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seems here to conduct him in the straight road to Bedlam.

These passages of Father Castel are so singular, that we could not help quoting them; but unfortunately all his fine promises came to nothing. He had constructed a model of his harpsichord, as he tells us himself, so early as the end of the year 1734, and he spent almost the remainder of his life, till the time of his death, which took place in 1757, in completing his instrument, but without success. This harpsichord, constructed at a great expence, as we are told by the author of his life, neither answered the author's intention, nor the expectation of the public. And indeed if there be any analógy between colours and sounds, they differ in so many other points, that it needs excite no wonder that this project should miscarry.

PROBLEM LVI.

To compose a Table representing all the Colours; and to determine their Number.

THOUGH Newton has proved the homogeneity of the colours into which the solar rays are decomposed, and the orange, green and purple produced by this decomposition are no less unalterable, by farther refraction, than the red, yellow and blue, it is however well known that with the three latter, the three former, and all the other colours of nature, can be imitated: for red combined with yellow, in different proportions, gives all the shades of orange; yellow and blue produce pure greens; red and blue violets, purples and indigoes; in a word the different com

all the rest.

binations of these compound colours, givé birth to On these principles is founded the invention of the chromatic triangle, which serves to represent them.

Construct an equilateral triangle, as seen Plate xv, fig. 51, and divide the two sides adjacent to the vertical angle into 13 equal parts: if parallel lines be then drawn through the points of division, in each side, they will form 91 equal rhombuses.

In the three angular rhombs place the three primitive colours, red, yellow, and blue, having an equal degree of strength, and as we may say of concentration; consequently, between the yellow and blue, there will be left II rhomboidal cells, which must be filled up in the following manner: in that nearest the yellow put 11 parts of yellow and I of red; in the next; to parts of yellow and 2 of red, &c; so that in the cell nearest the red there will be I part of yellow and 11 of red: by these means we shall have all the shades of orange, from the one nearest red to that nearest yellow. By filling up, in like manner, the intermediate cells, between red and blue, and between blue and yellow, the result will be all the shades of purple, and all those of green, in a similar gradation,

To fill up the other cells, let us take for example those of the third row below red, where there are three cells. The two extreme cells being filled up on the one side with a combination of 10 parts of red and 2 of yellow, and on the other with a combination of 10 parts of red and 2 of blue, the middle cell will be composed of 10 parts of red, I of blue and I of yellow.

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In the band immediately below, we shall have, for the same reason, in the first cell towards the

yellow, 9 parts of red and 3 of yellow; in the next, 9 parts of red, 2 of yellow and I of blue; in the third, 9 parts of red, 1 of yellow, and 2 of blue; in the fourth, 9 parts of red, and 3 of blue: and the case will be similar in regard to the lower bands; but we shall here content ourselves with detailing the colours in the last except one, or that above the band containing the greens, the cells of which must be filled up as follows: In

The 1st on the left, II parts yellow and of red.
The 2d, 10 parts yellow, I red, I blue.
The 3d, 9 parts yellow, 1 red,
The 4th, 8 parts yellow, I red,
The 5th, 7 parts yellow, I red,
The 6th, 6 parts yellow, I red,
The 7th, 5 parts yellow, I red,
The 8th, 4 parts yellow, I red,
The 9th, 3 parts yellow, I red,
The 10th, 2 parts yellow, I red,
The 11th, 1 part yellow, 1 red,
The 12th, o part yellow, I red,

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2 blue.

3 blue. 4 blue. 5 blue.

6 blue.

7 blue. 8 blue.

9 blue.

10 blue. 11 blue.

This band, as may be seen, contains all the greens of the lowest band into which one part of red has been thrown. In like manner, there will be found in the band parallel to the purples all the purples with which part of yellow has been mixed; and in the band parallel and contiguous to the oranges, all the orange colours with I part of blue.

In the central cell of the triangle there are 4 parts of red, 4 of blue, and 4 of yellow.

All these mixtures might be easily made with

colours ground exceedingly fine; and if the proper quantities were employed we have no doubt that they would produce all the shades of the different colours. But if all the colours of nature, from the lightest to the darkest, that is from black to white, be required, we shall find for each cell 12 degrees of gradation to white, and 12 others to black. If 91 therefore be multiplied by 24, we shall have 2184 perceptible colours; to which if we add 24 grays, formed by the combination of pure black and white, and white and black, the number of compound colours, which we believe to be distinguishable by the senses, will amount to 2218. But we ought not perhaps to consider as real colours those formed by the pure colours with black; for black only obscures, but does not colour, In this case the real colours with their shades, from the darkest to the lightest, ought to be reduced to 1092, which with white, a black, and 12 grays, will form 1106

colours.

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PROBLEM LVII.

On the Cause of the Blue Colour of the Sky.

THIS is a very remarkable phenomenon, though little attention is paid to it, as our eyes are so much accustomed to it from our infancy; and it would be difficult to explain it had not Newton's theory respecting light, by teaching us that it is decomposed into seven colours. of different degrees of refrangibility and reflexibility, afforded us the means of discovering the cause.

To explain this phenomenon, we shall observe then, that according to Newton's theory, so well

proved by experience, of the seven colours which the solar light produces when decomposed by the prism, the blue, indigo, and violet, are those easiest reflected, when they meet with a medium of a different density. But whatever may be the transparency of the air, that which surrounds our earth, and which constitutes our atmosphere, contains always a mixture of vapours more or less combined with it: hence it happens that the light of the sun and stars, sent back in a hundred different ways into the atmosphere, must' experience in it numberless inflections and reflections. But as the blue, indigo and violet rays are those chiefly sent back to us, at each of these reflections, from the minute particles of the vapours which they are obliged to pass through, it is necessary that the medium which sends them back should appear to assume a blue tint. This must even be the case if we suppose a perfect homogeneity in the atmosphere: for however homogeneous a transparent medium may be, it necessarily reflects a part of the rays of light which pass through it. But of all these rays, the blue are reflected with the greatest facility; consequently the air, even supposing it homoge neous, would assume a blue, or perhaps a violet colour.

It is for the same reason that the water of the sea appears of a blue colour when very pure, as is the case at a distance from the coasts, When illuminated by the sun a part of the rays enters the water, and another part is reflected; but the latter is composed chiefly of blue rays, and consequently it must appear blue.

This explanation is confirmed by a curious observation of Dr. Halley. This celebrated philoso

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