274
If thus, owing to the above causes, the upper outlines of these squares do not appear level with each other, the correspondence of the under outlines is the more observable; for since both colours, the red and the blue, are darks compared with the white (as in the former case they were light compared with the black), the red edge with its yellow border appears very distinctly under both. It exhibits itself under the warm red surface in its full force, and under the dark blue nearly as it appears under the black: as may be seen if we compare the edges and borders of the figures placed one above the other on the white ground.
275
In order to present these experiments with the greatest variety and perspicuity, squares of various colours are so arranged that the boundary of the black and white passes through them vertically. According to the laws now known to us, especially in their application to coloured objects, we shall find the squares as usual doubly coloured at each edge; each square will appear to be split in two, and to be elongated upwards or downwards. We may here call to mind the experiment with the grey figure seen in like manner on the line of division between black and white (257).
276
A phenomenon was before exhibited, even to illusion, in the instance of a red and blue square on a black ground; in the present experiment the elongation upwards and downwards of two differently coloured figures is apparent in the two halves of one and the same figure of one and the same colour. Thus we are still referred to the coloured edges and borders, and to the effects of their homogeneous and heterogeneous relations with respect to the real colours of the objects.
277
I leave it to observers themselves to compare the various gradations of coloured squares, placed half on black half on white, only inviting their attention to the apparent alteration which takes place in contrary directions; for red and yellow appear elongated upwards if on a black ground, downwards if on a white; blue, downwards if on a black ground, upwards if on a white. All which, however, is quite in accordance with the diffusely detailed examples above given.
278
Let the observer now turn the figures so that the before-mentioned squares placed on the line of division between black and white may be in a horizontal series; the black above, the white underneath. On looking at these squares through the prism, he will observe that the red square gains, by the addition of two red edges; on more accurate examination he will observe the yellow border on the red figure, and the lower yellow border upon the white will be perfectly apparent.
279
The upper red edge on the blue square is on the other hand hardly visible; the yellow border next it produces a dull green by mingling with the figure; the lower red edge and the yellow border are displayed in lively colours.
280
After observing that the red figure in these cases appears to gain by an addition on both Sides, while the dark blue, on one side at least, loses something; we shall see the contrary effect produced by turning the same figures upside down, so that the white ground be above, the black below.
281
For as the homogeneous edges and borders now appear above and below the blue square, this appears elongated, and a portion of the surface itself seems even more brilliantly coloured: it is only by attentive observation that we can distinguish the edges and borders from the colour of the figure itself.
282
The yellow and red squares, on the other hand, are comparatively reduced by the heterogeneous edges in this position of the figures, and their colours are, to a certain extent, vitiated. The blue edge in both is almost invisible. The violet border appears as a beautiful peach-blossom hue on the red, as a very pale colour of the same kind on the yellow; both the lower edges are green; dull on the red, vivid on the yellow; the violet border is but faintly perceptible under the red, but is more apparent under the yellow.
283
Every inquirer should make it a point to be thoroughly acquainted with all the appearances here adduced, and not consider it irksome to follow out a single phenomenon through so many modifying circumstances. These experiments, it is true, may be multiplied to infinity by differently coloured figures, upon and between differently coloured grounds. Under all such circumstances, however, it will be evident to every attentive observer that coloured squares only appear relatively altered, or elongated, or reduced by the prism, because an addition of homogeneous or heterogeneous edges produces an illusion. The inquirer will now be enabled to do away with this illusion if he has the patience to go through the experiments one after the other, always comparing the effects together, and satisfying himself of their correspondence.
Experiments with coloured objects might have been contrived in various ways: why they have been exhibited precisely in the above mode, and with so much minuteness, will be seen hereafter. The phenomena, although formerly not unknown, were much misunderstood; and it was necessary to investigate them thoroughly to render some portions of our intended historical view clearer. 284
In conclusion, we will mention a contrivance by means of which our scientific readers may be enabled to see these appearances distinctly at one view, and even in their greatest splendour. Cut in a piece of pasteboard five perfectly similar square openings of about an inch, next each other, exactly in a horizontal line: behind these openings place five coloured glasses in the natural order, orange, yellow, green, blue, violet. Let the series thus adjusted be fastened in an opening of the camera obscura, so that the bright sky may be seen through the squares, or that the sun may shine on them; they will thus appear very powerfully coloured. Let the spectator now examine them through the prism, and observe the appearances, already
familiar by the foregoing experiments, with coloured objects, namely, the partly assisting, partly neutralising effects of the edges and borders, and the consequent apparent elongation or reduction of the coloured squares with reference to the horizontal line. The results witnessed by the observer in this case, entirely correspond with those in the cases before analysed; we do not, therefore, go through them again in detail, especially as we shall find frequent occasions hereafter to return to the subject. — Note P.
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XIX. Achromatism and Hyperchromatism.
285
Formerly when much that is regular and constant in nature was considered as mere aberration and accident, the colours arising from refraction were but little attended to, and were looked upon as an appearance attributable to particular local circumstances.
286
But after it had been assumed that this appearance of colour accompanies refraction at all times, it was natural that it should be considered as intimately and exclusively connected with that phenomenon; the belief obtaining that the measure of the coloured appearance was in proportion to the measure of the refraction, and that they must advance pare passu with each other,
287
If, again, philosophers ascribed the phenomenon of a stronger or weaker refraction, not indeed wholly, but in some degree, to the different density of the medium, (as purer atmospheric air, air charged with vapours, water, glass, according to their increasing density, increase the so-called refraction, or displacement of the object;) so they could hardly doubt that the appearance of colour must increase in the same proportion; and hence took it for granted, in combining different mediums which were to counteract refraction, that as long as refraction existed, the appearance of colour must take place, and that as soon as the colour disappeared, the refraction also must cease.
288
Afterwards it was, however, discovered that this relation which was assumed to correspond, was, in fact, dissimilar; that two mediums can refract an object with equal power, and yet produce very dissimilar coloured borders.
289
It was found that, in addition to the physical principle to which refraction was ascribed, a chemical one was also to be taken into the account. We propose to pursue this subject hereafter, in the chemical division of ou
r inquiry, and we shall have to describe the particulars of this important discovery in our history of the doctrine of colours. What follows may suffice for the present.
290
In mediums of similar or nearly similar refracting power, we find the remarkable circumstance that a greater and lesser appearance of colour can be produced by. a chemical treatment; the greater effect is owing, namely, to acids, the lesser to alkalis. If metallic oxydes are introduced into a common mass of glass, the Coloured appearance through such glasses becomes greatly increased without any perceptible change of refracting power. That the lesser effect, again, is produced by alkalis, may be easily supposed.
291
Those kinds of glass which were first employed after the discovery, are called flint and crown glass; the first produces the stronger, the second the fainter appearance of colour.
292
We shall make use of both these denominations as technical terms in our present statement, and assume that the refractive power of both is the same, but that flint-glass produces the coloured appearance more strongly by one-third than the crown-glass. The diagram (Plate 3, fig. 2,) may serve in illustration.
293
A black surface is here divided into compartments for more convenient demonstration: let the spectator imagine five white squares between the parallel lines a, b, and c, d. The square No, 1, is presented to the naked eye unmoved from its place,
294
But let the square No. 2, seen through a crown-glass prism g, be supposed to be displaced by refraction three compartments, exhibiting the coloured borders to a certain extent; again, let the square No. 3, seen through a flint glass prism h, in like manner be moved downwards three compartments, when it will exhibit the coloured borders by about a third wider than No. 2.
295
Again, let us suppose that the square No. 4, has, like No. 2, been moved downwards three compartments by a prism of crown-glass, and that then by an oppositely placed prism h, of flint-glass, it has been again raised to its former situation, where it now stands.
296
Here, it is true, the refraction is done away with by the opposition of the two; but as the prism h, in displacing the square by refraction through three compartments, produces coloured borders wider by a third than those produced by the prism g, so, notwithstanding the refraction is neutralised, there must be an excess of coloured border remaining. (The position of this colour, as usual, depends on the direction of the apparent motion (204) communicated to the square by the prism h, and, consequently, it is the reverse of the appearance in the two squares 2 and 3, which have been moved in an opposite direction.) This excess of colour we have called Hyperchromatism, and from this the achromatic state may be immediately arrived at.
297
For assuming that it was the square No. 5 which was removed three compartments from its first supposed place, like No. 2, by a prism of crown-glass g, it would only be necessary to reduce the angle of a prism of flint-glass h, and to connect it, reversed, to the prism g, in order to raise the square No. 5 two degrees or compartments; by which means the Hyperchromatism of the first case would cease, the figure would not quite return to its first position, and yet be already colourless. The prolonged lines of the united prisms, under No. 5, show that a single complete prism remains: again, we have only to suppose the lines curved, and an object-glass presents itself. Such is the principle of the achromatic telescopes.
298
For these experiments, a small prism composed of three different prisms, as prepared in England, is extremely well adapted. It is to be hoped our own opticians will in future enable every friend of science to provide himself with this necessary instrument,
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XX. Advantages of Subjective Experiments.-Transition to the Objective.
299
We have presented the appearances of colour as exhibited by refraction, first, by means of subjective experiments; and we have so far arrived at a definite result, that we have been enabled to deduce the phenomena in question from the doctrine of semitransparent’ mediums and double images.
300
In statements which have reference to nature, everything depends on ocular inspection, and these experiments are the more satisfactory as they may be easily and conveniently made. Every amateur can procure his apparatus without much trouble or cost, and if he is a tolerable adept in pasteboard contrivances, he may even prepare a great part of his machinery himself. A few plain surfaces, on which black, white, grey, and coloured objects may be exhibited alternately on a light and dark ground, are all that is necessary. The spectator fixes them before him, examines the appearances at the edge of the figures conveniently, and as long as he pleases; he retires to a greater distance, again approaches, and accurately observes the progressive states of the phenomena.
301
Besides this, the appearances may be observed with sufficient exactness through small prisms, which need not be of the purest glass. The other desirable requisites in these glass instruments will, however, be pointed out in the section which treats of the apparatus.
302
A great advantage in these experiments, again, is, that they can be made at any hour of the day in any room, whatever aspect it may have. We have no need to wait for sunshine, which in general is not very propitious to northern observers.
303
The objective experiments, on the contrary, necessarily require the sun-light which, even when it is to be had, may not always have the most desirable relation with the apparatus placed opposite to it. Sometimes the sun is too high, sometimes too low, and withal only a short time in the meridian of the best situated room. It changes its direction during the observation; the observer is forced to alter his own position and that of his apparatus, in consequence of which the experiments in many cases become uncertain. If the sun shines through the prism it exhibits all inequalities, lines, and bubbles in the glass, and thus the appearance is rendered confused, dim, and discoloured.
304
Yet both kinds of experiments must be investigated with equal accuracy. They appear to be opposed to each other, and yet are always parallel. What one order of experiments exhibits the other exhibits likewise, and yet each has its peculiar capabilities, by means of which certain effects of nature are made known to us in more than one way.
305
In the next place there are important phenomena which may be exhibited by the union of subjective and objective experiments. The latter experiments again have this advantage, that we can in most cases represent them by diagrams, and present to view the component relations of the phenomena. In proceeding, therefore, to describe the objective experiments, we shall so arrange them that they may always correspond with the analogous subjective examples; for this reason, too, we annex to the number of each paragraph the number of the former corresponding one. But we set out by observing generally that the reader must consult the plates, that the scientific investigator must be familiar with the apparatus in order that the twin-phenomena in one mode or the other may be placed before them.
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XXI.Refraction Without the Appearance of Colour.
306 (195, 196).
That refraction may exhibit its effects without producing an appearance of colour, is not to be demonstrated so perfectly in objective as in subjective experiments. We have, it is true, unlimited spaces which we can look at through the prism, and thus convince ourselves that no colour appears where there is no boundary; but we have no unlimited source of light which we can cause to act through the prism. Our light comes to us from circumscribed bodies; and the sun, which chiefly produces our prismatic appearances, is itself only a small, circumscribed, luminous object
307
We may, however, consider every larger opening through which the sun shines, every larger medium through which the sun-light is transmitted and made to deviate from its course, as so far unlimited that we can confine our attention to th
e centre of the surface without considering its boundaries,
308 (197)
If we place a large water-prism in tilde large bright space is refracted upwards by it on the plane intended to receive the image, and the middle of this illumined space will be colourless. The same effect may be produced if we make the experiment with glass prisms having angles of few degrees: the appearance may be produced even through glass prisms, whose refracting angle is sixty degrees, provided we place the recipient surface near enough.
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XXII.Conditions of the Appearance of Colour.
309 (198)
Although, then, the illumined space before mentioned appears indeed refracted and moved from its place, but not coloured, yet on the horizontal edges of this space we observe a coloured appearance. That here again the colour is solely owing to the displacement of a circumscribed object may require to be more fully proved.
The luminous body which here acts is circumscribed: the sun, while it shines and diffuses light, is still an insulated object. However small the opening in the lid of a camera obscura be made, still the whole image of the sun will penetrate it. The light which streams from all parts of the sun’s disk, will cross itself in the smallest opening, and form the angle which corresponds with the sun’s apparent diameter. On the outside we have a cone narrowing to the orifice; within, this apex spreads again, producing on an opposite surface a round image, which still increases in size in proportion to the distance of the recipient surface from the apex. This image, together with all other objects of the external landscape, appears reversed on the white surface in question in a dark room.
Works of Johann Wolfgang von Goethe Page 308