Scientific Memoirs/1/Memoirs on Colours in general, and particularly on a new Chromatic Scale deduced from Metallochromy for Scientific and Practical Purposes

by Leopoldo Nobili

Article V.

Memoir on Colours in general, and particularly on a new Chromatic Scale deduced from Metallochromy for Scientific and Practical Purposes. By M. Leopold Nobili of Reggio.

From the Bibliothèque Universelle des Sciences, &c. vol. xliv. xlv. Geneva.
(1830, vol. ii. p. 337, vol. iii. p. 35, Aug. and Sept.)

I DISCOVERED in 1826 a new class of facts and gave them the name of electro-chemical appearances. The following is one of the principal experiments connected with those facts.

A plate of platina is laid horizontally at the bottom of a vessel made of glass or china. A platina point is vertically suspended over this in such a manner that the distance between the point and the plate may be about half a line. A solution of acetate of lead is next poured into the vessel so as not only to cover the plate, but to rise two or three lines higher than the point. The plate and the point are now brought into communication, the former with the positive and the latter with the negative pole of an electric pile. At the moment when the voltaic circuit is closed, a series of rings similar to those formed at the centre of the Newtonian lenses is to be seen on the surface of the plate precisely under the point. This fact, which could not fail to strike any one observing it for the first time, led me to the discovery of others, which I have communicated to the public in four successive Memoirs^[1]. I foresaw from the very first the advantages that the arts were likely to derive from this new method of colouring metals; but it was not until toward the close of 1827 that I began to attend seriously to its application. My first attempts I forbear to mention, being more desirous to call attention to the productions which I obtained in the course of 1828, and in the November of that year presented to the French Institute. These productions consisted of several plates of coloured metal, and excited the particular attention of that illustrious body by the beauty and vividness of their tints, the precision of their outlines, and the softness of their blendings^[2].

The invention being now so far advanced as to be entitled to a place among the arts, it was thought that it should have its distinctive appellation, and by the advice of the same illustrious body, that of Metallochromy was adopted. Since that period I have made such improvements in my method that the first results, though they appeared satisfactory at the time, make but a sorry figure when compared with those now obtained. One of the great difficulties consisted in the necessity of producing a uniformity of tint on plates of certain dimensions; for, my colours being obtained by the effect of very thin plates applied to the surface of metals, it is easy to conceive how hard it was to preserve such plates of a uniform thickness over the whole of an extensive surface. Great however as the difficulties were, I thought I owed it both to art and to science to do my utmost to surmount them. I thought it due to art, because this would be extended by means of the uniformity of the tints, and to science, because in the tints produced by plates of a particular thickness the experimental philosopher would find the means of investigating with peculiar advantage the nature and properties of colours.

At present I abstain from all detail relative to the method of obtaining the homogeneous tints. The principle of the electro-chemical appearances seems now so fertile in results that its full development requires a particular treatise. It will be a work of considerable labour, and I have already commenced it by collecting and classifying all the materials of this new department of physics in which, besides the other methods of coloration, I intend to explain in detail those connected with the production of uniform tints. In this place it is sufficient to state that these tints are produced by substituting plates for the platina point which forms the coloured rings.

The object of this Memoir is more limited. It is to arrange these homogeneous tints in their natural order, so that they may form a scale or gamut which I shall henceforth designate by the epithet chromatic.

Science never consults its interests so truly as when it aims at some useful object connected with the arts. Such, I would fain hope, will be the direction of these researches. Artists, it is true, being generally unacquainted with physical theories, will find it difficult to follow me in my inquiries. My labour, however will not be altogether useless to them, if, as I intended, I have succeeded in treating certain parts of the subject in a manner likely to bring them within the reach of every understanding.

The formation of the chromatic scales requires considerable time and a hand well practised in work of this description. As they might be generally useful I regret that the difficulty of their construction renders a prompt and wide-spread circulation of them impossible. I have tried and am still trying to have them copied in oil and water colours, but the attempts hitherto made give little or no hope that the best executed copies can give more than an imperfect idea of the original colours.

The effect produced by these tints when disposed in the order set forth in the scale baffles description; it bears a resemblance however to that produced on the ear by a scale of semitones executed by a perfect voice. I have shown my scale to several, and especially to those erudite and learned persons who have favoured me with a passing visit at Reggio. In all it excited but one feeling of delight. So gradual indeed is the transition from one tint to another and such the harmony with which they are blended, that if the eye be accidentally turned away, it reverts in a moment as if moved by an irresistible desire to gaze still longer on the display. This statement is no exaggeration. It is but the mere fact, in respect to which a language much more glowing would be perfectly consistent with truth: so overpowering is the charm which, if I may use the expression, pervades the scale of our coloured plates.

Chromatic Scale.

This scale consists of forty-four tints, each of which is applied to a plate of steel. A Table subjoined to this Memoir exhibits the forty-four plates arranged one under the other in a column, and opposite to each number is the name of its peculiar tint. These tints are disposed in the same order as the layers or thin plates by which they are produced. The colour of the thinnest plate is placed first, and the others follow in the order of the progressively increasing thickness of the plates^[3]. In this arrangement I cannot be mistaken, because the layers or thin plates which produce the several colours are all applied by the same electro-chemical process. The pile, the solution, the distances remain exactly the same. There is nothing variable but the duration of the action, which in respect to the layer No. 1. is very short, a little longer in respect to the second, and increases progressively from the lowest to the highest number. Other criterions also contribute to verify the accuracy with which its place is assigned to each tint.

These colours are produced by very thin layers or plates analogous to those which produce the colours in soap-bubbles and the rings observed by Newton around the point of contact of two slightly convex glasses or lenses. The order of the latter colours should therefore correspond exactly with that of my scale. It does so in fact; but that the correspondence may be perceived, it will be necessary first to rectify some errors which have arisen respecting the rings of Newton, either in consequence of their small dimensions, or of their having been examined under the influence of some prejudice.

Our scale embraces the extent of the first four rings, and consists, as we have already stated, of fourty-four tints.

The tints of No.	1	to No.	10	(inclusive) correspond to the	1st	ring.
	11		28		2nd	—
	29		38		3rd	—
	39		44		4th	—

Fundamental Principle.

It is well known that the colours of the thin layers around the point of contact of Newton's glasses are formed in the following manner. At the point which allows all the rays of the transmitted light to pass there appears a dark speck, and this remains the same whatever may be the quality of the light. If the incident light is white, the central speck is succeeded by several irises or concentric rings. If the light is homogeneous or produced by one species of rays, the irises are changed into rings of the same colour as the incident rays, and separated from each other by dark intervals. These rings, whatever be their colour, have their commencement all at the verge of the central speck, but they occupy different spaces. The violet rings are the narrowest and nearest; the red are the widest and most distant; the rings of the intermediate colours are of intermediate dimensions and at intermediate distances. When the incident light is white, the series of homogeneous rings are formed simultaneously and overlap each other; all the colours are intermixed in different proportions, and none stands isolated. It is to these combinations that we are to attribute the tints of the thin layers which we are about to analyse on our scale.

First Ring.— From No. 1 to No. 10 (inclusive).

The Scale commences with the blond^[4] colour: of this there are four gradations, the first of which is silvery, and 2, 3, 4 are gradually deeper. The blond is succeeded by the tawny^[5]. Of this there are three species, 5, 6, 7; the last of which is called a copper-red on account of the analogy it bears to the colour of that metal. No. 8 is an ochre colour, No. 9 a violaceous ochre, and No. 10 a violaceous fire-red.

According to Newton the first ring should be composed of

Blue, White, Yellow, Orange, Red.

I find neither blue, nor the tints placed after the white and designated as yellow and orange. It seems to me that the tints of Newton's ring may be defined easily enough. They differ essentially from yellow and orange, and are in reality nothing else than the blond and tawny colours of our scale mixed together. Of this we shall have a direct proof by compressing these seven tints into a space as narrow as that which they occupy in Newton's first ring: for as soon as this is done we see the orange-yellow^[6] which succeeds the white in the ring make its appearance. The blond and tawny colours of the scale are very compound tints: they possess a certain fieriness on account of the red which enters into their composition, have a slight resemblance to the colours of gold and copper, and are very difficult to be imitated, because their composition is such as to remove them further than the others from the prismatic colours. In nature they are found particularly in

1. The hair of animals.
2. The feathers of birds.
3. The fibres of certain species of dry wood, such as the walnut-tree, the pear-tree, &c.
4. The beard of corn, such as wheat, barley, rye, &c.
5. The smoke at the top of a flame.
6. The decoctions of roasted grain, such as barley, coffee, &c.
7. The halo seen around the moon when overcast with fog or light clouds.

The colours which the clouds assume are in general

Black, or very pure ash-colour;
White, or very light ash-colour;
The colour of smoke or coffee;
Red, more or less fiery;
Blue, very deep, and sometimes approaching to violet.

These are exactly the tints that would constitute the first ring were we to include in it the first two colours of the second ring. The tints of smoke result from the more or less thorough blending of the blond and the tawny; those of fire from Nos. 8, 9, and 10; the deep blue is produced by the Nos. 10, 11, 12, which are the deepest tints of the scale.

The first blond is properly that of light hair in childhood, and it is a fact worthy of remark, that as children grow older it becomes progressively deeper and deeper, in the order of the Nos. 2, 3, 4 in the scale. The perfect resemblance of the first tints on the scale to those which we observe about the moon when she is surrounded by clouds is equally remarkable: it seems in fact that this luminous appearance may be thus definitively explained. Tints of this kind do not arise from refraction and diffraction; they are produced only by means of thin plates: the luminous halo in question is therefore a phænomenon produced by thin plates.

This observation, combined with the fact that the tints exhibited by the clouds in every variety of aspect are almost all comprised in the first ring, leads to another consequence relative to the constitution of vesicular vapours. The measurements and experiments of Newton have shown what are the dimensions of the layers of air, of water, and of glass, which produce the colours of the several rings. The red of No. 10 is the last tint of the first ring: the indigo (No. 12) belongs to the second, and the thickness of the layer of water which produces it by reflexion is about the ten-millionth part of an English inch. As we know then, on the one hand, that the vesicular vapours are formed of water, and on the other that they do not reflect or transmit any tint beyond No. 12, we may conclude that their external film is in no case thicker than the ten-millionth part of an inch.

This result appears to me so decidedly certain as to be entitled to a place in science.

Second Ring. — From No. 11 to No. 28 (inclusive).

This interval commences at the deep violet No. 11, and extends to the lake-red No. 28. It comprises the most beautiful of all the gradations; namely,

Blue, Azure, Yellow, Orange, Red.

Newton places a green tint between the azure and the yellow. My scale exhibits no trace of green, and, with whatever attention I have examined Newton's second ring, I have never been able to perceive, in the place where the green should be found, anything but white tinged with azure and answering to the Nos. 15, 16, 17 of my scale. It is true that in the solar spectrum we meet with green in passing from the blue to the yellow: but the colours of the prism are simple, those of the thin plates are compound, and the order of their succession resembles but very imperfectly that of the colours in the prismatic spectrum^[7].

My scale is developed in such a manner that no illusion can take place. The interval comprised in the second ring is entirely free from green; neither is it to be found in the first order. Hence it is inferred, that among the thin layers of the two first orders there is none capable of reflecting any portion of green. The result is curious, and we have remarked it in the hope that, under different circumstances, it may be turned to account.

In speaking of the tints of the first ring we have stated that they are further removed than the others from the nature of the prismatic colours. The tints which, on the contrary, approach it most nearly are those of the second ring: yet even these are too distinct from it to be confounded with the simple colours of the prism. We have the sky, their type in nature, constantly before our eyes; for who is there that knows not the dawn, "with rosy forehead and golden feet"? Beginning with No. 12 of the scale, let us run our eye over it as far as No. 28, and we shall find the tints of the sky disposed there in the order in, which they present themselves in the magnificent spectacle of the dawning day. This succession, as we have already observed, is the most beautiful of all: Newton's second ring gives no idea of it, because its colours are not, and cannot be, sufficiently developed to produce the effect. Painters, if I mistake not, will do well to avail themselves of this part of the scale: they will find in it a faithful copy of the beautiful tints of the morning, and endeavour to transfer them to their compositions. Natural philosophers will not fail to remark, that among the various tints of the sky there is no trace of green. This would heretofore have been found a perplexing circumstance, but may now be satisfactorily explained, merely by reflecting that the tints of the sky belong to the second order, in which also there is no tinge of green. From the blue to the yellow the transition is through a very faint gradation of azure-yellow, and this is observed to be exactly the case in nature.

The tints produced by vapours and clouds belong to the second order. They contain in general more fire than the natural tints of the sky, but this quality is nothing in comparison with the purity, vividness and variety displayed in the tints of the second order. The appearance of the sun is never so magnificent as when the air is perfectly pure. Toward evening the lower regions of the atmosphere are always more or less charged with vapours, the air no longer retains its morning transparency, and the setting of the sun is attended by a fiery tint which greatly mars the tranquil beauty of the spectacle. It is to those vapours that we are to attribute the inflamed appearance of the sky, because they possess the power of transmitting the tints of the first order, and these are of that fiery cast. Were it not for this circumstance the setting of the sun might justly vie with its rising.

Philosophers had long since settled their opinions as to the colours of the sky. These they explained by assigning to the air the property of reflecting the higher colours of the spectrum (violet, indigo, &c.), and that of transmitting the lower, (red, orange, &c.). The explanation was correct so far as it went, but to make it complete the exact quality of the tints should be determined by indicating the order to which they belong. It was necessary also to ascertain how light is affected by the presence of vapours. The considerations which we have just stated will perhaps supply both these deficiencies.

Thrrd and Fourth Rings. — From No. 29 to 38, and from 39 to 44.

These two rings comprise (if I may use the expression) the richest tints. The tints of the first ring are distinguished by their fiery and metallic appearance; those of the second by their transparency and vividness; those of the third and fourth by their intensity, and by the presence of green, which is wanting in the first and second orders. The first appearance of green is in the third order at No. 32: it appears again in the fourth order at No. 41. These two greens differ but little from one another, and are both beautiful in a very high degree: they have a strong resemblance to the green of the emerald. The tints of the third ring do not differ much from those of the fourth: their most marked difference consists in the diminution of transparency observable in passing from the third to the fourth order.

The colours contained in these two series abound in the three kingdoms of nature; the vegetable kingdom however seems to present them in the greatest proportion.

The predominant colours in these two parts of the scale are the red, the green, and the yellow-green. There is here, properly speaking, no species of blue, but its absence is counterbalanced by the presence of the green, which is not to be found in the first two rings. It would seem as if the blue belonged peculiarly to the spacious vault of heaven, and the green to the surface of the earth. They are two dominant colours in nature, but their domains are separated, and the separation seems to me not to be accidental. It was necessary, I suppose, that the atmosphere should be composed of the most subtile particles, in order that they might remain suspended in space; the earth did not require to be of so delicate a texture. Hence we have two very distinct orders of particles or thin layers; the terrestrial, which are grosser and capable of reflecting the green tints; and the aërial, which are more subtile and capable of reflecting the azure tints.

Laws of Varying Colours.

Newton had observed that the colours of the rings changed their position as the angle of incidence, under which they were viewed, was changed. In certain rings a certain colour viewed at an incidence nearly perpendicular appears to form a given circle, but expands and forms a larger circle if viewed obliquely. These changes are much more perceptible in the outer than the inner rings. An obliquity of 40°, for instance, is sufficient to change the tone of a colour of the fourth order, though at the same angle of incidence a colour of the first or the second order undergoes little or no change. We must not omit to mention the effect of refraction, which is to render the transitions from one tint to another more slow in proportion to the greater density of the substance which forms the thin layer. This law may be included in the first, because the rings produced by dense layers are interior in reference to the correspondmg rings produced by layers of inferior density, and the exterior rings are the more liable to change.

The colours of the scale are produced by thin plates, and are subject to the same laws as those of Newton's rings. It seems to me, however, that in respect to the law of the changing colours there is an anomaly that has not yet been mentioned. The higher tints comprised between the red (No. 44) and the yellow (No. 21) conform to the general law. If we view these tints at a certain inclination, we see No. 44 change to No. 43, No. 43 to No. 42, and so on in succession, each superior number exhibiting the appearance of the next inferior number. This law prevails until we come to No. 21 : after this the phænomenon changes. The beautiful yellows 19 and 20 become azure-green; the brighter yellows 18 and 17 are changed to red; the azures 16 and 15 become yellowish; the blues 14 and 13 suffer no change, and with them the anomaly ends, for the general law prevails again from No. 12 to No. 1 inclusive.

This difference has not been indicated until now, and, as I mention it for the first time, I deem it necessary to state that it escapes the eye when we endeavour to observe it in Newton's rings, in consequence perhaps of their being so limited in extent^[8]. The anomaly prevails in the central part of the second ring, where the thin plate reflects a great quantity of white light, and this part is the brightest of our scale. I remark this circumstance, in order that it may receive due attention from those who would thoroughly investigate this point. In such an investigation it will probably be necessary to take into account the variations of the law of refraction, when the obliquities of inclination are great,—such, for example, as those to which we must have recourse in order to account for the changes of tone in the colours of the first two rings.

Exceptions to the Law of Varying Colours.

If bodies where composed of thin layers such as those which form the chromatic scale and Newton's rings, their colours would change with every change of incidence, conformably to the law which we have just indicated. In nature the number of those colours that change is but small in comparison with those that remain fixed. Hence it may be inferred, either that the colours of bodies depend in general on a principle different from that of the colours of thin plates, or that this principle is modified in its application, the bodies not being constituted exactly as such an explanation would require. A few observations will perhaps be sufficient to fix our ideas on this very interesting point in the theory of colours.

Varying Colours in Nature.

In each of the three kingdoms of nature we have specimens of these colours. The animal kingdom especially affords some that are highly interesting, both in respect to their number and their beauty. It will be sufficient to mention the wings of butterflies and insects, and above all the feathers of different birds. Who is there that does not know, for instance, the variety of pleasing hues displayed in the plumage of the peacock? In this case, as well as in others of a similar kind, the colour that we observe is not given out by one continuous surface, such as that of a single plate: it is produced by a multitude of threads or fibres, so nicely overlapping one another that they seem to form a perfect plane, although they are really but a vast number of distinct minute surfaces, the position and thickness of which it would be necessary to know in order to apply the general law to them with any prospect of success. The phænomenon possesses all the characteristics of that produced by thin plates; but instead of a single layer, the number in this case is infinite, and, though disposed in an order calculated to excite our admiration, still it complicates the action of the light so as to prevent us from tracing it through all its variations.

The varying hue most frequently exhibited by the plumage of birds, is a beautiful green of the same intensity as No. 32. This number in the scale retains almost all its intensity, even at an inclination of 40°: at an angle of 50" it presents the appearance of No. 31, which is a purple colour with a greenish tinge; beyond that the original colour completely vanishes, and in its stead we have the violet-lake of No. 30.

But the varying green of feathers begins to change much sooner: when the inclination is near the 40th degree, it already presents the violaceous tint of No. 12. The intermediate steps of the transition can- not be discerned, — a decisive proof that the surfaces of the fibres which produce the green when the incidence is perpendicular, are not those which produce it when the incidence is oblique. The transition from No. 32 to No. 12 is so abrupt as to warrant this inference.

At all events the properties of the varying hues presented in nature are sufficiently interesting to be made the subject of a specific inquiry. I am at present engaged in collecting these colours, and hope that naturalists and experimental philosophers will contribute whatever they can toward the execution of a design likely to be attended with advantages, not only to Optics, but to other branches of science.

Unvarying Colours.

Nature presents a multitude of colours corresponding with the colours of the scale; but these are extremely changeable, while the natural colours are altogether unchangeable, except in the particular cases specified in the last paragraph but one. Let us fix our attention for a moment on the green, which is more prevalent than any other colour. Every herb, every leaf, is more or less of this colour. The green tints in the scale, of whatever order they may be, become red when the incidence is oblique: the same colours in herbs and leaves furnish no sign of such a transformation.

We know already, that the changes of tone to which the tints of the thin plates are subject diminish as the density of the plates increases. Were the substance of herbs and leaves much more dense than that of water, it might be said that it is owing to their excessive density that they suffer no perceptible change of tint from obliquity of incidence. But their density is far from being considerable; it is not so great as that of water. The phænomenon must therefore be explained in a different, and, as I think, in the following manner.

In applying the principle of the thin layers or plates to the explanation of the colours of bodies, it is supposed that those bodies are composed of layers analogous to the air and water introduced between Newton's glasses. Bodies are undoubtedly formed of very subtile particles; but have those particles or elementay groups the form of plates or laminae? It does not appear so; it seems rather, on the principles of crystallography, which divides them into cubes, octahedrons, tetrahedrons, &c., that their forms are [polyhedral] solids. This circumstance makes a serious difference, and ought to be attentively examined.

Let us take, for example, the cubical, which is one of the simplest forms. Let us suppose the section of one of these cubes made in the plane of reflexion, and $ab$ the side or face on which the incident rays fall. In passing from the perpendicular incidence $om$ to the oblique incidences $pm$, $gm$, it is evident that, allowance being made for the effect of refraction, the last ray subjected to the influence of interference would be the ray $pm$ which passes through the angle $a$. It falls on the inferior surface $cd$ at the middle point $m$, and, being reflected in the direction $mo'$, reaches the eye at $o'$: every more oblique ray, such as $gm$, falls beyond the face $ab$, meets the vertical face $ac$, and contributes nothing to the coloration, which depends on the distance of the two faces $ab$ and $cd$. In order to comprise the ray $gm$ within this interval, $ab$ should be prolonged to $a'$ on the side of the incident, and to $b'$ on the side of the reflected rays. But as it terminates at $a$ and $b$, its field of coloration is confined within the limits $mp$, $mo'$. Now the angle $omp$, the sine of which is ${\frac {1}{\sqrt {5}}}$ (because $abcd$ is a square) does not amount to 27°, and this is an opening too small to admit the manifestation of any change whatever in the tints.

If the refraction (which precedes the reflexion) tends, as is evidently the case, to enlarge the field of coloration, it has a still greater tendency to diminish the effect of the change of the tints. It may therefore be considered certain, that the integrant particles of which bodies are composed cannot, in general, favour the play of the varying colours, unless, in defiance of all other observations taken collectively, we assign them a very considerable magnitude.

After the foregoing reflexions there remains, so far as I can see, but one point to be cleared. It being once admitted that the field of coloration of the integrant molecules is confined within narrow limits, how then, it will be asked, do bodies appear coloured in every direction? In general the molecules hold, in the bodies which they form, all sorts of positions, and are divided, relatively to the eye, into two classes; those of the one presenting their faces, and those of the others their angles toward the observer. The first are those which colour bodies; the second are those which in one position of the mass contribute, but in another do not contribute, to its coloration. In short, the eye is always in the field of coloration of a vast number of particles. When the field of one particle disappears, it is replaced by the field of another; so that the entire system always continues of a certain colour. Symmetrical arrangements present an exception, and we have already treated of these in the preceding paragraph.

Metallic Colours.

According to painters there are but three primitive colours, red, yellow, and blue. By combining these tints in various proportions with black and white they form the others. In richness and variety their productions are far surpassed by those of the thin laminæ. If we imagine one of the colours of the laminæ combined with another, we have the impression of a new tint. The combinations that may be obtained in this way are almost innumerable, and, it will be said, need well be so, in order to match the variety which nature exhibits. Such is our opinion too; but we shall not attempt to conceal the difficulty presented by the fact, that several of the natural colours, especially those of the metallic substances, have but a very slight resemblance to the colours of thin plates, among which it were vain to seek, for example, either the yellow of gold or the red of copper. The colours of the plates which approach them most nearly are found among the first seven or eight tints of the scale. The gold might be placed among the blond colours, and the copper among the tawny; but the difference is still so striking that it would be unwarrantable, before it is accounted for, to put entire and implicit confidence in the principle of the laminæ.

This principle requires, as a primary condition, that the integrant molecules of bodies should be transparent. It is true that almost all bodies reduced to a certain degree of tenuity are permeable to light; but it is equally true that the existence of a single body perfectly opaque and yet exhibiting a colour, would render it necessary to look for another principle of coloration besides Newton's, which is applicable only to diaphanous substances.

In my Memoirs on the electro-chemical appearances, I have shown that they are not exclusively produced by one of the poles of the pile. The appearances which constitute the chromatic scale are due to the electro-negative elements of the solution (oxygen and acid), which being transferred by the current to the positive pole, are there spread out into thin transparent films, from which all the colours of the scale arise. The electro-positive elements (such as hydrogen and the metallic bases) are, on the contrary, transferred to the negative pole, and there deposited in layers which never produce the colours of thin plates. Here it is impossible to mistake in any case, but more particularly in respect to the solutions of certain salts with a base of gold or of copper, which produce negative appearances invariably of the same colour as the metallic base. It cannot be said in this case that the substance has not been brought to the degree of tenuity necessary to render it transparent. The electro-chemical layers commence with the first degree of attenuation at the positive as well as the negative pole. If the layers of the positive pole produce the ordinary colours of the plates, while the oppo- site pole completely fails to present any other than that of the metallic base, it necessarily follows, either that these bases are perfectly opaque, or at least that their transparency is so imperfect as to render it impossible to apply the general laws to them, unless with very important restrictions. Indeed we have here a decisive proof that the colours which depend on the tenuity of plates are not to be traced on all classes of bodies; that they can be produced by those bodies only which are endowed with a certain degree of transparency; and that metallic substances are too opaque to be numbered among these. This is a positive fact, and ought therefore, without any regard to particular systems, to be entered in the register of science.

Gold and Copper.

It cannot be doubted, says Newton, that the colours of gold and copper belong to the second or the third order^[9]/ To us they seem, on the contrary, to belong to the first order, that being the only one which includes tints of a metallic appearance. If we only recollect that the first colours of the scale are far from being distinct in the first of Newton's rings, we shall feel less surprised that it should be necessary to correct the classification of that great philosopher. The resemblance in question is, however, as we have observed already, very far from being perfect. The tints that come nearest to the yellow of gold are the blond colours Nos. 2 and 3: but these are evidently less yellow, and at the same time more compounded than the colour of gold; for they contain a tinge of green, which does not exist in the more decided colour of gold. Transparent gold-leaf appears green when held before the light: this fact has been classed by several persons among the phænomena connected with thin laminæ, because these laminæ are known to reflect a given colour, in the same position in which they transmit its complementary colour. However I will say with a great philosopher, that "there is in Newton's rings no yellow that has green for its complement: the colour transmitted is invariably the blue; and this fact accords with the construction given by Newton for the composition of colours. But extract from this blue (which is necessarily compounded) a certain number of violet and blue rays, such as may be absorbed by the substance of gold, and there will remain greenf^[10].

It is a fact demonstrated by a great number of observations, that light in its passage through coloured substances is partially absorbed and extinguished. This fact not only renders Biot's explanation plausible, but warrants the supposition that light undergoes in reflexion a diminution analogous to that which takes place in its transmission. For if some of the rays destined to be transmitted are absorbed by the very substance of the gold, how can all the other rays, which are destined to be reflected in the interior of the same substance, escape undiminished? If the phænomenon be incomplete in respect to transmission, it will be equally so in respect to reflexion, and the tint formed will be necessarily different from that produced by the ordinary thin plates, which are so transparent as to arrest no species of rays whatsoever.

The blond, as already observed, contains a tinge of green which is not found in the beautiful yellow of gold. If we leave out this green, by supposing it absorbed in the process of reflexion, the result will be a tint very closely resembling, if not exactly equal to, that of gold.

The red of copper requires a similar reduction. The colour nearest to it is the tawny of No. 7. But this contains a cast of violet, which is not in the copper, and the removal of it will make the resemblance, if not complete, certainly much less imperfect.

It is not my purpose in this place to enter further into the question, or to investigate the causes to which it is owing, that coloured bodies absorb certain rays more rapidly than others. The fact itself is proved, and it is unnecessary to go further for the attainment of our object, which was to discover the cause of the great difference between metallic colours and those of thin plates.

Colours developed on Metals by the Action of Fire.

The prismatic colours produced on steel and copper by the action of heat are universally known. Analogous colours are also exhibited by tin, bismuth, lead, &c., when they are in a state of fusion.

As to these colours, the most generally received opinion is, that they depend on a principle of oxidation. Berzelius calls the metallic layer which is thus coloured a suboxide^[11].

I have always entertained some doubts as to the correctness of this explanation; because each degree of oxidation has a colour peculiar to itself, and in no way related to that variety of tints of which we speak. I was also struck by the well-known practice of giving steel a violet colour in order to secure it from rust. We know that this colour is produced by means of fire, in the process of giving steel a particular temper, — a temper which is called violet, because it is produced simultaneously with the colour. Were this tint, as it is presumed to be, the effect of oxidation, it would, in my opinion, instead of preventing, serve only to accelerate oxidation. A very high degree of polish, I allow, will keep off rust for a long time, but cannot stop it when once the action has commenced.

But this is not all: the superficial colours of which we speak are changeable, and belong evidently to the same class as those produced by thin plates. Now the pure metals, as we have already seen, are, from their opacity, incapable of this species of coloration. Can they acquire that capacity in their first degree of oxidation by becoming suddenly transparent in consequence of their union with a small quantity of oxygen? The hypothesis far exceeds the bounds of probability, and the phænomenon requires to be otherwise explained.

Let us return, for an instant, to the experiment of the coloured rings developed on a surface of platina by means of the electro-chemical apparatus described in the beginning of this Memoir. The platina surface belongs to the positive pole of the pile, and the electro-negative elements of the solution (which in the present case are the oxygen of water and the acid of acetate of lead) are deposited at this pole. I will not undertake to say by what species of affinity or force it is that these elements are attracted to each other and spread out into thin films on the platina. It is certain, however, that they attach themselves to the platina without oxidizing it in the slightest degree. We must not suppose that this happens because platina is a metal difficult to be oxidized. Iron and steel belong to the class of metals most easily oxidized, and yet it is well known that they will bear to be covered with electro-negative layers without becoming rusted. My electro-chemical experiments, multiplied and varied in a thousand ways, leave no room for reasonable doubt on this point: they show that oxygen and certain acids may adhere to the surfaces of metals without producing the slightest chemical change in them. This is a novel state for oxygen and the acids, and is distinguished from their ordinary combination by the three following peculiarities: 1st, The metal retains, beneath the deposited layer, its natural brilliancy; 2nd, this layer produces the phænomenon of the coloured rings in all its beauty; 3rd, instead of oxidizing the metal, these electro-negative elements contribute to secure it against oxidation in every part to which they are applied^[12].

A fact so unprecedented is interesting to chemistry and is entitled to particular attention, as tending to enrich the science by the introduction of new ideas^[13]. Confining myself in this place to the colours produced on metals by the action of fire, I do not hesitate to say that I think their origin now placed beyond the reach of doubt. It may be safely laid down as a general proposition that the oxygen of the atmosphere produces them, not, as is supposed, by oxidizing the surface of the metal, but by becoming fixed in the form of a thin plate or film similar to those of the electro-chemical appearances.

Copper, tin, and bismuth are pure metals, and I know not any layer by which they could be coloured, except that which has been just mentioned. Let a plate of copper be laid on a piece of red-hot iron: the plate becomes gradually heated, and all at once exhibits the most beautiful colours, but they disappear as suddenly. Before it becomes coloured the plate has a metallic lustre; it subsequently ceases to shine, and becomes evidently oxidized. It is therefore at the moment when the colours manifest themselves that the oxygen of the air precipitates itself on the copper. In the next moment the chemical combination is effected, which takes place whenever the action of the heat is sufficiently prolonged. If the plate of copper be removed from the red-hot iron as soon as the first indication of a change of colour is perceived at any point, the process of coloration will then go on more slowly, the copper will not be oxidized, and the oxygen, which would produce this effect under a more prolonged action of the heat, now covers the plate with a film, which adheres to it like a varnish, and by its transparency produces the usual colours.

The origin of the violet colour given to steel to prevent it from rusting is the same. The layer however which produces this tint in the steel does not perhaps consist solely of oxygen, as it does when the metals are pure. Steel is a carburet of iron, and the oxygen of the air in being precipitated on this compound, becoming combined with the carbon in some manner or other might form the layer in question. At all events the layer does not change its nature; it is always electro-negative, and secures the metal from oxidation as effectually as the layers applied by the electro-chemical process.

The electro-chemical appearances are fonned with surprising rapidity, and the colours developed on metals exposed to the action of heat are produced with equal promptitude. It is therefore essential to the production of the phænomenon of thin plates that the electro-negative elements should be precipitated on the metal with a certain

substances to enter into combination with them. This idea, which accords with the spirit of other theories, being admitted, we see at once how these layers preserve the transparency required to produce the coloured rings, and do not attack the metal so long as they are kept at such a distance as to be unable to combine with its particles. Berzelius was more sensible of the difficulty, perhaps, than any one else: but would not an open avowal have been better than the attempt to evade it by the adoption of the term suboxide, which is quite as vague and undefined as the principle of oxidation, for which it was offered as a substitute? velocity. Does not the necessity of this condition show why these layers, in order to produce the desired effect, should be brought into contact with the metallic surface by the agency either of fire or electricity? The humid way is perhaps too tedious in all cases; it gradually oxidizes the surfaces of the metals, but never covers them with that thin and extended veil, the application of which requires a rapidity unattainable in this circumstance.

Nature presents in the specular iron a beautiful instance of the coloration which we have been considering. The ordinary colour of this ore is an iron gray; yet the faces of its crystals often display beautiful tints of every kind. They commence, in general, with the blue (No. 13) of the second, and go on as far as the reds (37 and 38) of the third order. These colours change as those of the scale do, and are so very like them that I thought they might be successfully imitated. I was not mistaken: a crystal of specular iron coloured by nature could not be distinguished from one coloured by the application of the electro-chemical process. There is no doubt as to the origin of these crystals; they are produced by fire, and it is that which has given them their colour by covering their surfaces with thin layers analogous to the electro-chemical. The humid way would have produced a very different effect: it would have destroyed their metallic brilliancy, and corroded their surfaces by the ordinary process of oxidation.

Singular Property of some Tints of the Scale.

A drop of alcohol is let fall on the violet (No. 11), and spread so as to cover part of the colour. The part thus made wet is no longer the same: we see instead of it a feeble tint resembling that of coffee mixed with milk; but the other part remains unchanged. The comparison can be instantaneously made, and the difference between the two tints is so striking, that we are at a loss to conceive how a transparent and very limpid film of alcohol can produce such a change in the violet colour on which it is placed. The alcohol gradually evaporates, and the colour recovers its former brilliancy.

Water, oil, and the different saline solutions produce the same effect; the thickness of the liquid film does not affect the phænomenon, and the colour undergoes the same change whether it be a thin film or a considerable mass. When transparent solids, such as glass, crystals, &c., are laid over the violet colour, it suffers no change. The liquids with which the plate is overspread adhere to its surface, so that this condition seems necessary to the production of the phænomenon.

Below the violet the indigo No. 12 and the blue No. 13, and (yet lower down) the red No. 10, the ochres Nos. 8 and 9 are subject to very marked variations. In the other colours of the scale when submitted to the experiment of the humid films no changes are visible, — none at least but such as are extremely slight in comparison with those which take place in the group of tints formed about the violet No. 11. There is no other fact connected with this. Such at least is my opinion, after having examined it under various aspects without being able to arrive at a satisfactory explanation. I am therefore unable to say more about it for the present.

Effect of Artificial Light during the Night.

It is an admitted fact, that we cannot judge of colours without the presence of daylight. But what changes do they undergo when viewed in the evening? The following are those that I have observed in the tints of my scale when examined at that time. The two conflicting opinions of those whom I consulted on this subject I forbear to mention.

1. The greens increase in beauty and intensity.

2. The yellows and the azure are tarnished and become deeper.

3. The blues and the indigo become greenish.

4. The violets approximate to a blue.

5. The violet-reds become more violet.

6. The first eight tijits of the scale become more like each other, and approach more nearly to the metallic colours.

7. The other tints remain nearly unchanged.

Some of those changes are produced even by day if the colours of the scale are viewed through a green crystal, and others if they are viewed through yellow or azure crystals. Artificial light is without doubt differently constituted from that of the sun: it contains probably a scanty mixture of red rays with an abundance of the yellow, green, and azure. But what is the coloured diaphragm that should be interposed in the passage of the light of day, in order to reduce it to the same proportions as that of night? The problem is an interesting one, but it remains as yet without solution.

Harmony of Colours.

My scale appears to all persons to be eminently harmonious. I have already mentioned the delight which it afforded those who saw it. I have now to add that artists are astonished not to find the green in its usual place, between the yellow and the azure colours of the second order. But I take the two finest greens in the scale, Nos. 32 and 41, and call upon the most accomplished artists to assign them a more suitable place than that which they occupy. Influenced by habit they unhesitatingly place them among the yellows and the blues of the second interval, having no doubt that this is their proper place. They are however soon undeceived by the result ; the green is found unpleasing here; the harmony is destroyed, and cannot be re-established until the colours are restored to their original position. But what is this harmony? It is an effect by a reference to the law of imaginary colours. It is necessary to give a brief development of the principle of this theory.

Let any colour whatsoever be exposed to some given degree of light and let the eyes be kept steadily fixed on it for some time: if the eyes be afterwards closed we have the impression of a different colour, which though it is never the same for one tint that it is for another, is always the same for the same tint. These colours, in some measure the offspring of the real colours, are called imaginary by philosophers, and by others they are named fantastic or accidental. The following is a table of them:—

Real Colour.	Corresponding imaginary Colour.
Red	Azure-green.
Golden	Indigo.
Green-yellow[14]	Violet.
Azure-green	Red.
Indigo	Golden.
Violet	Green-yellow.

After this table I cannot do better in reference to the present topic than give the following extract from Venturi.

"The combination or succession of those colours which have such a mutual correspondence, that the perception of the one is followed by the imaginary sensation of the other, is agreeable and harmonious."

"Women of good taste know the colour of the trimming which has a good or a bad effect in combination with the fundamental colour of their dress. Leonardo da Vinci promised to give a table showing the colours which harmonize with one another and those which do not^[15]: but he did not fulfill the promise, and no other painter that I know has pointed out precise rules for the harmony of colours. Several have observed merely that red combined with green has an agreeable effect; Newton apprises us that orange agrees with indigo; and Virgil was perhaps of the same opinion when he put this verse into the mouth of his Naiad,

Mollia luteola pingit vaccinia caltha.

"Mengs extols the union of violet and yellow; the same author says that the combination of red, yellow and azure is disagreeable^[16]; but that each of them should rather be joined with the colour intermediate between the two others; the red with the green, the yellow with the violet, and the azure with the orange."

"These different opinions have their origin and foundation in the transitions from the real to the imaginary state, which, as we have seen, naturally follow the involuntary movement of the retina; so that the general law of the harmony of the eye will be this: That the corresponding colours in the Table hereafter mentioned will be in harmony with one another."

"In fact, if the organ of vision, after having been fixed on an orange colour, directs itself spontaneously, and uninfluenced by any external impulse, towards the indigo, or vice versâ; or if in nature a violet-coloured hyacinth is placed beside a jonquil, and the optic axis is turned from the one flower upon the other, the centre of the retina passes over that succession of colours which is demanded by the nature of the organ and cannot be felt but with pleasure and satisfaction. These two colours harmonize, because the one leads to the other; and, for the contrary reason, if the eye has to pass from one colour to another, not corresponding with it in the table, it will necessarily have to make a disagreeable effort, because it will find itself in a position not in harmony with its former state. If the ocular harpsichord of Caslet were possible, the modulation of the colours would be executed on it according to the principle just laid down^[17]."

I will not deny that the aptitude of the retina to cause an imaginary to arise from a real colour is of some account in the effect produced by colour. I am even inclined to believe that colours attentively observed are, by this tendency of the organ, associated with a sentiment and endowed with an expression which they could not otherwise possess. This however would be a species of melody and not of harmony.

Harmony is an instantaneous effect produced on the mind by several colours united altogether independent of the development of imaginary colours. Before this development can take place, the eye must be fixed for some time on a real colour; nor is this all, it is also necessary that the real colour should be seen in a bright light. Now, when I have one or two colours before my eyes, I can judge of their harmony without being obliged to look at them for a long time or requiring a very bright light. If I observe them for a single instant, my judgement is already pronounced, with the same promptitude with which the ear decides when it is affected by the harmony of sounds. Suppose for a moment that real sounds had their corresponding imaginary sounds, and the latter were determined when the ear had been for some time affected by a single quality of sounds suitably sustained. In the first place, these imaginary sounds could make no impression except in the particular case in which the notes are sustained for some time; but if we suppose that they accompanied the real sound necessarily and in every circumstance, they would not be in harmony with it; they would be perceived an instant after it, and would produce melody.

When a particular colour is ill-assorted with another, the eye is offended, as the ear is hurt by a discord. If we pass from one of these colours to the other through the intermediate tints, the first feeling will be changed into an agreeable sensation. Our scale, I repeat it, produces the same agreeable impression upon all, and it is to the inimitable beauty of its colours, and the manner in which they melt into each other, that this effect is due.

According to the law of imaginary colours red harmonizes well with green. In our scale the lakes, which are the finest reds in nature, are between the green tints and the orange, and combine agreeably with both. According to the same law the violet should agree only with the yellow; in the scale the violet tints are between the azures and the ochres, where they produce a very fine effect. The same law is opposed to the combination of yellow and azure, but the scale proves that these two tints combine agreeably, provided they have a certain tone and a certain degree of brightness. It is unnecessary, I believe, to multiply instances. The beauty of the tints and the graduation of the transitions constitute together one of the first secrets of art revealed by the effect of the chromatic scale. But it is not always allowed us to resort to the graduation of the transitions, and the artist requires another guide to show him what he is to do in all circumstances. It cannot be doubted that as there are combinations of sounds more perfect to the ear than others, such as the octave, the fifth and the third, there are likewise concords of colours more pleasing to the eye than others. But these concords should be determined. The field of inquiry is still new; it is possible however that the pursuit may be attended with most success by having recourse to the chromatic scale, which presents the tints in their greatest purity, and so arranged as to form the gamut of colours. This circumstance is an additional recommendation of the scale to the attention of philosophers as well as of artists.

Concluding Reflexions on the Qualities of Colours considered both philosophically and pictorially.

In physics it is usual to speak only of the brightness of colours. But besides being more or less bright, they are more or less intense or deep, beautiful, cheerful, &c. These epithets have been long in common use and are constantly on the lips of painters. In my opinion it is time that they should be admitted into science, and reduced to a more determinate signification than they have in ordinary language.

Brightness.

All who observe the seven colours of the spectrum will instantly perceive that they differ greatly in brightness. The clearest of them is the yellow. Fraunhofer, who has analysed the spectrum with so much care, assigns to that colour the highest degree of brightness.

The tints of our scale as well as the natural colours are far from being pure: they are all composed of several others. Hence arises a law of brightness different from that of the prismatic colours. The clearest on our scale are,

1st,	The azures	Nos.	16	and	17.
2nd,	The blonds		1	and	2.
3rd,	The yellows		18	and	19.

The most obscure tints are Nos. 10, 11, and 12, in which the violet and blue predominate.

Depth.

Depth, or intensity, and brightness are very different qualities. No one indeed confounds the intensity of a fine red with the brightness of a fine yellow. In the scale of the latter quality the white occupies the first place. A bright tint may be considered as a mixture, in which there is a little colour with a great quantity of white light; and, vice versâ, a strong or deep colour, as a mixture of much colour with a little white light. Painters therefore when they want to give brightness to their colours add white, but when they want to increase their intensity they add a different colour.

The most intense colours of the scale are the lakes, especially No. 28 and No. 29. The feeblest are the azures No. 16 and No. 17, the blonds No. 1 and No. 2, and the yellow No. 18.

Some colours strengthen each other; some have no such effect. Thus, for example, the red of the spectrum combined with the violet forms a very beautiful lake, which is a much more vivid red than that of the prism. The same red combined with the green forms a mixture which possesses more intensity. The tints of the scale include all the prismatic colours, and their strength depends exactly on the proportion of the elements which enter into their composition. The lakes abound in red and violet, which are the two colours that give most depth to each other, as if one were the octave of the other. The sky-colours are too feeble, because with the exception of the blue, which they contain in a quantity rather excessive, the colours which enter into their composition will, when mixed, produce only white.

It is not strictly true that the intensity is in the inverse ratio of the brightness, because the more obscure tints Nos. 10, 11 and 12 are less intense than the lakes Nos. 28 and 29. Nevertheless there is a manifest relation between the two qualities; for it is certain that the feeblest colours are among those of the brightest class, and the most intense among those of the most obscure.

Thin plates according to their different degrees of tenuity reflect different colours; either these reflected colours are such as mutually to strengthen each other, so that there results from them a strong tint; or they do not strengthen each other, and the result of this is a white which predominates in the tint. Thus, the cause which generally renders it impossible to obtain brightness of tint unless by sacrificing intensity, is sufficiently demonstrated.

Beauty and Monotony.

Beauty consists in a certain variety which some tints possess in a higher degree than others. The yellow, for example, and the red of the spectrum have a tone peculiar to themselves: the golden contains the essence of the red and the yellow, and is more agreeable to the eye than either.

The most beautiful tints in the scale commence at the orange colours 22 and 23, and continue to the end.

The first element of pleasing is variety; in this point of view the purity and homogeneity of a colour are defects, of which philosophical painters must have been sensible when they recommended the use of compound in preference to simple colours^[18].

The purest tint of the scale is perhaps that of the yellow No. 19. At the first glance it is extremely pleasing, but soon becomes monotonous and the eye turns away for relief to the higher tints, each of which produces the sensation of several colours. A painting in which there is much yellow will therefore always fail to please on account of this monotony; for its effect is most disagreeable.

Nothing can be more beautiful than the varying colours: when we call them varying it is unnecessary to say why they please. Painters, we know, in order to give a finish to their productions, overlay them with certain tints. The colours of the painting appear through the tint, are mingled but not confounded with it, and thus are produced a variety and vividness unattainable by any other means.

Warmth and Coldness.

Those tints which contain the element of red are by painters called warm, and those in which the element of azure abounds are termed cold.

Red is the strongest and the most vivid colour: it is the colour of fire and of blood, and it warms and inflames all the tints into which it is introduced.

If the idea of warmth is associated with red, azure gives rise to a very different feeling: it is indeed preeminently the cold colour.

Yellow approaches more nearly to the nature of red than to that of azure, and is consequently rather warm than cold. Pure green cannot be said to be cold or warm: it inclines however to the former or to the latter accordingly as it is combined with blue or with yellow.

Cheerfulness and Gloominess.

Cheerfulness is not to be confounded with beauty, nor gloominess with monotony: they are more distinct sensations and seem to belong, the first to the lower colours of the spectrum, such as the red, orange, &c., and the second to the superior colours, such as the violet, indigo, &c.

The most gloomy tints on the scale are, according to the generally received opinion, those of Nos. 10, 11 and 12, in which the higher colours of the spectrum abound. These colours, it cannot be denied, are also the least bright, and this quality may well be the cause of the gloominess which is felt in viewing them.

It is possible however that there may be in this case an unknown general law, which it would be worth while to investigate with the aid of the analogies afforded by acoustic phænomena, of which the principles are better known.

On the Pathetic and the Cheerful in Music and Painting.

An exclamation or shout of joy consists of notes ascending from the grave to the acute; a cry proceeding from grief or pain consists, on the contrary, of notes descending from the acute to the grave. It is not more singular than true, although it has never before been remarked, that the same notes sung or executed on an instrument will produce in the ascending scale a very different effect from that which they produce in the descending scale. In the first case the feeling excited is decidedly cheerful; in the second it is as decidedly sad. This is a fact which in both a physical and a physiological point of view remains yet unexplained, but may serve nevertheless as a law for all analogous cases.

Violet is a colour which certainly awakes a feeling of sadness. Can it be owing to a similar law that it produces such a sensation? I inspect the table of imaginary colours, and find that the green-yellow corresponds to the violet. We know that according to the theory of vibrations the violet is produced by shorter and the red by longer vibrations. The transition then from the violet, which is the real colour, to the green-yellow, which is the imaginary, is a transition from the acute to the grave, and analogous to that which takes place in the notes that produce sadness. The only difference between the two cases is, that in the one the sensation is the direct and immediate effect of the notes conveyed to the ear from without, whilst in the other the eye receives from without nothing more than the impression of the violet colour, the rest of the effect depending on the internal action of the optical nerves which are endowed with the power of passing of themselves from the real to the imaginary colour. A difference of this kind however is not incompatible with the existence of the analogy: it only leads to the inference that the eye possesses the more exquisite sensibility, since in this organ a mere disposition or tendency is sufficient to produce an effect which in the ear is due to an external cause: for, the superior delicacy of the eye is evidently the cause of the existence of these imaginary colours, which have no counterpart in the other sense, — no succession of imaginary sounds resulting from those which had previously reached the tympanum.

In music there is a well-known and long-established distinction between harmony and melody: the former arises from a certain series of sounds produced all at the same time, the latter from the succession of certain sounds produced according to a certain rule. Can the science of colours lay claim to a similar distinction? I look at a fine painting, and am at once struck with the harmonious disposition of its beautiful colours. This is the first feeling excited, and it is excited in a moment. I afterwards examine and study the composition by looking attentively now at one point and then at another. The merit of the piece was at first confined to the beauty and harmony of the tints; now the same tints being observed with more attention awaken, or tend to awaken, the idea of the imaginary colours, and thus acquire an expression which was wanting to them when they were passed rapidly over. It has already been observed that the green-yellow arose from the violet, and that the latter colour had a tendency to produce a sensation of sadness on account of its involving a necessary transition from an acute to a grave tone. The lower colours of the spectrum (the red and the golden) have as their imaginary colours azure-green and indigo. In both these cases the passage is from the grave to the acute, and the two colours should, according to the law under consideration, excite a feeling of cheerfulness. The theoretical inference is confirmed by every one's experience.

This analogy between sounds and colours may, after all, be rather apparent than real. I thought myself bound nevertheless to mention it, with a view to its development, and on account of the new ideas which it might suggest.

Additional Note on the Law of Varying Colours.

In speaking of this law, I have remarked an analogy which presents itself in the central tints of the second ring. After having concluded my labours it occurred to me to examine this interval once more, and I noticed a fact which had escaped me in my first inquiries. Beginning with the perpendicular incidence, in order to pursue the examination through the other incidences, I observed the rings attentively. As my point of view I took the central part of the second ring, and there, at an angle between 70° and 80°, I perceived a new ring formed. This appearance was not accompanied by the disappearance of any of the other rings: it was really a new ring formed under this great inclination at the centre of the second, which was at first almost entirely white. I shall distinguish this ring from the others by the epithet intruded^[19]. My rings can easily be so enlarged that the intruded ring may occupy a space two or three lines in breadth. The tints composing it will then be seen very distinctly, and will correspond exactly with those which are seen in detail on the plates 20, 19, 18, 17, 16 and 15; with this difference only, that, in place of these tints, a ring will be seen composed of green, red and yellow.

When the rings are smaller, as they usually are when obtained under the platina point, the intruded ring appears in the same place, and the observation, though made under circumstances less favourable, is equally decisive.

Newton's rings give no idea of this phænomenon: they vanish from the eye of the observer before the last degrees of obliquity are attained, and are consequently unavailable in an observation for which these great inclinations are an indispensable condition. The smallness of the dimensions of the rings cannot cause the observation to fail, whenever it can be made on my rings whether large or small.

I cover a portion of my rings with a layer of alcohol, oil, or water, &c., and when the observation is made at the before-mentioned inclination of from 70° to 80°, the intruded ring appears only where the humid layer is wanting. Thus the phænomenon connects itself still more with the law of refraction. In my opinion there are but few facts that can put a theory so severely to the test as this, and the theory which can completely explain it will have every claim to credit.

I shall always add to my chromatic scales a plate exhibiting on its surface the coloured rings as much enlarged as is requisite for the convenient study of the properties of the intruded ring. This I feel the more inclined to do, as these large rings are likely to be useful in other respects; they will serve, for instance, as a key to the chromatic scale, which is in reality no more than the development of the rings themselves; and this development is indispensable when we would judge of a colour. In the coloured rings, however large they may be, there is always found between every two tints a third into which they melt: its tone and the feeling which it produces are always confounded with those of the contiguous tints. For this inconvenience there is no remedy but to isolate the tints, so that the eye may be fixed on each of them without receiving at the same time any sensation from the others. The chromatic scale affords this advantage in its detached plates, not to mention the other advantages which in the course of this Memoir it has been proved to possess, and which it is therefore unnecessary to enumerate here.

Reggio, June 29, 1830.

Chromatic Scale.

44	Lacca-rosea.	Laque-rose.	Rose-lake.	(30
43	Verde-giallo-rossic c.	Vert-jaune rougeâtre.	Reddish yellow-green.	(28
42	Verde-giallo.	Vert-jaunâtre.	Yellowish-green.	(27
41	Verde.	Vert.	Green.	(26
40	Violaceo-verdognolo.	Violet-verdâtre.	Greenish-violet.	(25
39	Lacca-violacea.	Laque-violette.	Violet-lake.	(24
38	Lacca-rosea.	Laque-rose.	Rose-lake.	(22
37	Rancio-roseo.	Orange-rose.	Rose-orange.
36	Rancio-verde.	Orange-verdâtre.	Greenish-orange.	(21
35	Verde-rancio.	Vert-orangé.	Orange-green.
34	Verde-giallo.	Vert-jaune.	Yellow-green.	(20
33	Verde-giallognolo.	Vert-jaunâtre.	Yellowish-green.
32	Verde.	Vert.	Green.	(19
31	Porpora-verdognola.	Pourpre-verdâtre.	Greenish-purple.	(18
30	Lacca-turchiniccia.	Laque-bleuâtre.	Blueish-lake.	(17
29	Lacca-purpurea.	Laque-pourprée.	Purpled-lake.	(16
28	Lacca-accesa.	Laque éclatante.	Brilliant-lake.	(15
27	Lacca.	Laque.	Lake.
26	Lacca-rancia.	Laque-orangée.	Orange-lake.	(14
25	Rosso-rancio.	Rouge-orangé.	Orange-red.
24	Rancio-rosso.	Orange-rouge.	Red-orange.
23	Rancio-rossiccio.	Orange-rougeâtre.	Reddish-orange.
22	Rancio.	Orange.	Orange.	(13
21	Giallo-rancio.	Jaune-orangé.	Orange-yellow.
20	Giallo-acceso.	Jaune éclatant.	Brilliant-yellow.
19	Giallo.	Jaune.	Yellow.
18	Giallo-chiarissimo.	Jaune très-clair.	Very bright yellow.	(12
17	Celeste-giallognolo.	Azur-jaunâtre.	Yellowish-azure.
16	Celeste.	Azur.	Azure.
15	Bleu-chiaro.	Bleu-clair.	Clear-blue.
14	Bleu.	Bleu.	Blue.
13	Bleu-carico.	Bleu-foncé.	Deep-blue.
12	Indaco.	Indigo.	Indigo.	(10
11	Violetto.	Violet.	Violet.	(8
10	Rosso-violaceo.	Rouge-violet.	Violet-red.	(7
9	Ocria-violacea.	Ocre-violette.	Violet-ochre.
8	Ocria.	Ocre.	Ochre.
7	Rosso di rame.	Rouge de cuivre.	Copper-red.	(6
6	Fulvo-acceso.	Fauve éclatant.	Brilliant-tawny.
5	Fulvo.	Fauve.	Tawny.
4	Biondo-acceso.	Blond éclatant.	Brilliant-blond.	(5
3	Biondo d'oro.	Blond-doré.	Golden-blond.
2	Biondo.	Blond.	Blond.
1	Biondo-argentino.	Blond-argentin.	Silver-blond.	(4

1. Biblioth. Univ. vol. xxxiii. xxxiv, xxxv. xxxvi. (Old Series.) Annales de Chimie et de Physique, vol. xxxiv. and xxxv.
2. [A specimen of the productions of this beautiful art was presented by the inventor to the Royal Society, in whose Library it may be seen.—Edit.]
3. The numerals placed within parentheses (in the Table) are designed to indicate the thickness of the plates which produce the different colours. These numbers are taken from Newton's table, the fractional parts only being omitted. The numbers are those which apply to thin layers of water. The unit of measure is the milionth part of an English inch. Our scale should then commence with a layer measuring four of these units in thickness and end with a layer measuring thirty, if we suppose our electro-chemical layers to possess the same refractive power as water. It is probably somewhat less. At all events it is useful to have these numbers immediately before our eyes, in order that we may know, if not the absolute, at least the relative thickness of the attenuated layers which eflectively cover our plates of steel.
4. [The term blond employed in the original has been retained in the translation to avoid the difficulty of giving an exact equivalent. Those brownish tints which m reference to human hair we term light or fair are evidently intended — Edit.]
5. [In the original the name of this colour is fauve, from the Latin fulvus; and the author says that he employs it in order to avoid the circumlocution of 'lion-colour'. — Edit.]
6. The absence of the blue does not affect the theory of the colours of thin plates: indeed I take it as a necessary consequence of the theory. All the homogeneous 'rings commence at the same place; namely, at the verge of the central speck. In this position the thin plate reflects rays of every kind, and this circumstance it is that gives the white without any trace of blue. It is perhaps to the contrast between the white and the black that we are to ascribe the illusion at the place where the two contrary appearances are produced.
7. Professor Amici has been so kind as, at my request, to employ all the means at his command in a careful examination of Newton's rings. He has seen them exactly as I have; for he has found neither blue in the first nor green in the second ring. I value the testimony of my illustrious friend and colleague too highly not to avail myself of it in this case.
8. See additional Note at the end.
9. Optics, Book II. part 3. prop. 5.
10. Biot, Traité de Physique, vol. iv. p. 127.
11. Some persons fancy that the phænomenon arises from the mere displacing of the parts, and thus exclude the intervention of any other substance. According to this notion it is but the metal dividing itself into laminæ of different degrees of thickness, and thus becoming capable of producing the different colours. Such an opinion, however, is opposed to a positive fact already demonstrated; I mean the fact of their opacity being in all cases too great to admit of their furnishing laminae sufficiently transparent to produce the colours in question.
12. In order to give an idea of the efficacy of this preservative, it will be sufficient to quote the following experiment performed in Paris two years ago. I took two steel plates of the same quality and polish. I coloured one of them by the ordinary process, and exposed both in the open air to all the vicissitudes of a rainy autumn. At the end of a month the uncoloured plate was all rusted; the other had lost a little of its colour but was free from rust.
13. If it were allowed me to offer an hypothesis relative to this novel state, I should say that the electro-negative elements disposed in thin layers on the surface of the metals are at too great a distance from the molecules of these
14. When the names of two colours are thus joined, the idea intended to be conveyed is that of the intermediate tint.
15. On Painting, chap. 89.
16. Mengs, Leçons de Peinture.
17. Venturi, Recherche Physique sur les Couleurs, for which the prize of the Italian Society was awarded. Modena, 1802.
18. Leçons Pratiques de Peinture, § v.
19. It may not be useless, perhaps, to mention that my rings are inverse to those of Newton; his begin at the centre, mine at the circumference, where, from the nature of the electro-chemical process, the thinnest layers are deposited: the thickest layers are evidently those of the centre.