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angle from the vertex, will be greater or less, in proportion to the square of its distance from the vertex. For the area of the image is proportional to the square of its diameter, by 19. E. 6. and this is proportional to the square of the focal distance, by 2. E. 6. Therefore as the intensity of force in the rays of light to burn any object is as the area of the glass directly, and as the area of the solar image inversely, it will also be as the square of the diameter of the glass directly, and as the square of its focal distance inversely.

Cor. 1. Therefore in two lenses or mirrors of the same diameter, the power of burning will be inversely as the squares of their focal distances.

Cor. 2. And in two lenses or mirrors of the same focal distance, the power of burning will be as the squares of their diameters.

The heat of a common wood-fire is about thirtyfive times the heat of the rays of the sun in their common state; as it is found by experiment to raise the mercury in the thermometer about thirty-five times as high as the heat of the sun can raise it. Would we therefore make a glass of a given diameter, that should burn with the intensity of a wood-fire; the area of the solar spot in it, must be only one thirty-fifth part of the bigness of the sun: the diameter of the glass being equal to the apparent diameter of the sun.

A mirror designed either for the purposes of burning, or the copious reflexion of light, should be made of the whitest, and at the same time of the hardest metal we can procure. Because the harder the metal is, the more perfect polish will it receive; and the whiter the metal is, the more copiously will it reflect the rays of light; since the rays of the sun, when thrown promiscuously upon any body in their natural state, give us the

idea of white: and therefore a white body will reflect. more of them than a body of any other colour, all other circumstances being equal. If a mirror were made of black marble, though of a considerable diameter, it would scarcely condense the rays of the sun to such a degree as to produce any sensible heat. Villette made a mirror of about four feet diameter, and near three feet focus, which condensed the rays of the sun 1750 times as much as in their common state, and therefore burned with an intensity 490 times more than a woodfire. But to make the rays from the moon burn, was an effect 7000 times greater than what it could produce.

OPACITY AND TRANSPARENCY..

WHEN the rays of light fall upon any body, some of them are reflected from the surface to the eye, which render that surface visible: if any of them after entering the pores of the body should be reflected to the eye by any of the internal particles, these particles will also become visible: and should a sufficient number be reflected to the eye from all the internal particles of any body, the whole would become visible, and the body would be denominated transparent or diaphonous. But if the rays of light, after entering the pores of the body, be variously reflected from particle to particle in different directions, so that they are suffocated and lost, and few or none of them come to the eye from the internal parts of the body, to render them visible, the body is said to be opake; and nothing but the external surface of such a body can be seen by us, as the internal particles return no rays to the eye, by which they might be seen.

Although the whole body may be opake, yet the minute parts, of which it is composed, may transmit

the rays of light, and become transparent; as is evi dent in the thin plates of an oyster-shell.

The transparency of a body depends upon the smallness of its pores. Because if they were large, there would be an irregular reflexion of the light, from the air which fills them. Although paper is opake, yet when its pores are filled with a substance of nearly the same density with itself, such as oil or water, it becomes transparent. If a number of plates of polished glass be laid together, so as to admit a thin plate of air between each of them, the rays of light, in passing through them, will be variously reflected by the air, but few of them will be transmitted through the whole, and it will thereby become opake. But if the plates of air be removed, and water substituted in their place, or if the polished surfaces of the glass be brought into close contact, the rays of light will be transmitted, and the whole will be transparent. A piece of transparent glass is rendered opake, by being reduced to a powder, and having its pores greatly enlarged; so is water or beer, when agitated into froth. Therefore the pores of bodies must not be less than of a certain assignable dimension, to render them opake; for by making them less, or filling them with a body denser than air, they become transparent. We need not be much surprised at this, when we reflect upon the extreme minuteness of the particles of light, and the possibility of having the solid parts of a body in any assignable proportion to the pores, and yet none of these pores exceeding any given diameter or magnitude.

REFRACTION OF LIGHT.

WHEN a ray of light passes out of one medium, into another of different density, in a direction perpendicular to the surface of the second medium, it is accelerated or retarded in its motion, according as the second medium into which the ray enters, is of greater or less density than the other; but it suffers no change in its direction. As there are more particles in a given space, in the surface of the denser medium, than in the rarer, to attract the ray of light, while it is approaching the denser medium, and the attractive force is exerted in the direction in which the ray moves, its motion will be accelerated for a small space before and after its entrance into the medium; until the attraction in contrary directions become equal. But when it is moving out of a denser into a rarer medium, its motion for the same reason will be retarded.

If a ray of light fall obliquely on a denser medium, while it is moving through a rarer, it will not only have its velocity increased, but will also have its direction altered into another, nearer to the perpendicular to the surface of the denser medium at the point of incidence. For it is then acted on by two forces; by one in the direction of its own motion, and by the attractive force of the denser medium in a direction perpendicular to its surface. The ray must therefore move in the diagonal of a parallelogram, whose sides are in the directions of these forces; that is, it must move in a direction nearer to the perpendicular, making the angle of refraction less than the angle of incidence. But if the ray move out of a denser into a rarer medium, it will be refracted from the perpendicular, making the angle of refraction greater than the angle of incidence: so that what was before the angle

of incidence, now becomes the angle of refraction, and vice versa.

This may be illustrated by a well known experi ment. Let a dollar be placed in the bottom of a bason on the floor, and if you recede from it, until a ray from the farther edge of it, just passing by the edge of the bason, reach the eye, so that the whole dollar becomes invisible; in this position of the eye, if the bason be filled with water, the whole dollar will become visible; as the ray, which now comes from the nearer edge of the dollar, is refracted from the perpendicular, upon its passage out of the water into the air, and thereby is brought low enough to enter the eye.

The velocity of the ray of light, after it enters a denser medium, is to its velocity before it enters it, as the sine of the angle of incidence to the sine of the angle of refraction. For the greater that the attractive force of the denser medium is, the more will the ray be bent towards the perpendicular, and the less will be the sine of the refracted angle. The attractive force of the denser medium acts in right lines perpendicular to its surface, whereas the direction of the incident ray is supposed to be oblique to the surface of the denser medium. The diagonal, therefore, which the refracted ray will describe by the joint influence of these two forces, must lie nearer to the stronger of these forces, and we say in the proportion of the sines inversely. Let RO* be a ray of light moving through a rarer medium ATB, and incident on the denser medium BGA in the point O; instead of going on in the same direction ROG, it will be refracted into the line OF, and have its velocity increased in the proportion of RC to FD, or the sine of the angle of inci

* See Plate 4, fig. 5,

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