at E, exactly midway between R and F, and then, being reflected along the line E A, the lady sees her foot in the direction of this last line, the image of the foot appearing at B', just as far behind the looking-glass as the real foot is before it. Now, it is plain that the whole of the mirror from E downwards is perfectly useless, and that the lady may dispense with this portion, and see her full figure in a looking-glass which is only half her height.

It is easy to see that by reflection we can alter the direction of a ray of light just as we please; and that by means of reflectors suitably disposed we can see round corners, and over walls or houses far higher than we are ourselves. At the siege of Sebastopol, when a gun was fired, the English sailors could not resist the temptation of peeping over their defences to see the effect of the shot. They thus exposed themselves to the Russian riflemen, and many of them were picked off. A friend of mine devised the following simple arrangement to enable them to indulge their curiosity without endangering their lives :

A B (Fig. 3) is a square wooden tube about 18 inches long; a, near the end of the tube, is a hole in the side, and a', at the other end, a similar hole.

The line m n represents a bit of looking-glass placed across the tube as in the figure, and m'n' is a second piece of lookingglass placed in a similar manner. Now, let D be the embankment or parapet, behind which the sailors are concealed. By placing the tube as in the figure the light from the Russians would enter the tube along the line R o, be reflected downwards to o', and thence again to the

eye of the observer placed at E, who would see all that was going on. In this way the operations of an enemy might be watched without any exposure whatever on the part of those watching them. I sometimes meet an old man in one of the London parks

with an instrument founded upon these principles. He extracts a great deal of money from ignorant people by making them believe that the instrument enables them to see through deal-boards or through each other's bodies.

SECT. 3. I have thus far spoken of the reflection of light, I want now to speak of its refraction.

M

B

FIG. 4.

N

Let M N (Fig. 4) be the section of a plate or of a glass of water, with parallel surfaces, and let A B be a beam of light which falls perpendicularly upon the surface of the plate. A portion of this beam is reflected, but a portion goes straight through the transparent plate to c without deviating to the right or to the left. But if a beam, like A' B, fall obliquely on the plate, it does not pursue a straight course, which is that marked by the dotted line; but it is bent or refracted at B, passes on to d, where it is refracted back again, so that after leaving the plate its course is parallel to its course before entering it, but not in the same straight line. When the ray enters from air into glass or water, it is bent towards the perpendicular A c; and when it leaves the glass or water, it is bent from the perpendicular. Let us apply this law. When a boy, I have often made a mistake regarding the depth of water, and before I could swim I sometimes placed myself in danger by going into water which was deeper than I imagined it to be. Let A B (Fig. 5) be the bottom, and C D the surface of a clear river or lake, and let p be a point, say a pebble, at the bottom. Let us suppose a boy's eye placed above the surface about E. The ray from p, which ascends directly upwards so as

E

m

n

D

A

B

p

FIG. 5.

to cut the surface at right angles, reaches the eye without any

refraction, but no other ray from the pebble does this. Take, for example, the rays p q, pr, at both sides of the perpendicular; when they reach the surface they are bent at the points q and r away from the perpendicular. Now, the eye above the water takes no notice of this bending. It sees the object from which the rays come in the direction in which the rays enter the eye, and if we produce the rays p m, q n, backward, their point of intersection, o, is the point at which the pebble really appears to rest. To the eye the rays appear to proceed from this point. Thus, not only is a single pebble, but the whole bottom of the river raised, so as to make the water appear much more shallow than it really is.

E

If, instead of looking straight down through the water, you look obliquely, the bottom will appear to be raised; and now you will have no difficulty in understanding the following very pretty and very common experiment. A B (Fig. 6) is a basin, and c is a piece of coin placed at the bottom of it. Let the eye be placed at E, so that the edge of the basin shall cut off the view of the coin. Now fill the

FIG. 6.

B

basin with water; in consequence of the refraction which I have just explained, its whole bottom will be apparently raised, say to the level A B, and the coin will come into view. This experiment is very easily made, and I would advise you to make it.

SECT. 4. Light passes freely through transparent bodies. Air is transparent, and so is water. Have you ever asked yourselves how it is that a mixture of air and water, as in foam, or in vapour, or in the clouds, can so completely intercept the light? The reason is exactly the same as that given for the enfeebling of the sound of the Orinoco Falls, to which I have already adverted. ing from one transparent substance to another of different refrangibility, a portion of light is always reflected. Now foam is an intimate mixture of air and water. The light which strikes the foam passes incessantly from air to water, and from water to air; at each passage a portion of the light is reflected, and the process is

In pass

repeated so often as at last to cut off the light altogether. If you pound any transparent solid to powder, the little grains taken separately will be transparent, but heaped together they are mixed with air, and the powder is consequently white and opaque. This is the reason why common salt and pounded glass are white and opaque; the effect is wholly due to the repeated reflection of the light at the limiting surfaces of the solid, and the air contained between its grains.

I have said that this is the case with substances having different refrangibility, or which, in other words, possess different powers of bending the rays of light. Air possesses this power, but glass, or salt, or water, possesses it in a much higher degree, and hence the effect of their mixture. But if two transparent substances possess the same refrangibility, there is no reflection at their joining surfaces, and the light passes through both, as if it were a single substance. I remember once being startled by the following fact. I had the transparent eye of an ox, which I wished to preserve; I put it in a glass of water, but, to my astonishment, it at once disappeared. I thought at first it had suddenly melted, but found that this was not the case. The eye was quite safe at the bottom of the glass. When I became older I learned the cause of this; I found that the humour of the eye possessed a refrangibility almost exactly equal to that of water; the consequence was, that there was hardly any reflection from the limiting surfaces of both, and hence no means of seeing the eye.

Now what must the effect be if you take a white pervious body, the opaqueness of which is due to the air mixed up with it, and insinuate into its pores a liquid possessing a refrangibility equal, or nearly equal, to itself? You would thereby expel the air, destroy, or greatly diminish, the repeated internal reflection, and make the substance more transparent. This is the entire philosophy of the transparent paper used by engineers and surveyors. The paper fibres are semi-transparent, but air exists in the pores of the paper, and to this its whiteness and opaqueness are due. If we dip the paper in spirits of turpentine, the liquid fills the pores, driving out the air. The turpentine has nearly the same refrangibility as the paper fibres, and hence its effect is to render the paper transparent. The darkness of spots of grease on paper, or on linen, and the darkened colour of a white towel when you dip it into water, are due to the same cause. How beautiful and interesting these common facts appear when they are properly understood!

SECT. 5. If time permitted, I should like very much to talk to you about the eye, and to explain to you the manner in which it acts upon light. You know what the pupil of the eye is. When you look at a very small dot, a cone of rays, the base of which is the pupil, and the point of which is the dot, enters the eye. Well, the eye has it in its power to squeeze these rays so together that they shall form a little dot upon a screen at the back of the eye, exactly the same as the dot at which you are looking and from which the rays come. This screen is a network, formed by the optic nerve, and is called the retina. Not only is this the case with a single point, but when you look at a man, or at a town, or at an extensive landscape, the eye possesses the power of rebuilding, out of the rays proceeding from these objects, an exact image of them upon the retina. And if you could look at the back of your neighbour's eye when he sees a horse, or a house, or a tree, you would see painted upon his retina an image of the house, or horse, or tree. It is in this way that the nerve receives intelligence of the world without, and this intelligence it afterwards transmits to the brain. With regard to the image upon the retina, the following is known, or believed, to take place. When the image of a strongly illuminated body falls upon the retina, the image encroaches a little beyond its proper limits, because of the intensity of its light. And the object from which the light comes appears, on this account, to be larger than it really is. This effect is called irradiation. Standing at a sufficient distance from a piece of wire brought to a white heat by an electric current, the wire, which in reality may not be thicker than a hair, will appear thicker than a goose quill. You have heard, I have no doubt, of the old moon in the new moon's arms: you have seen the new moon embracing the dim sphere of the satellite, and appearing to be part of a larger sphere! This is due to irradiation, which makes the illuminated rim of the moon appear larger than it really is. Another point to be noticed is the time which a luminous impression remains upon the eye. I have already spoken of the time required for an excitement of the nerve of hearing to subside. Now the impression of an instantaneous luminous flash remains upon the retina for about the tenth of a second; so that if the eye receives say twenty flashes per second, although these flashes might be really distinct, still the source from which they emanated would appear as a constant light. I have made an experiment in which a flame is quenched and re