as a beautiful peach-blossom hue on the red, as a very pale colour of the same kind on the yellow; both the lower edges are green; dull on the red, vivid on the yellow; the violet border is but faintly perceptible under the red, but is more apparent under the yellow.

283.

Every inquirer should make it a point to be thoroughly acquainted with all the appearances here adduced, and not consider it irksome to follow out a single phenomenon through so many modifying circumstances.These experiments, it is true, may be multiplied to infinity by differently coloured figures, upon and between differently coloured grounds.Under all such circumstances, however, it will be evident to every attentive observer that coloured squares only appear relatively altered, or elongated, or reduced by the prism, because an addition of homogeneous or heterogeneous edges produces an illusion.The inquirer will now be enabled to do away with this illusion if he has the patience to go through the experiments one after the other, always comparing the effects together, and satisfying himself of their correspondence.

Experiments with coloured objects might have been contrived in various ways: why they have been exhibited precisely in the above mode, and with so much minuteness, will be seen hereafter.The phenomena, although formerly not unknown, were much misunderstood; and it was necessary to investigate them thoroughly to render some portions of our intended historical view clearer.

284.

In conclusion, we will mention a contrivance by means of which our scientific readers may be enabled to see these appearances distinctly at one view, and even in their greatest splendour.Cut in a piece of pasteboard five perfectly similar square openings of about an inch, next each other, exactly in a horizontal line: behind these openings place five coloured glasses in the natural order, orange, yellow, green, blue, violet.Let the series thus adjusted be fastened in an opening of the camera obscura, so that the bright sky may be seen through the squares, or that the sun may shine on them; they will thus appear very powerfully coloured.Let the spectator now examine them through the prism, and observe the appearances, already familiar by the foregoing experiments, with coloured objects, namely, the partly assisting, partly neutralising effects of the edges and borders, and the consequent apparent elongation or reduction of the coloured squares with reference to the horizontal line. The results witnessed by the observer in this case, entirely correspond with those in the cases before analysed; we do not, therefore, go through them again in detail, especially as we shall find frequent occasions hereafter to return to the subject. —Note P.

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XIX.

ACHROMATISM AND HYPERCHROMATISM.

285.

Formerly when much that is regular and constant in nature was considered as mere aberration and accident, the colours arising from refraction were but little attended to, and were looked upon as an appearance attributable to particular local circumstances.

286.

But after it had been assumed that this appearance of colour accompanies refraction at all times, it was natural that it should be considered as intimately and exclusively connected with that phenomenon; the belief obtaining that the measure of the coloured appearance was in proportion to the measure of the refraction, and that they must advance pari passu with each other.

287.

If, again, philosophers ascribed the phenomenon of a stronger or weaker refraction, not indeed wholly, but in some degree, to the different density of the medium, (as purer atmospheric air, air charged with vapours, water, glass, according to their increasing density, increase the so-called refraction, or displacement of the object;) so they could hardly doubt that the appearance of colour must increase in the same proportion; and hence took it for granted, in combining different mediums which were to counteract refraction, that as long as refraction existed, the appearance of colour must take place, and that as soon as the colour disappeared, the refraction also must cease.

288.

Afterwards it was, however, discovered that this relation which was assumed to correspond, was, in fact, dissimilar; that two mediums can refract an object with equal power, and yet produce very dissimilar coloured borders.

289.

It was found that, in addition to the physical principle to which refraction was ascribed, a chemical one was also to be taken into the account. We propose to pursue this subject hereafter, in the chemical division of our inquiry, and we shall have to describe the particulars of this important discovery in our history of the doctrine of colours. What follows may suffice for the present.

290.

In mediums of similar or nearly similar refracting power, we find the remarkable circumstance that a greater and lesser appearance of colour can be produced by a chemical treatment; the greater effect is owing, namely, to acids, the lesser to alkalis.If metallic oxydes are introduced into a common mass of glass, the coloured appearance through such glasses becomes greatly increased without any perceptible change of refracting power.That the lesser effect, again, is produced by alkalis, may be easily supposed.

291.

Those kinds of glass which were first employed after the discovery, are called flint and crown glass; the first produces the stronger, the second the fainter appearance of colour.

292.

We shall make use of both these denominations as technical terms in our present statement, and assume that the refractive power of both is the same, but that flint-glass produces the coloured appearance more strongly by one-third than the crown-glass. The diagram (Plate 3, fig.2,) may serve in illustration.

293.

A black surface is here divided into compartments for more convenient demonstration: let the spectator imagine five white squares between the parallel lines a, b, and c, dThe square No.1, is presented to the naked eye unmoved from its place.

294.

But let the square No. 2, seen through a crown-glass prism g, be supposed to be displaced by refraction three compartments, exhibiting the coloured borders to a certain extent; again, let the square No. 3, seen through a flint glass prism h, in like manner be moved downwards three compartments, when it will exhibit the coloured borders by about a third wider than No.2.

295.

Again, let us suppose that the square No. 4, has, like No. 2, been moved downwards three compartments by a prism of crown-glass, and that then by an oppositely placed prism h, of flint-glass, it has been again raised to its former situation, where it now stands.

296.

Here, it is true, the refraction is done away with by the opposition of the two; but as the prism h, in displacing the square by refraction through three compartments, produces coloured borders wider by a third than those produced by the prism g, so, notwithstanding the refraction is neutralised, there must be an excess of coloured border remaining.(The position of this colour, as usual, depends on the direction of the apparent motion (204) communicated to the square by the prism h, and, consequently, it is the reverse of the appearance in the two squares 2 and 3, which have been moved in an opposite direction.)This excess of colour we have called Hyperchromatism, and from this the achromatic state may be immediately arrived at.

297.

For assuming that it was the square No. 5 which was removed three compartments from its first supposed place, like No. 2, by a prism of crown-glass g, it would only be necessary to reduce the angle of a prism of flint-glass h, and to connect it, reversed, to the prism g, in order to raise the square No.5 two degrees or compartments; by which means the Hyperchromatism of the first case would cease, the figure would not quite return to its first position, and yet be already colourless. The prolonged lines of the united prisms, under No. 5, show that a single complete prism remains: again, we have only to suppose the lines curved, and an object-glass presents itself. Such is the principle of the achromatic telescopes.

298.

For these experiments, a small prism composed of three different prisms, as prepared in England, is extremely well adapted.It is to be hoped our own opticians will in future enable every friend of science to provide himself with this necessary instrument.

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XX.

ADVANTAGES OF SUBJECTIVE EXPERIMENTS.—TRANSITION TO THE OBJECTIVE.

299.

We have presented the appearances of colour as exhibited by refraction, first, by means of subjective experiments; and we have so far arrived at a definite result, that we have been enabled to deduce the phenomena in question from the doctrine of semi-transparent mediums and double images.

300.

In statements which have reference to nature, everything depends on ocular inspection, and these experiments are the more satisfactory as they may be easily and conveniently made.Every amateur can procure his apparatus without much trouble or cost, and if he is a tolerable adept in pasteboard contrivances, he may even prepare a great part of his machinery himself.A few plain surfaces, on which black, white, grey, and coloured objects may be exhibited alternately on a light and dark ground, are all that is necessary.The spectator fixes them before him, examines the appearances at the edge of the figures conveniently, and as long as he pleases; he retires to a greater distance, again approaches, and accurately observes the progressive states of the phenomena.

301.

Besides this, the appearances may be observed with sufficient exactness through small prisms, which need not be of the purest glass.The other desirable requisites in these glass instruments will, however, be pointed out in the section which treats of the apparatus.[1]

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302.

A great advantage in these experiments, again, is, that they can be made at any hour of the day in any room, whatever aspect it may have.We have no need to wait for sunshine, which in general is not very propitious to northern observers.

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OBJECTIVE EXPERIMENTS.

303.

The objective experiments, on the contrary, necessarily require the sun-light which, even when it is to be had, may not always have the most desirable relation with the apparatus placed opposite to it.Sometimes the sun is too high, sometimes too low, and withal only a short time in the meridian of the best situated room.It changes its direction during the observation, the observer is forced to alter his own position and that of his apparatus, in consequence of which the experiments in many cases become uncertain.If the sun shines through the prism it exhibits all inequalities, lines, and bubbles in the glass, and thus the appearance is rendered confused, dim, and discoloured.

304.

Yet both kinds of experiments must be investigated with equal accuracy.They appear to be opposed to each other, and yet are always parallel. What one order of experiments exhibits the other exhibits likewise, and yet each has its peculiar capabilities, by means of which certain effects of nature are made known to us in more than one way.

305.

In the next place there are important phenomena which may be exhibited by the union of subjective and objective experiments.The latter experiments again have this advantage, that we can in most cases represent them by diagrams, and present to view the component relations of the phenomena.In proceeding, therefore, to describe the objective experiments, we shall so arrange them that they may always correspond with the analogous subjective examples; for this reason, too, we annex to the number of each paragraph the number of the former corresponding one.But we set out by observing generally that the reader must consult the plates, that the scientific investigator must be familiar with the apparatus in order that the twin-phenomena in one mode or the other may be placed before them.

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XXI.

REFRACTION WITHOUT THE APPEARANCE OF COLOUR.

306 (195, 196).

That refraction may exhibit its effects without producing an appearance of colour, is not to be demonstrated so perfectly in objective as in subjective experiments.We have, it is true, unlimited spaces which we can look at through the prism, and thus convince ourselves that no colour appears where there is no boundary; but we have no unlimited source of light which we can cause to act through the prism.Our light comes to us from circumscribed bodies; and the sun, which chiefly produces our prismatic appearances, is itself only a small, circumscribed, luminous object.

307.

We may, however, consider every larger opening through which the sun shines, every larger medium through which the sun-light is transmitted and made to deviate from its course, as so far unlimited that we can confine our attention to the centre of the surface without considering its boundaries.

308 (197).

If we place a large water-prism in the sun, a large bright space is refracted upwards by it on the plane intended to receive the image, and the middle of this illumined space will be colourless. The same effect may be produced if we make the experiment with glass prisms having angles of few degrees: the appearance may be produced even through glass prisms, whose refracting angle is sixty degrees, provided we place the recipient surface near enough.

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XXII.

CONDITIONS OF THE APPEARANCE OF COLOUR.

309 (198).

Although, then, the illumined space before mentioned appears indeed refracted and moved from its place, but not coloured, yet on the horizontal edges of this space we observe a coloured appearance.That here again the colour is solely owing to the displacement of a circumscribed object may require to be more fully proved.

The luminous body which here acts is circumscribed: the sun, while it shines and diffuses light, is still an insulated object.However small the opening in the lid of a camera obscura be made, still the whole image of the sun will penetrate it. The light which streams from all parts of the sun's disk, will cross itself in the smallest opening, and form the angle which corresponds with the sun's apparent diameter. On the outside we have a cone narrowing to the orifice; within, this apex spreads again, producing on an opposite surface a round image, which still increases in size in proportion to the distance of the recipient surface from the apex. This image, together with all other objects of the external landscape, appears reversed on the white surface in question in a dark room.

310.

How little therefore we have here to do with single sun-rays, bundles or fasces of rays, cylinders of rays, pencils, or whatever else of the kind may be imagined, is strikingly evident.For the convenience of certain diagrams the sun-light may be assumed to arrive in parallel lines, but it is known that this is only a fiction; a fiction quite allowable where the difference between the assumption and the true appearance is unimportant; but we should take care not to suffer such a postulate to be equivalent to a fact, and proceed to further operations on such a fictitious basis.

311.

Let the aperture in the window-shutter be now enlarged at pleasure, let it be made round or square, nay, let the whole shutter be opened, and let the sun shine into the room through the whole window; the space which the sun illumines will always be larger according to the angle which its diameter makes; and thus even the whole space illumined by the sun through the largest window is only the image of the sun plus the size of the opening. We shall hereafter have occasion to return to this.

312 (199).

If we transmit the image of the sun through convex glasses we contract it towards the focus.In this case, according to the laws before explained, a yellow border and a yellow-red edge must appear when the spectrum is thrown on white paper.But as this experiment is dazzling and inconvenient, it may be made more agreeably with the image of the full moon.On contracting this orb by means of a convex glass, the coloured edge appears in the greatest splendour; for the moon transmits a mitigated light in the first instance, and can thus the more readily produce colour which to a certain extent accompanies the subduing of light: at the same time the eye of the observer is only gently and agreeably excited.

313 (200).

If we transmit a luminous image through concave glasses, it is dilated. Here the image appears edged with blue.

314.

The two opposite appearances may be produced by a convex glass, simultaneously or in succession; simultaneously by fastening an opaque disk in the centre of the convex glass, and then transmitting the sun's image.In this case the luminous image and the black disk within it are both contracted, and, consequently, the opposite colours must appear.Again, we can present this contrast in succession by first contracting the luminous image towards the focus, and then suffering it to expand again beyond the focus, when it will immediately exhibit a blue edge.

315 (201).

Here too what was observed in the subjective experiments is again to be remarked, namely, that blue and yellow appear in and upon the white, and that both assume a reddish appearance in proportion as they mingle with the black.

316 (202, 203).

These elementary phenomena occur in all subsequent objective experiments, as they constituted the groundwork of the subjective ones. The process too which takes place is the same; a light boundary is carried over a dark surface, a dark surface is carried over a light boundary. The edges must advance, and as it were push over each other in these experiments as in the former ones.

317 (204).

If we admit the sun's image through a larger or smaller opening into the dark room, if we transmit it through a prism so placed that its refracting angle, as usual, is underneath; the luminous image, instead of proceeding in a straight line to the floor, is refracted upwards on a vertical surface placed to receive it.This is the moment to take notice of the opposite modes in which the subjective and objective refractions of the object appear.

318.

If we look through a prism, held with its refracting angle underneath, at an object above us, the object is moved downwards; whereas a luminous image refracted through the same prism is moved upwards. This, which we here merely mention as a matter of fact for the sake of brevity, is easily explained by the laws of refraction and elevation.

319.

The luminous object being moved from its place in this manner, the coloured borders appear in the order, and according to the laws before explained.The violet border is always foremost, and thus in objective cases proceeds upwards, in subjective cases downwards.

320 (205).

The observer may convince himself in like manner of the mode in which the appearance of colour takes place in the diagonal direction when the displacement is effected by means of two prisms, as has been plainly enough shown in the subjective example; for this experiment, however, prisms should be procured of few degrees, say about fifteen.

321 (206, 207).

That the colouring of the image takes place here too, according to the direction in which it moves, will be apparent if we make a square opening of moderate size in a shutter, and cause the luminous image to pass through a water-prism; the spectrum being moved first in the horizontal and vertical directions, then diagonally, the coloured edges will change their position accordingly.

322 (208).

Whence it is again evident that to produce colour the boundaries must be carried over each other, not merely move side by side.

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XXIII.

CONDITIONS OF THE INCREASE OF COLOUR.

323 (209).

Here too an increased displacement of the object produces a greater appearance of colour.

324 (210).

This increased displacement occurs,

1.By a more oblique direction of the impinging luminous object through mediums with parallel surfaces.

2.By changing the parallel form for one more or less acute angled.

3.By increased proportion of the medium, whether parallel or acute angled; partly because the object is by this means more powerfully displaced, partly because an effect depending on the mere mass co-operates.

4. By the distance of the recipient surface from the refracting medium so that the coloured spectrum emerging from the prism may be said to have a longer way to travel.

5.When a chemical property produces its effects under all these circumstances: this we have already entered into more fully under the head of achromatism and hyperchromatism.

325 (211).

The objective experiments have this advantage that the progressive states of the phenomenon may be arrested and clearly represented by diagrams, which is not the case with the subjective experiments.

326.

We can observe the luminous image after it has emerged from the prism, step by step, and mark its increasing colour by receiving it on a plane at different distances, thus exhibiting before our eyes various sections of this cone, with an elliptical base: again, the phenomenon may at once be rendered beautifully visible throughout its whole course in the following manner:—Let a cloud of fine white dust be excited along the line in which the image passes through the dark space; the cloud is best produced by fine, perfectly dry, hair-powder.The more or less coloured appearance will now be painted on the white atoms, and presented in its whole length and breadth to the eye of the spectator.

327.

By this means we have prepared some diagrams, which will be found among the plates.In these the appearance is exhibited from its first origin, and by these the spectator can clearly comprehend why the luminous image is so much more powerfully coloured through prisms than through parallel mediums.

328 (212).

At the two opposite outlines of the image an opposite appearance presents itself, beginning from an acute angle;[1] the appearance spreads as it proceeds further in space, according to this angle. On one side, in the direction in which the luminous image is moved, a violet border advances on the dark, a narrower blue edge remains next the outline of the image. On the opposite side a yellow border advances into the light of the image itself, and a yellow-red edge remains at the outline.

329 (213).

Here, therefore, the movement of the dark against the light, of the light against the dark, may be clearly observed.

330 (214).

The centre of a large object remains long uncoloured, especially with mediums of less density and smaller angles; but at last the opposite borders and edges touch each other, upon which a green appears in the centre of the luminous image.

331 (215).

Objective experiments have been usually made with the sun's image: an objective experiment with a dark object has hitherto scarcely been thought of.We have, however, prepared a convenient contrivance for this also.Let the large water-prism before alluded to be placed in the sun, and let a round pasteboard disk be fastened either inside or outside.The coloured appearance will again take place at the outline, beginning according to the usual law; the edges will appear, they will spread in the same proportion, and when they meet, red will appear in the centre[2]. An intercepting square may be added near the round disk, and placed in any direction ad libitum, and the spectator can again convince himself of what has been before so often described.

332 (216).

If we take away these dark objects from the prism, in which case, however, the glass is to be carefully cleaned, and hold a rod or a large pencil before the centre of the horizontal prism, we shall then accomplish the complete immixture of the violet border and the yellow-red edge, and see only the three colours, the external blue, and yellow, and the central red.

333.

If again we cut a long horizontal opening in the middle of a piece of pasteboard, fastened on the prism, and then cause the sun-light to pass through it, we shall accomplish the complete union of the yellow border with the blue edge upon the light, and only see yellow-red, green and violet.The details of this are further entered into in the description of the plates.

334 (217).

The prismatic appearance is thus by no means complete and final when the luminous image emerges from the prism.It is then only that we perceive its elements in contrast; for as it increases these contrasting elements unite, and are at last intimately joined.The section of this phenomenon arrested on a plane surface is different at every degree of distance from the prism; so that the notion of an immutable series of colours, or of a pervading similar proportion between them, cannot be a question for a moment.

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XXIV.

EXPLANATION OF THE FOREGOING PHENOMENA.

335 (218).

As we have already entered into this analysis circumstantially while treating of the subjective experiments, as all that was of force there is equally valid here, it will require no long details in addition to show that the phenomena, which are entirely parallel in the two cases, may also be traced precisely to the same sources.

336 (219).

That in objective experiments also we have to do with circumscribed images, has been already demonstrated at large.The sun may shine through the smallest opening, yet the image of the whole disk penetrates beyond.The largest prism may be placed in the open sun-light, yet it is still the sun's image that is bounded by the edges of the refracting surfaces, and produces the accessory images of this boundary.We may fasten pasteboard, with many openings cut in it, before the water-prism, yet we still merely see multiplied images which, after having been moved from their place by refraction, exhibit coloured edges and borders, and in these mere accessory images.

337 (235).

In subjective experiments we have seen that objects strongly relieved from each other produce a very lively appearance of colour, and this will be the case in objective experiments in a much more vivid and splendid degree.The sun's image is the most powerful brightness we know; hence its accessory image will be energetic in proportion, and notwithstanding its really secondary dimmed and darkened character, must be still very brilliant.The colours thrown by the sun-light through the prism on any object, carry a powerful light with them, for they have the highest and most intense source of light, as it were, for their ground.

338.

That we are warranted in calling even these accessory images semi-transparent, thus deducing the appearances from the doctrine of the semi-transparent mediums, will be clear to every one who has followed us thus far, but particularly to those who have supplied themselves with the necessary apparatus, so as to be enabled at all times to witness the precision and vivacity with which semi-transparent mediums act.

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XXV.

DECREASE OF THE APPEARANCE OF COLOUR.

339 (243).

If we could afford to be concise in the description of the decreasing coloured appearance in subjective cases, we may here be permitted to proceed with still greater brevity while we refer to the former distinct statement.One circumstance, only on account of its great importance, may be here recommended to the reader's especial attention as a leading point of our whole thesis.

340 (244, 247).

The decline of the prismatic appearance must be preceded by its separation, by its resolution into its elements.At a due distance from the prism, the image of the sun being entirely coloured, the blue and yellow at length mix completely, and we see only yellow-red, green, and blue-red.If we bring the recipient surface nearer to the refracting medium, yellow and blue appear again, and we see the five colours with their gradations.At a still shorter distance the yellow and blue separate from each other entirely, the green vanishes, and the image itself appears, colourless, between the coloured edges and borders.The nearer we bring the recipient surface to the prism, the narrower the edges and borders become, till at last, when in contact with the prism, they are reduced to nothing.

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XXVI.

GREY OBJECTS.

341 (218).

We have exhibited grey objects as very important to our inquiry in the subjective experiments.They show, by the faintness of the accessory images, that these same images are in all cases derived from the principal object.If we wish here, too, to carry on the objective experiments parallel with the others, we may conveniently do this by placing a more or less dull ground glass before the opening through which the sun's image enters.By this means a subdued image would be produced, which on being refracted would exhibit much duller colours on the recipient plane than those immediately derived from the sun's disk; and thus, even from the intense sun-image, only a faint accessory image would appear, proportioned to the mitigation of the light by the glass.This experiment, it is true, will only again and again confirm what is already sufficiently familiar to us.

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XXVII.

COLOURED OBJECTS.

342 (260).

There are various modes of producing coloured images in objective experiments.In the first place, we can fix coloured glass before the opening, by which means a coloured image is at once produced; secondly, we can fill the water-prism with coloured fluids; thirdly, we can cause the colours, already produced in their full vivacity by the prism, to pass through proportionate small openings in a tin plate, and thus prepare small circumscribed colours for a second operation.This last mode is the most difficult; for owing to the continual progress of the sun, the image cannot be arrested in any direction at will.The second method has also its inconveniences, since not all coloured liquids can be prepared perfectly bright and clear.On these accounts the first is to be preferred, and deserves the more to be adopted because natural philosophers have hitherto chosen to consider the colours produced from the sun-light through the prism, those produced through liquids and glasses, and those which are already fixed on paper or cloth, as exhibiting effects equally to be depended on, and equally available in demonstration.

343.

As it is thus merely necessary that the image should be coloured, so the large water-prism before alluded to affords us the best means of effecting this. A pasteboard screen may be contrived to slide before the large surfaces of the prism, through which, in the first instance, the light passes uncoloured. In this screen openings of various forms may be cut, in order to produce different images, and consequently different accessory images. This being done, we need only fix coloured glasses before the openings, in order to observe what effect refraction produces on coloured images in an objective sense.

344.

A series of glasses may be prepared in a mode similar to that before described (284); these should be accurately contrived to slide in the grooves of the large water-prism.Let the sun then shine through them, and the coloured images refracted upwards will appear bordered and edged, and will vary accordingly: for these borders and edges will be exhibited quite distinctly on some images, and on others will be mixed with the specific colour of the glass, which they will either enhance or neutralize.Every observer will be enabled to convince himself here again that we have only to do with the same simple phenomenon so circumstantially described subjectively and objectively.

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XXVIII.

ACHROMATISM AND HYPERCHROMATISM.

345 (285, 290).

It is possible to make the hyperchromatic and achromatic experiments objectively as well as subjectively.After what has been already stated, a short description of the method will suffice, especially as we take it for granted that the compound prism before mentioned is in the hands of the observer.

346.

Let the sun's image pass through an acute-angled prism of few degrees, prepared from crown-glass, so that the spectrum be refracted upwards on an opposite surface; the edges will appear coloured, according to the constant law, namely, the violet and blue above and outside, the yellow and yellow-red below and within the image.As the refracting angle of this prism is undermost, let another proportionate prism of flint-glass be placed against it, with its refracting angle uppermost.The sun's image will by this means be again moved to its place, where, owing to the excess of the colouring power of the prism of flint-glass, it will still appear a little coloured, and, in consequence of the direction in which it has been moved, the blue and violet will now appear underneath and outside, the yellow and yellow-red above and inside.

347.

If the whole image be now moved a little upwards by a proportionate prism of crown-glass, the hyperchromatism will disappear, the sun's image will be moved from its place, and yet will appear colourless.

348.

With an achromatic object-glass composed of three glasses, this experiment may be made step by step, if we do not mind taking out the glasses from their setting.The two convex glasses of crown-glass in contracting the sun's image towards the focus, the concave glass of flint-glass in dilating the image beyond it, exhibit at the edges the usual colours.A convex glass united with a concave one exhibits the colours according to the law of the latter.If all three glasses are placed together, whether we contract the sun's image towards the focus, or suffer it to dilate beyond the focus, coloured edges never appear, and the achromatic effect intended by the optician is, in this case, again attained.

349.

But as the crown-glass has always a greenish tint, and as a tendency to this hue may be more decided in large and strong object-glasses, and under certain circumstances produce the compensatory red, (which, however, in repeated experiments with several instruments of this kind did not occur to us,) philosophers have resorted to the most extraordinary modes of explaining such a result; and having been compelled, in support of their system, theoretically to prove the impossibility of achromatic telescopes, have felt a kind of satisfaction in having some apparent ground for denying so great an improvement. Of this, however, we can only treat circumstantially in our historical account of these discoveries.

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XXIX.

COMBINATION OF SUBJECTIVE AND OBJECTIVE EXPERIMENTS.

350.

Having shown above (318) that refraction, considered objectively and subjectively, must act in opposite directions, it will follow that if we combine the experiments, the effects will reciprocally destroy each other.

351.

Let the sun's image be thrown upwards on a vertical plane, through a horizontally-placed prism. If the prism is long enough to admit of the spectator also looking through it, he will see the image elevated by the objective refraction again depressed, and in the same place in which it appeared without refraction.

352.

Here a remarkable case presents itself, but at the same time a natural result of a general law.For since, as often before stated, the objective sun's image thrown on the vertical plane is not an ultimate or unchangeable state of the phenomenon, so in the above operation the image is not only depressed when seen through the prism, but its edges and borders are entirely robbed of their hues, and the spectrum is reduced to a colourless circular form.

353.

By employing two perfectly similar prisms placed next each other, for this experiment, we can transmit the sun's image through one, and look through the other.

354.

If the spectator advances nearer with the prism through which he looks, the image is again elevated, and by degrees becomes coloured according to the law of the first prism.If he again retires till he has brought the image to the neutralized point, and then retires still farther away, the image, which had become round and colourless, moves still more downwards and becomes coloured in the opposite sense, so that if we look through the prism and upon the refracted spectrum at the same time, we see the same image coloured according to subjective and objective laws.

355.

The modes in which this experiment may be varied are obvious. If the refracting angle of the prism, through which the sun's image was objectively elevated, is greater than that of the prism through which the observer looks, he must retire to a much greater distance, in order to depress the coloured image so low on the vertical plane that it shall appear colourless, and vice versâ

356.

It will be easily seen that we may exhibit achromatic and hyperchromatic effects in a similar manner, and we leave it to the amateur to follow out such researches more fully.Other complicated experiments in which prisms and lenses are employed together, others again, in which objective and subjective experiments are variously intermixed, we reserve for a future occasion, when it will be our object to trace such effects to the simple phenomena with which we are now sufficiently familiar.

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XXX.

TRANSITION.

357.

In looking back on the description and analysis of dioptrical colours, we do not repent either that we have treated them so circumstantially, or that we have taken them into consideration before the other physical colours, out of the order we ourselves laid down.Yet, before we quit this branch of our inquiry, it may be as well to state the reasons that have weighed with us.

358.

If some apology is necessary for having treated the theory of the dioptrical colours, particularly those of the second class, so diffusely, we should observe, that the exposition of any branch of knowledge is to be considered partly with reference to the intrinsic importance of the subject, and partly with reference to the particular necessities of the time in which the inquiry is undertaken. In our own case we were forced to keep both these considerations constantly in view. In the first place we had to state a mass of experiments with our consequent convictions; next, it was our especial aim to exhibit certain phenomena (known, it is true, but misunderstood, and above all, exhibited in false connection,) in that natural and progressive development which is strictly and truly conformable to observation; in order that hereafter, in our polemical or historical investigations, we might be enabled to bring a complete preparatory analysis to bear on, and elucidate, our general view. The details we have entered into were on this account unavoidable; they may be considered as a reluctant consequence of the occasion. Hereafter, when philosophers will look upon a simple principle as simple, a combined effect as combined; when they will acknowledge the first elementary, and the second complicated states, for what they are; then, indeed, all this statement may be abridged to a narrower form; a labour which, should we ourselves not be able to accomplish it, we bequeath to the active interest of contemporaries and posterity.

359.

With respect to the order of the chapters, it should be remembered that natural phenomena, which are even allied to each other, are not connected in any particular sequence or constant series; their efficient causes act in a narrow circle, so that it is in some sort indifferent what phenomenon is first or last considered; the main point is, that all should be as far as possible present to us, in order that we may embrace them at last from one point of view, partly according to their nature, partly according to generally received methods.

360.

Yet, in the present particular instance, it may be asserted that the dioptrical colours are justly placed at the head of the physical colours; not only on account of their striking splendour and their importance in other respects, but because, in tracing these to their source, much was necessarily entered into which will assist our subsequent enquiries.

361.

For, hitherto, light has been considered as a kind of abstract principle, existing and acting independently; to a certain extent self-modified, and on the slightest cause, producing colours out of itself.To divert the votaries of physical science from this mode of viewing the subject; to make them attentive to the fact, that in prismatic and other appearances we have not to do with light as an uncircumscribed and modifying principle, but as circumscribed and modified; that we have to do with a luminous image; with images or circumscribed objects generally, whether light or dark: this was the purpose we had in view, and such is the problem to be solved.

362.

All that takes place in dioptrical cases,—especially those of the second class which are connected with the phenomena of refraction,—is now sufficiently familiar to us, and will serve as an introduction to what follows.

363.

Catoptrical appearances remind us of the physiological phenomena, but as we ascribe a more objective character to the former, we thought ourselves justified in classing them with the physical examples.It is of importance, however, to remember that here again it is not light, in an abstract sense, but a luminous image that we have to consider.

364.

In proceeding onwards to the paroptrical class, the reader, if duly acquainted with the foregoing facts, will be pleased to find himself once more in the region of circumscribed forms. The shadows of bodies, especially, as secondary images, so exactly accompanying the object, will serve greatly to elucidate analogous appearances.

365.

We will not, however, anticipate these statements, but proceed as heretofore in what we consider the regular course.

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XXXI.

CATOPTRICAL COLOURS.

366.

Catoptrical colours are such as appear in consequence of a mirror-like reflection.We assume, in the first place, that the light itself as well as the surface from which it is reflected, is perfectly colourless.In this sense the appearances in question come under the head of physical colours.They arise in consequence of reflection, as we found the dioptrical colours of the second class appear by means of refraction.Without further general definitions, we turn our attention at once to particular cases, and to the conditions which are essential to the exhibition of these phenomena.

367.

If we unroll a coil of bright steel-wire, and after suffering it to spring confusedly together again, place it at a window in the light, we shall see the prominent parts of the circles and convolutions illumined, but neither resplendent nor iridescent.But if the sun shines on the wire, this light will be condensed into a point, and we perceive a small resplendent image of the sun, which, when seen near, exhibits no colour.On retiring a little, however, and fixing the eyes on this refulgent appearance, we discern several small mirrored suns, coloured in the most varied manner; and although the impression is that green and red predominate, yet, on a more accurate inspection, we find that the other colours are also present.

368.

If we take an eye-glass, and examine the appearance through it, we find the colours have vanished, as well as the radiating splendour in which they were seen, and we perceive only the small luminous points, the repeated images of the sun.We thus find that the impression is subjective in its nature, and that the appearance is allied to those which we have adverted to under the name of radiating halos (100).

369.

We can, however, exhibit this phenomenon objectively.Let a piece of white paper be fastened beneath a small aperture in the lid of a camera-obscura, and when the sun shines through this aperture, let the confusedly-rolled steel-wire be held in the light, so that it be opposite to the paper.The sun-light will impinge on and in the circles of the wire, and will not, as in the concentrating lens of the eye, display itself in a point; but, as the paper can receive the reflection of the light in every part of its surface will be seen in hair-like lines, which are also iridescent.

370.

This experiment is purely catoptrical; for as we cannot imagine that the light penetrates the surface of the steel, and thus undergoes a change, we are soon convinced that we have here a mere reflection which, in its subjective character, is connected with the theory of faintly acting lights, and the after-image of dazzling lights, and as far as it can be considered objective, announces even in the minutest appearances, a real effect, independent of the action and reaction of the eye.

371.

We have seen that to produce these effects not merely light but a powerful light is necessary; that this powerful light again is not an abstract and general quality, but a circumscribed light, a luminous image. We can convince ourselves still further of this by analogous cases.

372.

A polished surface of silver placed in the sun reflects a dazzling light, but in this case no colour is seen.If, however, we slightly scratch the surface, an iridescent appearance, in which green and red are conspicuous, will be exhibited at a certain angle.In chased and carved metals the effect is striking: yet it may be remarked throughout that, in order to its appearance, some form, some alternation of light and dark must co-operate with the reflection; thus a window-bar, the stem of a tree, an accidentally or purposely interposed object produces a perceptible effect.This appearance, too, may be exhibited objectively in the camera-obscura.

373.

If we cause a polished plated surface to be so acted on by aqua fortis that the copper within is touched, and the surface itself thus rendered rough, and if the sun's image be then reflected from it, the splendour will be reverberated from every minutest prominence, and the surface will appear iridescent.So, if we hold a sheet of black unglazed paper in the sun, and look at it attentively, it will be seen to glisten in its minutest points with the most vivid colours.

374.

All these examples are referable to the same conditions.In the first case the luminous image is reflected from a thin line; in the second probably from sharp edges; in the third from very small points.In all a very powerful and circumscribed light is requisite.For all these appearances of colour again it is necessary that the eye should be at a due distance from the reflecting points.

375.

If these observations are made with the microscope, the appearance will be greatly increased in force and splendour, for we then see the smallest portion of the surfaces, lit by the sun, glittering in these colours of reflection, which, allied to the hues of refraction, now attain their highest degree of brilliancy.In such cases we may observe a vermiform iridescence on the surface of organic bodies, the further description of which will be given hereafter.

376.

Lastly, the colours which are chiefly exhibited in reflection are red and green, whence we may infer that the linear appearance especially consists of a thin line of red, bounded by blue on one side and yellow on the other. If these triple lines approach very near together, the intermediate space must appear green; a phenomenon which will often occur to us as we proceed.

377.

We frequently meet with these colours in nature.The colours of the spider's web might be considered exactly of the same class with those reflected from the steel wire, except that the non-translucent quality of the former is not so certain as in the case of steel; on which account some have been inclined to class the colours of the spider's web with the phenomena of refraction.

378.

In mother-of-pearl we perceive infinitely fine organic fibres and lamellæ in juxta-position, from which, as from the scratched silver before alluded to, varied colours, but especially red and green, may arise.

379.

The changing colours of the plumage of birds may also be mentioned here, although in all organic instances a chemical principle and an adaptation of the colour to the structure may be assumed; considerations to which we shall return in treating of chemical colours.

380.

That the appearances of objective halos also approximate catoptrical phenomena will be readily admitted, while we again do not deny that refraction as well may here come into the account.For the present we restrict ourselves to one or two observations; hereafter we may be enabled to make a fuller application of general principles to particular examples.

381.

We first call to mind the yellow and red circles produced on a white or grey wall by a light placed near it (88).Light when reflected appears subdued, and a subdued light excites the impression of yellow, and subsequently of red.

382.

Let the wall be illumined by a candle placed quite close to it.The farther the light is diffused the fainter it becomes; but it is still the effect of the flame, the continuation of its action, the dilated effect of its image.We might, therefore, very fairly call these circles reiterated images, because they constitute the successive boundaries of the action of the light, and yet at the same time only present an extended image of the flame.

383.

If the sky is white and luminous round the sun owing to the atmosphere being filled with light vapours; if mists or clouds pass before the moon, the reflection of the disk mirrors itself in them; the halos we then perceive are single or double, smaller or greater, sometimes very large, often colourless, sometimes coloured.

384.

I witnessed a very beautiful halo round the moon the 15th of November, 1799, when the barometer stood high; the sky was cloudy and vapoury.The halo was completely coloured, and the circles were concentric round the light as in subjective halos.That this halo was objective I was presently convinced by covering the moon's disk, when the same circles were nevertheless perfectly visible.

385.

The different extent of the halos appears to have a relation with the proximity or distance of the vapour from the eye of the observer.

386.

As window-panes lightly breathed upon increase the brilliancy of subjective halos, and in some degree give them an objective character, so, perhaps, with a simple contrivance in winter, during a quickly freezing temperature, a more exact definition of this might be arrived at.

387.

How much reason we have in considering these circles to insist on the image and its effects, is apparent in the phenomenon of the so-called double suns. Similar double images always occur in certain points of halos and circles, and only present in a circumscribed form what takes place in a more general way in the whole circle. All this will be more conveniently treated in connexion with the appearance of the rainbow. —Note Q

388.

In conclusion it is only necessary to point out the affinity between the catoptrical and paroptical colours.

We call those paroptical colours which appear when the light passes by the edge of an opaque colourless body.How nearly these are allied to the dioptrical colours of the second class will be easily seen by those who are convinced with us that the colours of refraction take place only at the edges of objects. The affinity again between the catoptrical and paroptical colours will be evident in the following chapter.

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XXXII.

PAROPTICAL COLOURS.

389.

The paroptical colours have been hitherto called peri-optical, because a peculiar effect of light was supposed to take place as it were round the object, and was ascribed to a certain flexibility of the light to and from the object.

390.

These colours again may be divided into subjective and objective, because they appear partly without us, as it were, painted on surfaces, and partly within us, immediately on the retina.In this chapter we shall find it more to our purpose to take the objective cases first, since the subjective are so closely connected with other appearances already known to us, that it is hardly possible to separate them.

391.

The paroptical colours then are so called because the light must pass by an outline or edge to produce them. They do not, however, always appear in this case; to produce the effect very particular conditions are necessary besides.

392.

It is also to be observed that in this instance again light does not act as an abstract diffusion (361), the sun shines towards an edge.The volume of light poured from the sun-image passes by the edge of a substance, and occasions shadows.Within these shadows we shall presently find colours appear.

393.

But, above all, we should make the experiments and observations that bear upon our present inquiry in the fullest light.We, therefore, place the observer in the open air before we conduct him to the limits of a dark room.

394.

A person walking in sun-shine in a garden, or on any level path, may observe that his shadow only appears sharply defined next the foot on which he rests; farther from this point, especially round the head, it melts away into the bright ground.For as the sun-light proceeds not only from the middle of the sun, but also acts cross-wise from the two extremes of every diameter, an objective parallax takes place which produces a half-shadow on both sides of the object.

395.

If the person walking raises and spreads his hand, he distinctly sees in the shadow of each finger the diverging separation of the two half-shadows outwards, and the diminution of the principal shadow inwards, both being effects of the cross action of the light.

396.

This experiment may be repeated and varied before a smooth wall, with rods of different thicknesses, and again with balls; we shall always find that the farther the object is removed from the surface of the wall, the more the weak double shadow spreads, and the more the forcible main shadow diminishes, till at last the main shadow appears quite effaced, and even the double shadows become so faint, that they almost disappear; at a still greater distance they are, in fact, imperceptible.

397.

That this is caused by the cross-action of the light we may easily convince ourselves; for the shadow of a pointed object plainly exhibits two points.We must thus never lose sight of the fact that in this case the whole sun-image acts, produces shadows, changes them to double shadows, and finally obliterates them.

398.

Instead of solid bodies let us now take openings cut of various given sizes next each other, and let the sun shine through them on a plane surface at some little distance; we shall find that the bright image produced by the sun on the surface, is larger than the opening; this is because one edge of the sun shines towards the opposite edge of the opening, while the other edge of the disk is excluded on that side.Hence the bright image is more weakly lighted towards the edges.

399.

If we take square openings of any size we please, we shall find that the bright image on a surface nine feet from the opening, is on every side about an inch larger than the opening; thus nearly corresponding with the angle of the apparent diameter of the sun.

400.

That the brightness should gradually diminish towards the edges of the image is quite natural, for at last only a minimum of the light can act cross-wise from the sun's circumference through the edge of the aperture.

401.

Thus we here again see how much reason we have in actual observation to guard against the assumption of parallel rays, bundles and fasces of rays, and the like hypothetical notions.

402.

We might rather consider the splendour of the sun, or of any light, as an infinite specular multiplication of the circumscribed luminous image, whence it may be explained that all square openings through which the sun shines, at certain distances, according as the apertures are greater or smaller, must give a round image of light.

403.

The above experiments may be repeated through openings of various shapes and sizes, and the same effect will always take place at proportionate distances.In all these cases, however, we may still observe that in a full light and while the sun merely shines past an edge, no colour is apparent.

404.

We therefore proceed to experiments with a subdued light, which is essential to the appearance of colour.Let a small opening be made in the window-shutter of a dark room; let the crossing sun-light which enters, be received on a surface of white paper, and we shall find that the smaller the opening is, the dimmer the light image will be. This is quite obvious, because the paper does not receive light from the whole sun, but partially from single points of its disk.

405.

If we look attentively at this dim image of the sun, we find it still dimmer towards the outlines where a yellow border is perceptible.The colour is still more apparent if a vapour or a transparent cloud passes before the sun, thus subduing and dimming its brightness.The halo on the wall, the effect of the decreasing brightness of a light placed near it, is here forced on our recollection.(88.)

406.

If we examine the image more accurately, we perceive that this yellow border is not the only appearance of colour; we can see, besides, a bluish circle, if not even a halo-like repetition of the coloured border.If the room is quite dark, we discern that the sky next the sun also has its effect: we see the blue sky, nay, even the whole landscape, on the paper, and are thus again convinced that as far as regards the sun, we have here only to do with a luminous image.

407.

If we take a somewhat larger square opening, so large that the image of the sun shining through it does not immediately become round, we may distinctly observe the half-shadows of every edge or side, the junction of these in the corners, and their colours; just as in the above-mentioned appearance with the round opening.

408.

We have now subdued a parallactic light by causing it to shine through small apertures, but we have not taken from it its parallactic character; so that it can produce double shadows of bodies, although with diminished power.These double shadows which we have hitherto been describing, follow each other in light and dark, coloured and colourless circles, and produce repeated, nay, almost innumerable halos.These effects have been often represented in drawings and engravings.By placing needles, hairs, and other small bodies, in the subdued light, the numerous halo-like double shadows may be increased; thus observed, they have been ascribed to an alternating flexile action of the light, and the same assumption has been employed to explain the obliteration of the central shadow, and the appearance of a light in the place of the dark.

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409.

For ourselves, we maintain that these again are parallactic double shadows, which appear edged with coloured borders and halos.

410.

After having seen and investigated the foregoing phenomena, we can proceed to the experiments with knife-blades,[1] exhibiting effects which may be referred to the contact and parallactic mutual intersection of the half-shadows and halos already familiar to us.

411.

Lastly, the observer may follow out the experiments with hairs, needles, and wires, in the half-light produced as before described by the sun, as well as in that derived from the blue sky, and indicated on the white paper.He will thus make himself still better acquainted with the true nature of this phenomenon.

412.

But since in these experiments everything depends on our being persuaded of the parallactic action of the light, we can make this more evident by means of two sources of light, the two shadows from which intersect each other, and may be altogether separated.By day this may be contrived with two small openings in a window-shutter; by night, with two candles. There are even accidental effects in interiors, on opening and closing shutters, by means of which we can better observe these appearances than with the most careful apparatus. But still, all and each of these may be reduced to experiment by preparing a box which the observer can look into from above, and gradually diminishing the openings after having caused a double light to shine in. In this case, as might be expected, the coloured shadow, considered under the physiological colours, appears very easily.

413.

It is necessary to remember, generally, what has been before stated with regard to the nature of double shadows, half-lights, and the like.Experiments also should especially be made with different shades of grey placed next each other, where every stripe will appear light by a darker, and dark by a lighter stripe next it.If at night, with three or more lights, we produce shadows which cross each other successively, we can observe this phenomenon very distinctly, and we shall be convinced that the physiological case before more fully treated, here comes into the account (38).

414.

To what extent the appearances that accompany the paroptical colours, may be derived from the doctrine of subdued lights, from half-shadows, and from the physiological disposition of the retina, or whether we shall be forced to take refuge in certain intrinsic qualities of light, as has hitherto been done, time may teach. Suffice it here to have pointed out the conditions under which the paroptical colours appear, and we may hope that our allusion to their connexion with the facts before adduced by us will not remain unnoticed by the observers of nature.

415.

The affinity of the paroptical colours with the dioptrical of the second class will also be readily seen and followed up by every reflecting investigator.Here, as in those instances, we have to do with edges or boundaries; here, as in those instances, with a light, which appears at the outline.How natural, therefore, it is to conclude that the paroptical effects may be heightened, strengthened, and enriched by the dioptrical.Since, however, the luminous image actually shines through the medium, we can here only have to do with objective cases of refraction: it is these which are strictly allied to the paroptical cases.The subjective cases of refraction, where we see objects through the medium, are quite distinct from the paroptical. We have already recommended them on account of their clearness and simplicity.

416.

The connexion between the paroptical colours and the catoptrical may be already inferred from what has been said: for as the catoptrical colours only appear on scratches, points, steel-wire, and delicate threads, so it is nearly the same case as if the light shone past an edge.The light must always be reflected from an edge in order to produce colour.Here again, as before pointed out, the partial action of the luminous image and the subduing of the light are both to be taken into the account.

417.

We add but few observations on the subjective paroptical colours, because these may be classed partly with the physiological colours, partly with the dioptrical of the second order.The greater part hardly seem to belong here, but, when attentively considered, they still diffuse a satisfactory light over the whole doctrine, and establish its connexion.

418.

If we hold a ruler before the eyes so that the flame of a light just appears above it, we see the ruler as it were indented and notched at the place where the light appears. This seems deducible from the expansive power of light acting on the retina (18).

419.

The same phenomenon on a large scale is exhibited at sun-rise; for when the orb appears distinctly, but not too powerfully, so that we can still look at it, it always makes a sharp indentation in the horizon.

420.

If, when the sky is grey, we approach a window, so that the dark cross of the window-bars be relieved on the sky; if after fixing the eyes on the horizontal bar we bend the head a little forward; on half closing the eyes as we look up, we shall presently perceive a bright yellow-red border under the bar, and a bright light-blue one above it.The duller and more monotonous the grey of the sky, the more dusky the room, and, consequently, the more previously unexcited the eye, the livelier the appearance will be; but it may be seen by an attentive observer even in bright daylight.

421.

If we move the head backwards while half closing the eyes, so that the horizontal bar be seen below, the phenomenon will appear reversed. The upper edge will appear yellow, the under edge blue.

422.

Such observations are best made in a dark room.If white paper is spread before the opening where the solar microscope is commonly fastened, the lower edge of the circle will appear blue, the upper yellow, even while the eyes are quite open, or only by half-closing them so far that a halo no longer appears round the white.If the head is moved backwards the colours are reversed.

423.

These phenomena seem to prove that the humours of the eye are in fact only really achromatic in the centre where vision takes place, but that towards the circumference, and in unusual motions of the eyes, as in looking horizontally when the head is bent backwards or forwards, a chromatic tendency remains, especially when distinctly relieved objects are thus looked at.Hence such phenomena may be considered as allied to the dioptrical colours of the second class.

424.

Similar colours appear if we look on black and white objects, through a pin-hole in a card. Instead of a white object we may take the minute light aperture in the tin plate of a camera obscura, as prepared for paroptical experiments.

425.

If we look through a tube, the farther end of which is contracted or variously indented, the same colours appear.

426.

The following phenomena appear to me to be more nearly allied to the paroptical appearances.If we hold up a needle near the eye, the point appears double.A particularly remarkable effect again is produced if we look towards a grey sky through the blades of knives prepared for paroptical experiments.We seem to look through a gauze; a multitude of threads appear to the eye; these are in fact only the reiterated images of the sharp edges, each of which is successively modified by the next, or perhaps modified in a parallactic sense by the oppositely acting one, the whole mass being thus changed to a thread-like appearance.

427.

Lastly, it is to be remarked that if we look through the blades towards a minute light in the window-shutter, coloured stripes and halos appear on the retina as on the paper.

428.

The present chapter may be here terminated, the less reluctantly, as a friend has undertaken to investigate this subject by further experiments.In our recapitulation, in the description of the plates and apparatus, we hope hereafter to give an account of his observations.[2]

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