drogen is almost invisible, and that of spirits of wine is very dull when compared with an ordinary lamp. Thirdly, it depends on the area or surface the shining body exposes, the brightness being greater according as that surface is greater. Fourthly, in the absorption which the light suffers in passing the medium through which it has to traverse-for even the most transparent obstructs it to a certain extent. And lastly, on the angle at which the rays strike the surface they illuminate, being most effective when they fall perpendicularly, and less in proportion as their obliquity increases. The first and last of the conditions here mentioned, as controlling the intensity of light—the effect of distance and of obliquity-may be illustrated as follows:

1st. That the intensity of light is inversely as the squares of the distance. Let B, Fig. 210, be an aperture in a piece of paper, through which rays coming from a small illuminated point, A, pass; let these rays be received on a second piece of paper, C, placed twice as far from A as is B, it will be found that they illuminate a surface which is twice as long and twice as broad as A, and therefore contains four times the area. If the paper be placed at D, three times as far from A as is B, the illuminated space will be three times as long and three times as broad as A, and contain nine times the surface. If it be at E, which is four times the distance, the surface will be sixteen times as great. All this arises from the rectilinear paths which the diverging rays take, and therefore a surface illuminated by a given light will receive, at distances represented by the numbers 1, 2, 3, 4, &c., quantities of light represented by the numbers 1,,, , &c., which latter are the inverse squares of the former numbers. 2nd. That the intensity of light is dependent on the angle at which the strike the receiving surface, being most effective when they fall perpendicularly, and less in proportion as the obliquity increases. Let there be two surfaces, D C and E C, Fig. 211, on which a beam of light, A B, falls on the former perpendicularly, and on the latter obliquely-the latter surface, in proportion to its obliquity, must have a larger area to receive all the rays which fall on D C. A given quantity of light,

rays

Fig. 211.

therefore, is diffused over a greater surface when it is received obliquely, and its effect is correspondingly less.

To compare different lights with one another, Count Rumford invented a process which goes under the name of the method of shadows. The principle is very simple. Of two lights, that which is the most brilliant will cast the deepest shadow, and with any light the shadow which is cast becomes less dark as the light is more distant. If, therefore, we wish to examine experimentally the brilliancy of two lights on Rumford's method, we take a screen of white paper, and setting in front of it an opaque rod, we place the lights in such a position that the two shadows arising shall be close together, side by side. Now the eye can, without any difficulty, determine which of the two is darkest; and by removing the light, which has cast it to a greater distance, we can, by a few trials, bring the two shadows to precisely the same degree of depth. Now measure the distances of the two lights from the screen, and the illuminating powers are as the squares of those distances.

Ritchie's photometer is an instrument for obtaining the same result; not, however, by the contrast of

shadows, but by the equal illumination of surfaces. It consists of a box, a b, Fig. 212, six or eight inches long, and one broad and deep, in the middle of which a wedge of wood, feg, with its angle, e, upward, is placed. This wedge is covered over with clean white paper, neatly doubled to a sharp line at e. In the top of the box there is a conical tube,

n

Fig. 212.

On

with an aperture, d, at its upper end, to which the eye is applied, and the whole may be raised to any suitable height by means of the stand, c. looking down through d, having previously placed the two lights, m n, the intensity of which we desire to determine on opposite sides of the box, they illuminate the paper surfaces exposed to them, e fto m, and eg to n, and the eye, at d, sees both those surfaces at once. By changing the position of the lights, we eventually make them illuminate the surfaces equally, and then measuring their distances from e, their illuminating powers are as the squares of those distances.

It is not possible to apply either of these methods in a satisfactory manner, where, as is unfortunately often the case, the lights to be examined differ in colour. The eye can form no judgment whatever of the relation of brightness of two surfaces when they are of different colours; and a very slight amount of tint completely destroys the accuracy of these processes. To some extent, in Ritchie's instrument, this may be avoided by placing a coloured glass at the aperture, d.

A third photometric method has recently been introduced; it has great advantages over either of the foregoing; and difference of colour, which in them is so serious an obstacle, serves in it actually to increase the accuracy of the result. The principle on which it is founded is as follows: If we take two lights, and cause one of them to throw the shadow of an opaque body upon a white screen, there is a certain distance to which, if we bring

the second light, its rays, illuminating the screen, will totally obliterate all traces of the shadow. This disappearance of the shadow can be judged of with great accuracy by the eye. It has been found that eyes of average sensitiveness fail to distinguish the effect of a light when it is in presence of another sixty-four times as intense. The precise number varies somewhat with different eyes; but to the same eye it is always the same. If there be any doubt as to the perfect disappearance of the shadow, the receiving screen may be agitated or moved a little. This brings the shadow, to a certain extent, into view again. Its place can then be traced, and, on ceasing the motion, the disappearance verified.

When, therefore, we desire to discover the relative intensities of light, we have merely to inquire at what distance they effect the total obliteration of a shadow, and their intensities are as the squares of those distances. This method has been employed for the determination of the quantities of light emitted by a solid at different temperatures, and found very exact.

Light does not pass instantaneously from one point to another, but with a measurable velocity. The ancients believed that its transmission was instantaneous, illustrating it by the example of a stick, which, when pushed at one end, simultaneously moves at the other. They did not know that even their illustration was false; for a certain time elapses before the further end of the stick moves; and, in reality, a longer time than light would require to pass over a distance equal to the length of the stick. But, in 1676, a Danish astronomer, Roemer, found, from observations on the eclipses of Jupiter's satellites, that light moves at the rate of about 192,000 miles in one second.

This singular observation may be explained as follows: Let S, Fig. 213,

Fig. 213.

be the sun, E the earth, moving in the orbit, E E, as indicated by the arrows; let J be Jupiter, and T his first satellite, moving in its orbit round him. It takes the satellite 42 hours, 28 minutes, 35 seconds, to pass from T to T-that is to say, through the planet's shadow. But, during this period of time, the earth moves in her orbit, from E to E', a space

of 2,880,000 miles. Now, it is found, under these circumstances, that the emersion of the satellite is 15 seconds later than it should have been. And it is clear that this is owing to the fact that the light requires 15 seconds to pass from E to E', and overtake the earth. Its velocity, therefore, in one second, must be 192,000 miles.

This beautiful deduction was corroborated by Dr. Bradley, in 1725, upon totally different principles, involving what is termed the aberration of the stars. The principle, which is somewhat difficult to explain, is clearly illustrated by Eisenlohr as follows: Let M N represent a ship, whose side is aimed at point-blank by a cannon at a. Now, if the vessel were at rest, a ball discharged in this manner would pass through the points b and c, so that the three points, a, b, and c, would all be in the same straight

line. But if the vessel itself move from M towards N, then the ball which entered at b would not come out at the opposite point, c, but at

some other point, d, as much nearer to the stern as is equal to the distance gone over by the vessel, from M to N, during the time of passage of the ball through her. The lines b c and b d, therefore, form an angle at b, whose magnitude depends on the position of b c and b d. The greater the velocity of the ball, as compared with the ship, the less the angle. Next, for the ship substitute in your mind the earth, and for the cannon any of the fixed stars; let the velocity, bc, of the cannon-ball now stand for that of light, and let d c be the velocity of the earth in her orbit. The angle, db c, is called the angle of aberration. It amounts to 20 seconds for all the stars; for they all exhibit the same alteration in their apparent position, being more backward than they really are in the direction of the earth's annual motion, as Bradley discovered. By a simple trigonometrical calculation, it appears from these facts that the velocity of light is 195,000 miles per second, a result nearly coinciding with the former.

Fig. 214.

CHAPTER XXXVI.

REFLECTION OF LIGHT.

Different kinds of Mirrors-General Law of Reflection—Case of Parallel, Converging, and Diverging Rays on Plane Mirrors-The KaleidoscopeProperties of Spherical Concave Mirrors-Properties of Spherical Convex Mirrors-Spherical Aberration-Mirrors of other Forms-Cylindrical Mirrors.

WHEN a ray of light falls upon a surface, it may be reflected, or transmitted, or absorbed.

We therefore proceed to the study of these three incidents which may happen to light, commencing with reflection.

Reflecting surfaces in optics are called mirrors; they are of various kinds, as of polished metal or glass. They differ also as respects the figure of their surfaces, being plane, convex, or concave; and again they are divided into such as are spherical, parabolic, elliptical, &c.

The general law which is at the foundation of this part of optics—the law of reflection-is as follows::

The angle of reflection is equal to the angle of incidence; the reflected ray is in the opposite side of the perpendicular; and the perpendicular, the incident, and the reflected rays are all in the same plane. Thus let, Fig. 215, be the reflecting surface; bi a perpendicular to it

at any point, ni a ray incident on the same point; the path of the reflected ray under the foregoing law will be id: such that it is on the opposite side of the perpendicular to the incident ray, that ni, ip, and id, are all in the same plane, and that the angle of incidence, n i p, is equal to the angle of reflection, i p d.

Reflection from mirror surfaces may be studied under three divisions--reflection from plane, from concave, and from convex mirrors.

When parallel rays fall on a plane mirror, they will be reflected parallel, and divergent and convergent rays will respectively diverge and converge at angles equal to their angles of incidence.

Fig. 215.
Thus, if from the

When rays diverging from a point fall on a mirror, they are reflected from it in such a manner as though they proceeded from a point as far behind it as it is in reality before it. This principle has already been explained in Chapter XXXI. It is illustrated in Fig. 216. point a two rays, a b, a c, diverge, they will, under the general law, be respectively reflected along b d, c e; and if these be produced they will intersect at a', as far behind the mirror as a is before it. The point a' is called the virtual focus.

Fig. 216.

From this it appears that any object seen in a plane mirror appears to be as far behind it as it is in reality before it.

If an object is placed between two parallel plane mirrors, each will produce a reflected image, and will also repeat the one reflected by the other. The consequence is, therefore, that there is an indefinite number of images produced, and in reality the number would be infinite, were the light not gradually enfeebled by loss at each successive reflection.

The kaleidoscope is a tube containing two plane mirrors, which run through it lengthwise, and are generally inclined at an angle of 60°. At one end of the tube is an arrangement by which pieces of coloured glass or other objects may be held, and at the other there is a cap with a small aperture. On placing the eye at this aperture the objects are reflected, and form a beautiful hexagonal combination; their position and appearance may be varied by turning the tube round on ts axis.

The principle upon which the kaleidoscope is constructed is the multiplication of the reflection of an object caused by placing it between two mirrors inclined towards each other at any angle, but usually at 60°. This instrument was invented or revived by Sir David Brewster, who took out a patent for it in 1817. The accompanying figure represents two

a

Fig. 217.

mirrors inclined towards each other at an angle, A B C, having an ob

K