Chapter 13

[1]See "Müller's Elements of Physiology," translated from the German by William Baly, M.D. "The laws of absorption," it has been observed, "have not been studied with so much success as those of other phenomena of physical optics, but some excellent observations on the subject will be found in Herschell's Treatise on Light in the Encyclopædia Metropolitana, § III."

[2]"Eckermann's Gespräche mit Goethe," vol. ii. p. 280. Leonardo da Vinci had made precisely the same observation. "A distant mountain will appear of a more beautiful blue in proportion as it is dark in colour. The illumined air, interposed between the eye and the dark mass, being thinner towards the summit of the mountain, will exhibit the darkness as a deeper blue andvice versâ."—Trattato della Pittura, p. 143. Elsewhere—"The air which intervenes between the eye and dark mountains becomes blue; but it does not become blue in (before) the light part, and much less in (before) the portion that is covered with snow."—p. 244.

[3]This supposes either that the mass was considerably thicker, or that there was a dark ground behind the head, and a light ground behind the rest of the figure.

[4]"Eckermann's Gespräche mit Goethe," vol. ii. p. 242.

[5]Scanelli, "Microcosmo della Pittura," Cesena, 1657, p. 114.

NOTE M.—Par. 177.

Without entering further into the scientific merits or demerits of this chapter on the "First Class of Dioptrical Colours," it is to be observed that several of the examples correspond with the observations of Leonardo da Vinci, and again with those of a much older authority, namely, Aristotle. Goethe himself admits, and it has been remarked by others, that his theory, in many respects, closely resembles that of Aristotle: indeed he confesses[1]that at one time he had an intention of merely paraphrasing that philosopher's Treatise on Colours.[2]

We have already remarked (Note on par.150) that Goethe's notion with regard to the production of warm colours, by the interposition of dark transparent mediums before a light ground, agrees with the practice of the best schools in colouring; and it is not impossible that the same reasons which may make this part of the doctrine generally acceptable to artists now, may have recommended the very similar theory of Aristotle to the painters of the fifteenth and sixteenth centuries: at all events, it appears that the ancient theory was known to those painters.

It is unnecessary to dwell on the fact that the doctrines of Aristotle were enthusiastically embraced and generally inculcated at the period in question;[3]but it has not beenobserved that the Italian writers who translated, paraphrased, and commented on Aristotle's Treatise on Colours in particular, were in several instances the personal friends of distinguished painters. Celio Calcagnini[4]had the highest admiration for Raphael; Lodovico Dolce[5]was the eulogist of Titian; Portius,[6]whose amicable relations with the Florentine painters may be inferred from various circumstances, lectured at Florence on the Aristotelian doctrines early in the sixteenth century. The Italian translations were later, but still prove that these studies were undertaken with reference to the arts, for one of them is dedicated to the painter Cigoli.[7]

The writers on art, from Leon Battista Alberti to Borghini, without mentioning later authorities, either tacitly coincide with the Aristotelian doctrine, or openly profess to explain it. It is true this is not always done in the clearest manner, and some of these writers might say with Lodovico Dolce, "I speak of colours, not as a painter, for that would be the province of the divine Titian."

Leonardo da Vinci in his writings, as in everything else, appears as an original genius. He now and then alludes generally to opinions of "philosophers," but he quotes no authority ancient or modern. Nevertheless, a passage on the nature of colours, particularly where he speaks of the colours of the elements, appears to be copied from Leon Battista Alberti,[8]and from the mode in which some of Leonardo's propositions are stated, it has been supposed[9]that he had been accustomed at Florence to the form of the Aristotelian philosophy. At all events, some of the most important of his observations respecting light and colours, have a great analogy with those contained in the treatise in question. The following examples will be sufficient to prove this coincidence; the corresponding passages in Goethe are indicated, as usual, by the numbers of the paragraphs; the references to Leonardo's treatise are given at the bottom of the page.

ARISTOTLE."A vivid and brilliant red appears when the weak rays of the sun are tempered by subdued and shadowy white,"—154.LEONARDO"The air which is between the sun and the earth at sun-riseor sun-set, always invests what is beyond it more than any other (higher) portion of the air: this is because it is whiter."[10]A bright object loses its whiteness in proportion to its distance from the eye much more when it is illuminated by the sun, for it partakes of the colour of the sun mingled with the colour (tempered by the mass) of the air interposed between the eye and the brightness.[11]ARISTOTLE."If light is overspread with much obscurity, a red colour appears; if the light is brilliant and vivid, this red changes to a flame-colour."[12]—150, 160.LEONARDO."This (the effect of transparent colours on various grounds) is evident in smoke, which is blue when seen against black, but when it is opposed to the (light) blue sky, it appears brownish and reddening."[13]ARISTOTLE."White surfaces as a ground for colours, have the effect of making the pigments[14]appear in greater splendour."—594, 902.LEONARDO."To exhibit colours in their beauty, the whitest ground should be prepared. I speak of colours that are (more or less) transparent."[15]ARISTOTLE."The air near us appears colourless; but when seen in depth, owing to its thinness it appears blue;[16]for where the light is deficient (beyond it), the air is affected by the darkness and appears blue: in a very accumulated state, however, it appears, as is the case with water, quite white."—155, 158.LEONARDO."The blue of the atmosphere is owing to the mass of illuminated air interposed between the darkness above and the earth. The air in itself has no colour, but assumes qualities according to the nature of the objects which are beyond it. The blue of the atmosphere will be the more intense in proportion to the degree of darkness beyond it:" elsewhere—"if the air had not darkness beyond it, it would be white."[17]ARISTOTLE."We see no colour in its pure state, but every hue is variously intermingled with others: even when it is uninfluenced by other colours, the effect of light and shade modifies it in various ways, so that it undergoes alterations and appears unlike itself. Thus, bodies seen in shade or inlight, in more pronounced or softer sun-shine, with their surfaces inclined this way or that, with every change exhibit a different colour."LEONARDO."No substance will ever exhibit its own hue unless the light which illumines it is entirely similar in colour. It very rarely happens that the shadows of opaque bodies are really similar (in colour) to the illumined parts. The surface of every substance partakes of as many hues as are reflected from surrounding objects."[18]Aristotle."So, again, with regard to the light of fire, of the moon, or of lamps, each has a different colour, which is variously combined with differently coloured objects."LEONARDO."We can scarcely ever say that the surface of illumined bodies exhibits the real colour of those bodies. Take a white band and place it in the dark, and let it receive light by means of three apertures from the sun, from fire, and from the sky: the white band will be tricoloured."[19]ARISTOTLE."When the light falls on any object and assumes (for example) a red or green tint, it is again reflected on other substances, thus undergoing a new change. But this effect, though it really takes place, is not appreciable by the eye: though the light thus reflected to the eye is composed of a variety of colours, the principal of these only are distinguishable."LEONARDO."No colour reflected on the surface of another colour, tinges that surface with its own colour (merely), but will bemixed with various other reflections impinging on the same surface:" but such effects, he observes elsewhere, "are scarcely, if at all, distinguishable in a very diffused light."[20]ARISTOTLE."Thus, all combinations of colours are owing to three causes: the light, the medium through which the light appears, such as water or air, and lastly the local colour from which the light happens to be reflected."LEONARDO."All illumined objects partake of the colour of the light they receive."Every opaque surface partakes of the colour of the intervening transparent medium, according to the density of such medium and the distance between the eye and the object."The medium is of two kinds; either it has a surface, like water, &c., or it is without a common surface, like the air."[21]

ARISTOTLE.

"A vivid and brilliant red appears when the weak rays of the sun are tempered by subdued and shadowy white,"—154.

LEONARDO

"The air which is between the sun and the earth at sun-riseor sun-set, always invests what is beyond it more than any other (higher) portion of the air: this is because it is whiter."[10]

A bright object loses its whiteness in proportion to its distance from the eye much more when it is illuminated by the sun, for it partakes of the colour of the sun mingled with the colour (tempered by the mass) of the air interposed between the eye and the brightness.[11]

ARISTOTLE.

"If light is overspread with much obscurity, a red colour appears; if the light is brilliant and vivid, this red changes to a flame-colour."[12]—150, 160.

LEONARDO.

"This (the effect of transparent colours on various grounds) is evident in smoke, which is blue when seen against black, but when it is opposed to the (light) blue sky, it appears brownish and reddening."[13]

ARISTOTLE.

"White surfaces as a ground for colours, have the effect of making the pigments[14]appear in greater splendour."—594, 902.

LEONARDO.

"To exhibit colours in their beauty, the whitest ground should be prepared. I speak of colours that are (more or less) transparent."[15]

ARISTOTLE.

"The air near us appears colourless; but when seen in depth, owing to its thinness it appears blue;[16]for where the light is deficient (beyond it), the air is affected by the darkness and appears blue: in a very accumulated state, however, it appears, as is the case with water, quite white."—155, 158.

LEONARDO.

"The blue of the atmosphere is owing to the mass of illuminated air interposed between the darkness above and the earth. The air in itself has no colour, but assumes qualities according to the nature of the objects which are beyond it. The blue of the atmosphere will be the more intense in proportion to the degree of darkness beyond it:" elsewhere—"if the air had not darkness beyond it, it would be white."[17]

ARISTOTLE.

"We see no colour in its pure state, but every hue is variously intermingled with others: even when it is uninfluenced by other colours, the effect of light and shade modifies it in various ways, so that it undergoes alterations and appears unlike itself. Thus, bodies seen in shade or inlight, in more pronounced or softer sun-shine, with their surfaces inclined this way or that, with every change exhibit a different colour."

LEONARDO.

"No substance will ever exhibit its own hue unless the light which illumines it is entirely similar in colour. It very rarely happens that the shadows of opaque bodies are really similar (in colour) to the illumined parts. The surface of every substance partakes of as many hues as are reflected from surrounding objects."[18]

Aristotle.

"So, again, with regard to the light of fire, of the moon, or of lamps, each has a different colour, which is variously combined with differently coloured objects."

LEONARDO.

"We can scarcely ever say that the surface of illumined bodies exhibits the real colour of those bodies. Take a white band and place it in the dark, and let it receive light by means of three apertures from the sun, from fire, and from the sky: the white band will be tricoloured."[19]

ARISTOTLE.

"When the light falls on any object and assumes (for example) a red or green tint, it is again reflected on other substances, thus undergoing a new change. But this effect, though it really takes place, is not appreciable by the eye: though the light thus reflected to the eye is composed of a variety of colours, the principal of these only are distinguishable."

LEONARDO.

"No colour reflected on the surface of another colour, tinges that surface with its own colour (merely), but will bemixed with various other reflections impinging on the same surface:" but such effects, he observes elsewhere, "are scarcely, if at all, distinguishable in a very diffused light."[20]

ARISTOTLE.

"Thus, all combinations of colours are owing to three causes: the light, the medium through which the light appears, such as water or air, and lastly the local colour from which the light happens to be reflected."

LEONARDO.

"All illumined objects partake of the colour of the light they receive.

"Every opaque surface partakes of the colour of the intervening transparent medium, according to the density of such medium and the distance between the eye and the object.

"The medium is of two kinds; either it has a surface, like water, &c., or it is without a common surface, like the air."[21]

In the observations on trees and plants more points of resemblance might be quoted; the passages corresponding with Goethe's views are much more numerous.

It is remarkable that Leonardo, in opposition, it seems to some authorities,[22]agrees with Aristotle in reckoning black and white as colours, placing them at the beginning and end of the scale.[23]Like Aristotle, again, he frequently makes use of the term black, for obscurity; he even goes further,for he seems to consider that blue may be produced by the actual mixture of black and white, provided they are pure.[24]The ancient author, however, explains himself on this point as follows—"We must not attempt to make our observations on these effects by mixing colours as painters mix them, but by remarking the appearances as produced by the rays of light mingling with each other."[25]

When we consider that Leonardo's Treatise professes to embrace the subject of imitation in painting, and that Aristotle's briefly examines the physical nature and appearance of colours, it must be admitted that the latter sustains the above comparison with advantage; and it is somewhat extraordinary that observations indicating so refined a knowledge of nature, as regards the picturesque, should not have been taken into the account, for such appears to be the fact, in the various opinions and conjectures that have been expressed from time to time on the painting of the Greeks. The treatise in question must have been written when Apelles painted, or immediately before; and as a proofthat Aristotle's remarks on the effect of semi-transparent mediums were not lost on the artists of his time, the following passage from Pliny is subjoined, for, though it is well known, it acquires additional interest from the foregoing extracts.

"He (Apelles) passed a dark colour over his pictures when finished, so thin that it increased the splendour of the tints, while it protected the surface from dust and dirt: it could only be seen on looking into the picture. The effect of this operation, judiciously managed, was to prevent the colours from being too glaring, and to give the spectator the impression of looking through a transparent crystal. At the same time it seemed almost imperceptibly to add a certain dignity of tone to colours that were too florid." "This," says Reynolds, "is a true and artist-like description of glazing or scumbling, such as was practised by Titian and the rest of the Venetian painters."

The account of Pliny has, in this instance, internal evidence of truth, but it is fully confirmed by the following passage in Aristotle:—"Another mode in which the effect of colours is exhibited is when they appear through each other, as painters employ them when they glaze (ἐπαλειφοντες)[26]a (dark) colour over a lighter one; just as the sun, which is in itself white, assumes a red colour when seen through darkness and smoke. This operation also ensures a variety of colours, for there will be a certain ratio between those which are on the surface and those which are in depth."—De Sensu et Sensili.

Aristotle's notion respecting the derivation of colours from white and black may perhaps be illustrated by the following opinion on the very similar theory of Goethe.

"Goethe and Seebeck regard colour as resulting from the mixture of white and black, and ascribe to the differentcolours a quality of darkness (σκιερὸν), by the different degrees of which they are distinguished, passing from white to black through the gradations of yellow, orange, red, violet, and blue, while green appears to be intermediate again between yellow and blue. This remark, though it has no influence in weakening the theory of colours proposed by Newton, is certainly correct, having been confirmed experimentally by the researches of Herschell, who ascertained the relative intensity of the different coloured rays by illuminating objects under the microscope by their means, &c.

"Another certain proof of the difference in brightness of the different coloured rays is afforded by the phenomena of ocular spectra. If, after gazing at the sun, the eyes are closed so as to exclude the light, the image of the sun appears at first as a luminous or white spectrum upon a dark ground, but it gradually passes through the series of colours to black, that is to say, until it can no longer be distinguished from the dark field of vision; and the colours which it assumes are successively those intermediate between white and black in the order of their illuminating power or brightness, namely, yellow, orange, red, violet, and blue. If, on the other hand, after looking for some time at the sun we turn our eyes towards a white surface, the image of the sun is seen at first as a black spectrum upon the white surface, and gradually passes through the different colours from the darkest to the lightest, and at last becomes white, so that it can no longer be distinguished from the white surface"[27]—See par 40, 44.

It is not impossible that Aristotle's enumeration of the colours may have been derived from, or confirmed by, this very experiment. Speaking of the after-image of colours he says, "The impression not only exists in the sensorium in the act of perceiving, but remains when the organ is at rest. Thus if we look long and intently on any object,when we change the direction of the eyes a responding colour follows. If we look at the sun, or any other very bright object, and afterwards shut our eyes, we shall, as if in ordinary vision, first see a colour of the same kind; this will presently be changed to a red colour, then to purple, and so on till it ends in black and disappears."—De Insomniis.

[1]"Geschichte der Farbenlehre," in the "Nachgelassene Werke." Cotta, 1833.

[2]The treatise in question is ascribed by Goethe to Theophrastus, but it is included in most editions of Aristotle, and even attributed to him in those which contain the works of both philosophers; for instance, in the Aldine Princeps edition, 1496. Calcagnini says, the treatise is made up of two separate works on the subject, both by Aristotle.

[3]His authority seems to have been equally great on subjects connected with the phenomena of vision; the Italian translator of a Latin treatise, by Portius, on the structure and colours of the eye, thus opens his dedication to the Cardinal Ercole Gonzaga, of Mantua:—"Grande anzi quasi infinito è l'obligo che ha il mondo con quel più divino che umano spirito di Aristotile."

[4]In a letter to Ziegler the mathematician, Calcagnini speaks of Raphael as "the first of painters in the theory as well as in the practice of his art." This expression may, however, have had reference to a remarkable circumstance mentioned in the same letter, namely, that Raphael entertained the learned Fabius of Ravenna as a constant guest, and employed him to translate Vitruvius into Italian. This MS. translation, with marginal notes, written by Raphael, is now in the library at Munich. "Passavant, Rafael von Urbino."

[5]Lodovico Dolce's Treatise on Colours (1565) is in the form of a dialogue, like his "Aretino." The abridged theory of Aristotle is followed by a translation of the Treatise of Antonius Thylesius on Colours; this is adapted to the same colloquial form, and the author is not acknowledged: the book ends with an absurd catalogue of emblems. The "Somma della Filosofia d'Aristotile," published earlier by the same author, is a very careless performance.

[6]A Latin translation of Aristotle's Treatise on Colours, with comments by Simon Portius, was first published, according to Goethe, at Naples in 1537. In a later Florentine edition, 1548, dedicated to Cosmo I., Portius alludes to his having lectured at an earlier period in Florence on the doctrines of Aristotle, at which time he translated the treatise in question. Another Latin translation, with notes, was published later in the same century at Padua—"Emanuele Marguino Interprete:" but by far the clearest view of the Aristotelian theory is to be found in the treatise of Antonio Vidi Scarmiglione of Fuligno ("De Coloribus," Marpurgi, 1591). It is dedicated to the Emperor Rudolph II. Of all the paraphrases of the ancient doctrine this comes nearest to the system of Goethe; but neither this nor any other of the works alluded to throughout this Note are mentioned by the author in his History of the Doctrine of Colours, except that of Portius.

[7]An earlier Italian translation appeared in Rome, 1535. See "Argelatus Biblioteca degli Volgarizzatori."

[8]"Della Pittura e della Statua," Lib. I, p. 16, Milan edition, 1804. Compare with the "Trattato della Pittura," p. 141. Other points of resemblance are to be met with. The notion of certain colours appropriated to the four elements, occurs in Aristotle, and is indeed attributed to older writers.

[9]See the notes to the Roman edition of the "Trattato della Pittura."

[10]Page 237.

[11]Page 301.

[12]In the TreatiseDe Igne, by Theophrastus, we find the same notion thus expressed: "Brightness (τὸ λευκὸν) seen through a dark coloured medium (διὰ του μέλανος) appears red; as the sun seen through smoke or soot: hence the coal is redder than the flame." Scarmiglione, from whom Kircher seems to have copied, observes:—"Itaque color realis est lux opaca; licet id e plurimis apparentiis colligere. Luna enim in magnâ solis eclipsi rubra conspicitur, quia tenebris lux præpeditur ac veluti tegitur."—De Coloribus.

[13]Page 122.

[14]Τὰ ἂνθη: translatedfloresby Calcagnini and the rest, by Goethe,die Blüthe, the bloom. That the word sometimes signified pigments is sufficiently apparent from the following passage of Suidas (quoted by Emeric David, "Discours Historiques sur la Peinture Moderne")ἂνθεσι κεκοσμημέναι, οἶον ψιμμιωίῳ φύκει καὶ τοῖς ὸμοίοις. Variis pigmentis ornatæ, ut cerussâ, fuco, et aliis similibus. (Suid. in voc.Ἐξμηθισμένας.) A panel prepared for painting, with a white ground consolidated with wax, and perhaps mastic, was found in Herculaneum.

[15]Page 114.

[16]Ἐν βάθει δὲ θεωρουμίνου ιγγυτάτω φαίνεται τῶ χρώματι κυανονοειδὴς διὰ τὴν ὰραιότητα."But when seen in depth, it appears (even) in its nearest colour, blue, owing to its thinness." The Latin interpretations vary very much throughout. The point which is chiefly important is however plain enough, viz. that darkness seen through a light medium is blue.

[17]Page 136-430.

[18]Page 121, 306, 326, 387.

[19]Page 306.

[20]Page 104, 369.

[21]Page 236, 260, 328.

[22]"De' semplici colori il primo è il bianco: beuchè i filosofi non accettano nè il bianco nè il nero nel numero de' colori."—p. 125, 141. Elsewhere, however, he sometimes adopts the received opinion.

[23]Leon Battista Alberti, in like manner observes:—"Affermano (i filosofi) che le spezie de' colori sono sette, cioè, che il bianco ed il nero sono i duoi estremi, infra i quali ve n'è uno nel mezzo (rosso) e che infra ciascuno di questi duoi estremi e quel del mezzo, da ogni parte ve ne sono due altri." An absurd statement of Lomazzo, p. 190, is copied verbatim from Lodovico Dolce (Somma della Filos. d'Arist.); but elsewhere, p. 306, Lomazzo agrees with Alberti. Aristotle seems to have misled the two first, for after saying there are seven colours, he appears only to mention six: he says—"There are seven colours, if brown is to be considered equivalent to black, which seems reasonable. Yellow, again, may be said to be a modification of white. Between these we find red, purple, green, and blue."—De Sensu et Sensili. Perhaps it is in accordance with this passage that Leonardo da Vinci reckons eight colours.—Trattato, p. 126.

[24]Page 122, 142, 237.

[25]On the authority of this explanation the word μιλάν has sometimes been translated in the foregoing extractsobscurity, darkness.Raffaello Borghini, in his attempt to describe the doctrine of Aristotle with a view to painting, observes—"There are two principles which concur in the production of colour, namely, light and transparence." But he soon loses this clue to the best part of the ancient theory, and when he has to speak of the derivation of colours from white and black, he evidently understands it in a mere atomic sense, and adds—"I shall not at present pursue the opinion of Aristotle, who assumes black and white as principal colours, and considers all the rest as intermediate between them."—Il Riposo, 1. ii. Accordingly, like Lodovico Dolce, he proceeds to a subject where he was more at home, namely, the symbolical meaning of colours.

[25]On the authority of this explanation the word μιλάν has sometimes been translated in the foregoing extractsobscurity, darkness.

Raffaello Borghini, in his attempt to describe the doctrine of Aristotle with a view to painting, observes—"There are two principles which concur in the production of colour, namely, light and transparence." But he soon loses this clue to the best part of the ancient theory, and when he has to speak of the derivation of colours from white and black, he evidently understands it in a mere atomic sense, and adds—"I shall not at present pursue the opinion of Aristotle, who assumes black and white as principal colours, and considers all the rest as intermediate between them."—Il Riposo, 1. ii. Accordingly, like Lodovico Dolce, he proceeds to a subject where he was more at home, namely, the symbolical meaning of colours.

[26]This word is only strictly applied to unctuous substances, and may confirm the views of those writers who have conjectured that asphaltum was a chief ingredient in theatramentumof the ancients.

[27]"Elements of Physiology," by J. Müller, M.D., translated from the German by William Baly, M.D. London, 1839.

NOTE N.—Par. 246.

"The appearance of white in the centre, according to the Newtonian theory, arises from each line of rays forming its own spectrum. These spectra, superposing each other on all the middle part, leave uncorrected (unneutralised) colours only at the two edges."—S.F.[1]

[1]This was objected to Goethe when his "Beyträge sur Optik" first appeared; he answered the objection by a coloured diagram in the plates to the "Farbenlehre:" in this he undertakes to show that the assumed gradual "correction" of the colours would produce results different from the actual appearance in nature.

NOTE O.—Par. 252.

These experiments with grey objects, which exhibit different colours as they are on dark or light grounds, were suggested, Goethe tells us, by an observation of Antonius Lucas, of Lüttich, one of Newton's opponents, and, in the opinion of the author, one of the few who made any well-founded objections. Lucas remarks, that the sun acts merely as a circumscribed image in the prismatic experiments, and that if the same sun had a lighter background than itself, the colours of the prism would be reversed. Thus in Goethe's experiments, when the grey disk is on a dark ground, it is edged with blue on being magnified; when on a light ground it is edged with yellow. Goethe acknowledges that Lucas had in some measure anticipated his own theory.—Vol. ii. p. 440.

NOTE P.—Par. 284.

The earnestness and pertinacity with which Goethe insistedthat the different colours are not subject to different degrees of refrangibility are at least calculated to prove that he was himself convinced on the subject, and, however extraordinary it may seem, his conviction appears to have been the result of infinite experiments and the fullest ocular evidence. He returns to the question in the controversial division of his work, in the historical part, and again in the description of the plates. In the first he endeavours to show that Newton's experiment with the blue and red paper depends entirely on the colours being so contrived as to appear elongated or curtailed by the prismatic borders. "If," he says, "we take a light-blue instead of a dark one, the illusion (in the latter case) is at once evident. According to the Newtonian theory the yellow-red (red) is the least refrangible colour, the violet the most refrangible. Why, then, does Newton place a blue paper instead of a violet next the red? If the fact were as he states it, the difference in the refrangibility of the yellow-red and violet would be greater than in the case of the yellow-red and blue. But here comes in the circumstance that a violet paper conceals the prismatic borders less than a dark-blue paper, as every observer may now easily convince himself," &c.—Polemischer Theil, par. 45. Desaguliers, in repeating the experiment, confessed that if the ground of the colours was not black, the effect did not take place so well. Goethe adds, "not only not so well, but not at all."—Historischer Theil, p. 459. Lucas of Lüttich, one of Newton's first opponents, denied that two differently-coloured silks are different in distinctness when seen in the microscope. Another experiment proposed by him, to show the unsoundness of the doctrine of various refrangibility, was the following:—Let a tin plate painted with the prismatic colours in stripes be placed in an empty cubical vessel, so that from the spectator's point of view the colours may be just hidden by the rim. On pouring water into this vessel, all the colours become visible in the same degree; whereas, it was contended, if the Newtonian doctrine were true, somecolours would be apparent before others.—Historischer Theil, p. 434.

Such are the arguments and experiments adduced by Goethe on this subject; they have all probably been answered. In his analysis of Newton's celebratedExperimentum Crucis, he shows again that by reversing the prismatic colours (refracting a dark instead of a light object), the colours that are the most refrangible in Newton's experiment become the least so, andvice versâ.

Without reference to this objection, it is now admitted that "the difference of colour is not a test of difference of refrangibility, and the conclusion deduced by Newton is no longer admissible as a general truth, that to the same degree of refrangibility ever belongs the same colour, and to the same colour ever belongs the same degree of refrangibility."—Brewster's Optics, p. 72.

NOTE Q—Par. 387.

With the exception of two very inconclusive letters to Sulpice Boisserée, and some incidental observations in the conclusion of the historical portion under the head of entoptic colours, Goethe never returned to the rainbow. Among the plates he gave the diagram of Antonius de Dominis. An interesting chapter on halos, parhelia, and paraselenæ, will be found in Brewster's Optics, p. 270.

NOTE R.—Par. 478.

The most complete exhibition of the colouring or mantling of metals was attained by the late Cav. Nobili, professor of physical science in Florence. The general mode in which these colours are produced is thus explained by him:[1]—

"A point of platinum is placed vertically at the distance of about half a line above a lamina of the same metal laidhorizontally at the bottom of a vessel of glass or porcelain. Into this vessel a solution of acetate of lead is poured so as to cover not only the lamina of platinum, but two or three lines of the point as well. Lastly, the point is put in communication with the negative pole of a battery, and the lamina with the positive pole. At the moment in which the circuit is completed a series of coloured rings is produced on the lamina under the point similar to those observed by Newton in lenses pressed together."

The scale of colours thus produced corresponds very nearly with that observed by Newton and others in thin plates and films, but it is fuller, for it extends to forty-four tints. The following list, as given by Nobili, is divided by him into four series to agree with those of Newton: the numbers in brackets are those of Newton's scale. The Italian terms are untranslated, because the colours in some cases present very delicate transitions.[2]

First Series.1.Biondo argentino (4)[3].6.Fulvo acceso.2.Biondo.7.Rosso di rame (6).3.Biondo d'oro.8.Ocria.4.Biondo acceso (5).9.Ocria violacea.5.Fulvo.10.Rosso violaceo (7).Second Series.11.Violetto (8).20.Giallo acceso.12.Indaco (10).21.Giallo-rancio.13.Blu carico.22.Rancio (13).14.Blu.23.Rancio-rossiccio.15.Blu chiaro (11)24.Rancio-rosso.16.Celeste.25.Rosso-rancio.17.Celeste giallognolo.26.Lacca-rancia (14).18.Giallo chiarissimo (12).27.Lacca.19.Giallo.28.Lacca accesa (15).Third Series.29.Lacca-purpurea (16).34.Verde-giallo (20).30.Lacca-turchiniccia (17).35.Verde-rancio.31.Porpora-verdognola (18).36.Rancio-verde (21).32.Verde (19).37.Rancio-roseo.33.Verde giallognolo.38.Lacca-rosea (22).Fourth Series.39.Lacca-violacea (24).43.Verde-giallo rossiccio (28).40.Violaceo-verdognolo (25).44.Lacca-rosea (30).41.Verde (26).42.Verde-giallo (27).

"These tints," Professor Nobili observes, "are disposed according to the order of the thin mantlings which occasion them; the colour of the thinnest film is numbered 1; then follow in order those produced by a gradual thickening of the medium. I cannot deceive myself in this arrangement, for the thin films which produce the colours are all applied with the same electro-chemical process. The battery, the solution, the distances, &c., are always the same; the only difference is the time the effect is suffered to last. This is a mere instant for the colour of No. 1, a little longer for No. 2, and so on, increasing for the succeeding numbers. Other criterions, however, are not wanting to ascertain the place to which each tint belongs."

The scale differs from that of Newton, inasmuch as there is no blue in Nobili's first series and no green in the second: green only appears in the third and fourth series. "The first series," says the Professor, "is remarkable for the fire and metallic appearance of its tints, the second for clearness and brilliancy, the third and fourth for force and richness." The fourth, he observes, has the qualities of the third in a somewhat lesser degree, but the two greens are very nearly alike.

It is to be observed, that red and green are the principalingredients in the third and fourth series, blue and yellow in the second and first.

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