that if we could view the sun from half its present distance the apparent area which it would cover would be four times as great as that which it covers at present, and the light which the eye would receive from it would also be four times as great. We should thus get more light from the nearer sun in the proportion in which its size was increased; but if we could cut down or cover over this larger and nearer sun until it became of the same apparent size as the ordinary and more distant sun, then we should get precisely the same amount of light from it as we do at present. The same would take place in the case of a fire; the red body of the fire would grow no brighter as we approached it, but it would grow larger, and our eye would receive more light. If, however, we held a long narrow tube before our eye and viewed the fire through it, we should find no difference in the light that reached our eye until we had gone away so far that the fire did not fill up the field of view looking through the tube.

We thus see that the quality or intrinsic brightness of a luminous body does not vary with its distance, meaning by quality or brightness the light that would reach the eye by looking at the body through such a long narrow tube, and supposing the tube to be always so narrow, and the source of light always so large, that in looking through the tube we should see nothing else but this light.

But if the luminous body should be so distant as not to subtend any perceptible area, but rather to appear simply a luminous point like a star, we should not then be able to judge of its intrinsic brightness.

258. The intensity of light is measured by an instrument called a photometer; one of the simplest of these is that devised by Bunsen, who makes a grease spot in a sheet of porous paper.

This spot, if illuminated in front, will appear darker than the surrounding paper, but if illuminated behind it will appear brighter.

Now let a standard light, such as that from a wax candle of known dimensions, be placed behind the paper screen

and kept there in a fixed position during the experiment; the greased spot will shine out in consequence, and appear more luminous than the paper. Next place the light to be examined in front of the screen, and move it to such a distance that the grease spot is made as much darker than the paper by the light in front as it is made brighter by the fixed standard light behind, now appearing, in fact, of the same brightness as the paper.

Different lights may thus be compared with one another; for when the grease spot becomes of the same brightness as the paper, or in fact vanishes as a bright spot, it denotes that an amount of light has been thrown from in front upon the paper equal to that thrown upon it by the fixed standard light behind; and if we know at the same time the distance of the luminous object in front from the paper, we are enabled to measure the intensity of its light. Thus if one light causes the grease spot to vanish when placed at the distance of one foot in front of the screen, and another light when placed at the distance of two feet, we should conclude that the luminosity of the latter is four times as great as that of the former, inasmuch as the latter is found to produce the same effect as the former at double the distance, and we know that by doubling the distance the effect upon the screen is diminished four times (Art. 255).

259. We again remark the distinction between the illuminating power of a source of light and the inherent brightness or quality of the light.

The illuminating power is quantitative merely, and refers to the capacity of the light to illuminate a screen at a given distance. But the intrinsic luminosity takes account of the size of the luminous body as well. For instance, a large fire may produce the same illuminating effect as a couple of jets of gas; but the size of the fire is much larger, and if we place the gas between our eye and the fire we shall soon see that, size for size, the gas will give most light.

LESSON XXVIII.--REFLEXION Of Light.

260. From Plane Mirrors.--When a ray of light falls upon a plane and polished metallic surface, it is reflected according to the same law which holds for sound (Art. 142); that is to say, the angle of reflexion is equal to the angle of incidence, while both the incident and reflected rays are in a plane perpendicular to the surface of the mirror.

The truth of this law may be rendered visible to the eye by allowing a beam from the sun, or from an electric lamp, to fall upon a mirror in an otherwise dark room. The path of the ray, both before and after reflexion, will be rendered sufficiently visible by the floating particles of dust which are lit up as they encounter the beam. If the mirror be horizontal, it will be seen that both rays are in the same vertical plane, and also that if the incident ray falls rapidly towards the mirror the reflected ray rises as rapidly on the other side.

If a luminous substance be placed in front of a plane mirror, an image of the substance is seen, as it were, behind the mirror. We know that in reality there is no substance behind the mirror, although the rays of light which reach the eye from the mirror affect it in the same manner as if there were. This image of the luminous substance given by a plane mirror is therefore called a virtual image.

The following figure will assist in explaining the laws of the formation of images by plane mirrors. Let A denote a luminous point, and M M a plane mirror, and let the reflexion of the luminous point be viewed by the eye at D D'; also let A A' and BC denote lines perpendicular to the plane of the mirror.

CBD.

Now since BD is the reflexion of A B, it follows, from the law of reflexion (Art. 142), that the angle ABC is equal to But ABC is equal to B A A', since A A' and BC are parallel; also CBD is equal to BA' A for the same reason: hence it follows that BA A' is equal to B A' A, and hence that

AM = MA'; that is to say, A' is as much below the mirror as A is above it.

By similar reasoning it might be shown that the reflected line D'B' would, if prolonged, pass through the point A', making AM = M A' as before, and in fact all the rays from A which strike the mirror will, after reflexion, appear to

proceed from A'. We thus see that the point from which the reflected rays appear to proceed lies as much behind the reflecting surface as the luminous point which is the source of the rays lies before it.

We also see how in all cases to construct a figure which will show the apparent form and position of the virtual image of any substance reflected from a plane mirror.

Then let A B C D (Fig. 72) be an irregular body, of which we wish to study the reflexion in the mirror M. From the various points of the body A B C D drop perpendiculars upon the plane of the mirror, and continue them on the other side, until in all cases the lengths behind the mirror are equal to those in front. Then will the figure, formed by joining together the extremities of these lines, represent the apparent position and form of the reflected image.

We are all of us familiar with reflected images from plane mirrors, and it is well known that if a body be close in front

of a mirror its image will appear to be close behind, while if the body be a long way in front its image will be a long way behind.

The reflexion of the human figure in a vertical mirror will be erect, like the figure itself, but it will be left-handed, the right hand of the individual appearing as the left in the reflexion.

In like manner, if letters (Fig. 72) be written upon a wall in front of the mirror from left to right, or in the usual way, their reflected image will appear as if they had been written from right to left.

All these peculiarities of reflected images are easily understood if we bear in mind the rule that the reflected image of a point is as much behind the mirror as the point itself is in front.

261. Reflexion from Curved Mirrors.-When a ray of light strikes any point of a curved surface, in order to find the direction of the reflected ray we must first of all find the position of the tangent plane to the surface at that point. Now it is well known that for exceedingly small distances