s of the Academy of Sciences for the year 1743:

If a person look steadily and for a considerable time at a small red square painted upon white paper, he will at last observe a kind of green-coloured border surround the red square. If he now turn his eyes to some other part of the paper, he will see an imaginary square of a delicate green bordering on blue, and corresponding exactly in point of size with the red square. This imaginary square continues visible for some time, and indeed does not disappear till the eye has viewed successively a number of new objects. It is to this imaginary square that the improper name of accidental colour has been given. If the small square be yellow, the imaginary square or accidental colour is blue; the accidental colour of green is red; of blue, yellow; of white, black; and on the contrary, that of black is white.

The first person, as far as we know, who gave a satisfactory explanation of these phenomena was Professor Schreiber of Vienna, whose dissertation, translated by Mr Bernouilli, has been published in the 26th volume of the Journal de Physique.

In order to understand these phenomena, let us recollect, in the first place, that light consists of seven rays, namely, red, orange, yellow, green, blue, indigo, violet; that whiteness consists in a mixture of all these rays; and that those bodies which reflect but very little light are black. Those bodies that are of any particular colour, reflect a much greater quantity of the rays which constitute that particular colour than of any other rays. Red bodies reflect most red rays; green bodies, most green rays, and so on.

Let us recollect, in the second place, that when two impressions are made at the same time upon any of our organs of sensation, one of which is strong and the other weak, we only perceive the former. Thus if we examine by the prism the rays reflected by a red rose, we shall find that they are of four kinds, namely, red, yellow, green, and blue. In this case, the impression made by the red rays makes that made by the others quite insensible. For the same reason, when a person goes from broad daylight into an ill-lighted room, it appears to him at first perfectly dark, the preceding strong impression rendering him for some time incapable of feeling the weaker impression.

With the assistance of these two remarks, it will not be difficult to explain the phenomena of accidental colours. When a person considers attentively for some time a white square lying on any black substance (paper for instance), it is evident that the part of the retina on which the white square is painted, receives a stronger impression than any other part; at least the greatest number of rays strike upon it. A weaker impression, therefore, will act on it with much less force than upon the rest of the retina. Consequently, when the eye is turned from the white square to some other part of the black paper, a square is perceived of the same size with the white square, and much blacker that any other part of the paper; this is evidently in consequence of the weaker impression made by the rays reflected by the black paper upon that part of the eye previously fatigued by the copious reflection from the white square. For the very same reason, if, after looking for a sufficient cient time at a white square lying on a black ground, we turn our eyes upon a sheet of white paper, we perceive a very well defined black square. In this case, the part of the retina already fatigued is not so sensible to the rays reflected by the white paper as the other parts of it which have not been fatigued. The reason then that black is the accidental colour of white is sufficiently evident.

On the contrary, when we look a sufficient time at a black square lying upon a white ground, if we turn our eyes to any other part of the white paper, or even upon black paper, we shall perceive a small square answering to the black square, and much brighter than any other part of the paper; evidently because that part of the retina on which the black square was painted being less fatigued is more susceptible of impressions than any other part of the eye. Thus we see why the accidental colour of black is white, and why that of white on the contrary is black. These facts, indeed, have been long known, and they have been generally explained in this manner.

When a person has looked for a sufficient time at a red square placed on a sheet of white paper, and then turns his eyes to another part of the paper, that part of the retina on which the red was painted being fatigued, the red rays reflected from the white paper cease to make any sensible impression on it, and consequently there will be seen upon the white paper a square similar to the red square, and the colour of which is that which would result from the mixture of all the rays of light except the red. In general, therefore, the accidental colour is the colour which results from the mixture of all the rays of light, those rays excepted which are the same with the primitive colour.

Now, in order to discover these accidental colours, let us recollect the manner which Newton employed to determine the colour which results from the mixture of several others, the species and quantity of which are known. He did it by dividing the circumference of a circle, so that the arches are to one another in the proportion of a string shortened by degrees, in order to find one after another the notes of an octave; which is nearly the proportion that the different rays occupy when light is decomposed by means of the prism. Or suppose the circumference of the circle, as usual, divided into 360 degrees, the different rays, according to Benvenuti, should occupy the following arches:

- Red, 45° - Orange, 27° - Yellow, 48° - Green, 60° - Blue, 60° - Indigo, 40° - Violet, 89°

Let us now compare the action of colours on one another with that of different weights; and for that purpose let us suppose each colour concentrated in the centre of gravity of its arch. In order to find the colour resulting from any mixture, we have only to find the common centre of gravity of the arches which represent the different colours: The colour resulting from the mixture will be that of the arch to which the common centre of gravity approaches nearest. And if that common centre of gravity is not in the straight line which joins the centre of the circle, and the centre of gravity of the arch to which it is most contiguous, the resulting colour will approach more or less to the colour of the contiguous arch towards which the line, passing through the centre of the circle, and the common centre of gravity of the arches, falls. And farther, the resulting colour will be more or less deep according to the distance of the common centre of gravity from the centre of the circle.

In the case under consideration at present, namely, to determine the different accidental colours, the application of this method is remarkably easy; because only one of the seven primitive colours is excluded, and consequently the six colours from the mixture of which we wish to know the resulting colour are all contiguous. For it is evident, that the sum of the six arches, representing these six colours, will be divided into two equal parts by the line which passes through the centre of the circle and their common centre of gravity; and that if the same line be produced till it reaches the circumference of the circle on the other side, it will also divide the arch representing the seventh omitted colour into two equal parts.

Let us suppose, for instance, that the violet is omitted, and that we wanted to know the colour resulting from the mixture of the other six colours, we have only to bisect the arch representing the violet, and from the point of section to draw a diameter to the circle, the arch of the circle opposite to the violet through which the diameter passes will indicate the colour of the mixture. The arch representing the violet being 89°, let us take the half of it, which is 44°, and let us add to it 45° for the red, 27° for the orange, and 48° for the yellow, we shall have 115°, which wants 25° of half the circumference of the circle. If now we add the 60° for the green, the sum total will be 220°, considerably more than half the circumference; consequently the common centre of gravity is nearest the green arch; but it falls 10° nearer the yellow than the straight line which joins the centre of the circle and the centre of gravity of the green arch. Hence we see that the resulting colour will be green, but that it will have a shade of yellow.

It is evident, then, that the accidental colour of violet must be green with a shade of yellow; and this is actually the case, as any one may convince himself by making the experiment.

Suppose, now, we wanted to know the accidental colour of green, or, which is the same thing, the colour resulting from the mixture of all the primitive rays except the green. The green arch is 60°, the half of which is 30°; if to this we add 60° for the blue arch, and 40° for the indigo arch, we shall have 130°, or 50° degrees less than a semicircle. If to this we add the violet arch, which is 89°, we shall have 30° more than the semicircle; consequently the common centre of gravity falls nearest the violet, and it is 10° nearer the red arch than is the centre of gravity of the violet arch. Hence we know that the accidental colour of green will be violet or purple, with a shade of red: And experiment confirms this.

Buffon observed, that the accidental colour of blue was reddish and pale. Let us see whether we shall obtain the same result from our method. Let us suppose that Buffon employed a light blue. In that case, it to 30°, the half of the blue arch, we add 60° for the green, 48° for the yellow, and 27° for the orange, we shall have 165°, or 15° less than half the circumference of the circle. circle: Consequently the common centre will fall nearest the red ach, but within 1° of the orange. The accidental colour must therefore be red, with a shade of orange; or, which is the same thing, it must be a pale red.

In the same manner we may discover, that the accidental colour of indigo is yellow, inclining a good deal to orange; and that the accidental colour of indigo and blue together is orange, with a strong shade of red. Both of which correspond accurately with experiment.

It would be easy to indicate, in the same manner, the accidental colour of any primitive colour, if what has been said were not sufficient to explain the cause of accidental colours, and to show that their phenomena correspond exactly, both with the Newtonian theory of optics, and with what we know to be laws of our sensations in other particulars.

From the theory above given, which is that of Professor Scherfer, the following consequences may be deduced:

1. The accidental colour of a red square, lying upon a white or a black ground, ought to be blackish, if we call our eyes upon a red coloured surface.

2. If the surface upon which we look at a red square be itself coloured, if it be yellow, for instance, the white paper upon which we afterwards call our eyes will appear blue, with a green square in it corresponding to the original red square. And, in general, we ought to perceive the accidental colour of the ground on which the square is placed, as well as the square itself.

3. If while we are looking at the little square we change the situation of the eye, so that its image shall occupy a different place on the retina, when we turn our eyes to the white paper we shall see two squares, or at least one unlike the figure of the original one.

4. If the white paper on which we look be farther distant than the little square was, the imaginary square will appear considerably larger than the true one.

5. If while we are looking at the little square, we gradually make the eye approach to it, without altering its situation, the imaginary square will appear with a pale border. These, and many other consequences that might easily be deduced, will be found to take place constantly and accurately, if any one chooses to put them to the test of experiment; and therefore may be considered as a complete confirmation of the theory given above of the cause of accidental colours.

There is another circumstance respecting accidental colours which deserves attention. If we continue looking steadfastly at the little square longer than is necessary, in order to perceive its accidental colour, we shall at last see its border tinged with the accidental colour of the ground on which the square is lying. For instance, if a white square be placed upon blue paper, its border becomes yellow; if upon red paper, it becomes green; and it becomes reddish upon green. In like manner, the border of a yellow square becomes greenish upon a red ground, and that of a red square on a green ground becomes purple.

The cause of this phenomenon seems to depend upon the contraction and extension of the image of the square painted on the retina. We know for certain, that the diameter of the pupil changes during our inspecting the square; at first it becomes less, and afterwards increases. And though we cannot see what passes in the bottom of the eye, we can scarcely doubt that similar movements are going on there, if we attend to the changes that are continually taking place in the border of our little square; sometimes it is large, sometimes small; at one time it disappears altogether, and the next moment makes its appearance again.

There is another phenomenon connected with accidental colours, which it is not easy to explain; namely, that if we look at these little squares for a very long time, till the eye is very much fatigued, their accidental colours will appear even after we shut our eyes. The very same thing takes place if we attempt to look at a very luminous object; as the sun, for instance. Professor Scherfer thinks that this may be partly owing to the light which still passes through the eyelids. That some light passes through the eyelids is evident, because when we look towards a strong light with our eyelids shut, we see distinctly their colour, derived from the blood vessels with which they are filled; and if we pass our finger before our eyes, we see the shadow of the finger though our eyelids are shut, provided our eyes be turned towards the window. But that this light is not sufficient to explain the phenomenon in question is evident from this circumstance, that the same accidental colours make their appearance though we go immediately into the darkest place. Perhaps we have accounted for the phenomenon elsewhere (See Metaphysics, Encycl. no. 54.). We pass over the other conjectures of Professor Scherfer, which are exceedingly ingenious, but not sufficiently supported by facts to be admitted.Noah's dove, a small constellation in the southern hemisphere, consisting of 10 stars.