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We have here supposed that the rays diverged after their passage through the concave lens; but this is not absolutely necessary; they may be made only to converge less, and thereby unite in the axis of the lens, without the third convex lens, provided the necessary degree of convergency be effected by the first glass. But it is better, that it should be effected by two convex lenses than by one, as the aberration of the rays arising from the spherical figure of the glass is thereby corrected in some measure. Nor is it necessary that all the lenses should be ground to the same sphere, or be placed close to each other.

When the error arising from the different refrangibility of the rays is thus corrected; those arising from the eye-glasses, usually called the aberration of the rays, may also be lessened, as was hinted above, by increasing their number. If two eye-glasses of a given focal length were used, instead of one of half that focal length, they would, between them, produce the same degree of refraction that is produced by the one, and the visual angle comprehended between the extreme rays would be the same in both cases: but the refraction being equally divided between them, the error arising from the spherical figure of the lenses would be greatly lessened. This error is found to be proportional to the cube of the visual angle; but as half of the visual angle is produced by each glass, the error of aberration arising from each glass will be as the cube of half the visual angle, and the whole error from both will be as twice the cube of half the angle, which is only one fourth of the cube of the whole angle. For the cube of any number is four times as great as twice

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the cube of its half. 2x 1'==2. For the same reason,

if three eye-glasses were used to produce as great a visual angle as is produced by one, the error produced by all would be but a ninth part of the error produced by the one; for one ninth of the cube of any number is equal to three times the cube of its third part.

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3=3×1'. And if four glasses be used instead of one, the error is reduced to a sixteenth part.

Mr. Dolland has not only improved the object-glass of the refracting telescope, but also the eye-tube, by a new disposition of the eye-glasses, using five in number, and disposed in the following order. When the rays are refracted through the object glass, they are thereby made to converge to a distant focus, but meeting with the first eye-glass, they are united in a nearer focus, where they form an inverted image, which might be viewed by a second eye-glass placed at its focal distance from this image, but proceeding parallel through the second eye-glass, they fall upon a third, which would again converge them to a distant focus, but meeting with a fourth lens they are converged to a nearer focus, where a second image is formed, inverted with respect to the first, but erect as to the object. This secondary image is viewed by a fifth eye-glass placed at its focal distance from it. By this construction, it appears, that the telescope is compounded of two, each containing three glasses, counting the compound object-glass as one. They represent objects very distinctly, and are on some accounts preferable to reflectors, as more light is lost by reflexion than by transmission; as they are not so easily tarnished, and as they are as short as the others.

The solar telescope is no other than a common refracting telescope, having its end fast in a scioptric ball in a window shutter, that it may receive the direct

rays of the sun; and the eye-glass being placed at a little more than its focal distance from the image, the rays from it will be converged to a very distant focus on the opposite wall, in a darkened room, where an image will be formed, that may be viewed by the weakest eyes. Eclipses of the sun, and the transits of Venus and Mercury, may thus be seen with the great

est ease.

The magic lantern is only one or more convex lenses, whose focal distance either when single or compounded together is very short, and placed in the side of a box, at a small distance from coloured and transparent pictures on glass, so that a very large and surprising image of the same may be made on the opposite wall in a dark room. It is necessary that they be strongly enlightened by a candle, whose light should also be reflected by a plane speculum, through the convex lens in the side of the box. As this lens is placed at a little more than its focal distance from the object, a large and inverted image of it will be formed at a considerable distance on the opposite wall. No light, but what comes from the candle, should be suffered to fall upon the picture, lest the image be made obscure: and therefore the experiment should be made in a darkened room.

The solar microscope is of the same kind with the magic lantern, only here the objects are very small, and are enlightened by the rays of the sun, through a hole in the window-shutter, and reflected parallel to the floor, by a plane speculum on the outer side of the window. The rays thus transmitted pass through a convex lens, whose focal distance is about two inches and a half, fall upon the object, to enlighten it in a higher degree. The rays that come from the small

object thus enlightened pass through a convex lens, of one quarter of an inch focal distance, placed at a little more than the focal distance from the object, so that they may be converged to a very remote focus on the opposite wall, where a large and inverted image will be formed.

The camera obscura, or darkened room, performs its effects in the same manner, by means of a convex lens of considerable focal distance fixed in the windowshutter, whereby the images of external objects are painted within the room, upon a screen placed so as to receive the distinct images. The distance of the screen from the lens will depend upon the different distances of the external objects, and therefore it must be varied accordingly. No light should be admitted into the room, but what comes through the lens, from the objects; and the sight will be more agreeable, if the objects be enlightened by the sun shining on the side that is turned to the window.

The construction and use of any other optical instruments may very easily be understood from the principles already laid down, so that there is no need of dwelling any longer upon them.

An equal-altitude instrument is a telescope with horizontal and perpendicular wires, either three or five, placed at right angles to each other in the focus of the eye-glass; with two cylindrical arms from the middle of the telescope, tapering away to small terminations, which are to be supported in a couple of notches, that when these arms are placed horizontally by a spirit level, the telescope may move in a vertical circle. The supporters of the telescope are also constructed to turn round upon a perpendicular axis, so that it may move in any vertical circle, and be fixed at any altitude at

pleasure, while it is turned round on the perpendicu lar axis into any azimuth. The altitude to which the telescope is set, is noted by a graduated arch.

The principal design of this instrument is to find the time of the day, by observing the time when the sun has equal altitudes both in the forenoon and afternoon. For the middle moment between these observations is the time when the sun was on the meridian, nearly.

ASTRONOMY.

ASTRONOMY is that science which teaches the construction of the solar system, the magnitudes and distances of the bodies of which it consists; together with the fundamental laws, by which the motions of the heavenly bodies are regulated and preserved.

Nothing can exceed the grandeur and sublimity of the idea, which this science gives of the creation around us. By it we learn, that this earth on which we live, although apparently the largest with which we are acquainted, forms but a very small part in that vast asseinblage of bodies of which the universe is composed: that it would be absolutely invisible to eyes like ours, at the distance of the sun; nay, that its annual orbit, although near two hundred millions of miles in diameter, dwindles into an invisible point at the distance of the nearest of the fixed stars: That however large this earth appears to us, it would require nearly one million and a half of globes, each as large as it, or of eight thousand miles in diameter, to be moulded together, to form one as large as the sun: That some of the planets, those erratic bodies, which were formerly supposed to wander through the heavens without any fixed paths, are many hundred times larger

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