absolute brightness, the intensity of the illumination, at any distance d, is

ai d2

(7) A plane surface, whose dimensions are small in comparison with the distance, and which is perpendicular to the incident light, may, without sensible error, be considered as a portion of a spherical surface concentric with the luminary. The intensity of the illumination, therefore, or the quantity of light received upon a given portion of such a plane, is expressed by the formula of the preceding Article.

When the surface is inclined to the incident light, the quantity of the light received by any given portion is diminished in the ratio of unity to the sine of the angle of inclination. The intensity of the illumination is, therefore, diminished in the same proportion, and is expressed by the formula

ai sin 0
d2

being the inclination of the surface to the incident light.

(8) Experience proves that the eye is incapable of comparing directly two lights, so as to determine their relative intensity. But, although unable to estimate degrees, the eye can detect differences of intensity with much precision; and with this power it is enabled (by the help of the principles just established) to compare the intensities of two lights indirectly.

Let two portions of the same paper (or any similar reflecting surface) be so disposed, that one of them shall be illuminated by one of the lights to be compared, and the other by the other, the light being incident upon each at the same angle. Then let the distance of one of the lights be altered, until there is no longer any appreciable difference in the inten

sities of the illuminated portions. The illuminating powers of the two lights will then be as the squares of their respective distances; and their absolute brightnesses as the illuminating powers directly, and as their luminous surfaces inversely. For, if i and i' denote the absolute brightnesses of the two lights, a and a' the areas of the luminous surfaces, and d and d' their distances from the paper, the intensities of illumination are ai sin 0 a'' sin 0 d'2

d2

and

respectively; and these being rendered

The following simple and convenient mode of practising this method was suggested by Count Rumford. A small opaque cylinder is interposed between the lights to be compared and a screen; in this case it is obvious that each of the lights will cast a shadow, which is illuminated by the other light, while the remainder of the screen is illuminated by both lights conjointly. If, then, one of the lights be moved, until the shadows appear of equal intensity, their illuminations are equal, and, therefore, the illuminating powers of the two lights are to one another as the squares of their distances from the

screen.

(9) Light is propagated with a finite velocity.

This important discovery was made in the year 1676, by the Danish astronomer, Olaus Roemer. Roemer observed that when Jupiter was in opposition, and therefore nearest to the Earth, the eclipses happened earlier than they should according to the astronomical tables; while, when Jupiter was in conjunction, and therefore farthest, they happened later. He thence inferred that light was propagated with a finite velocity, and that the difference between the computed and observed times was due to the change of distance. This difference is found

to be 8m 13; and accordingly the velocity of light is such, that it traverses 192,500 miles in a second of time.

(10) The velocity of light, combined with that of the Earth in its orbit, was afterwards applied by Bradley to explain the phenomenon of the aberration of the fixed stars. From the theory of aberration so explained, it followed that the velocity of the light of the fixed stars is to the velocity of the Earth in its orbit, as radius to the sine of the maximum aberration. This latter quantity-the constant of aberration, as it is called

-is now found to be 20"-36; and the Earth's velocity being known, the velocity of the light of the fixed stars is deduced. The value so obtained is 191,500 miles in a second, which differs from that inferred from the eclipses of Jupiter's satellites, by only the th part of the whole.

00

From this it follows, that the direct light of the fixed stars, and the reflected light of the satellites, travel with the same velocity.

(11) The velocity of light, emanating from a terrestrial source, has been recently measured by M. Fizeau, by direct experiment. The first idea of this experiment was communicated to M. Arago, by the Abbè Laborde, a few years before; its principle will be understood from the following description.

Let the light of a lamp be reflected nearly perpendicularly by a mirror placed at a considerable distance; let a toothed wheel, the breadth of whose teeth is equal to that of the interval between them, be interposed near the luminous source; and let the mirror be so adjusted that the light passing through one of these intervals is reflected to that diametrically opposite. If the eye be placed behind the latter interval, the wheel being at rest, it will perceive the reflected ray, which has traversed a space equal to double the distance of the mirror from the wheel. But if, on the other hand, the wheel be made to revolve rapidly, its velocity may be such that the light transmitted through the opening at one extremity of the diameter

shall not pass through the opposite aperture on its return, but be intercepted by the adjacent tooth; and it will be continually invisible to the eye, so long as the wheel revolves with the same velocity. If the velocity of the wheel be doubled, the light will be transmitted, on its return, through the succeeding opening, and will reappear to the eye. If the velocity be trebled, the light will be intercepted by the next tooth, and there will be a second eclipse; and so on.

It is plain that if the velocity of the wheel, corresponding to the 1st, 2nd, 3rd, or mth eclipse, be known, the velocity of the light may be calculated. Thus, if the wheel makes n revolutions in a second, and has p teeth, the time of of one tooth across the same point of passage

space

=

1

пр

of a second. Consequently, the first eclipse will correspond

to

1

2np

of a second. But in the same time the light has twice

traversed the distance between the wheel and the mirror. If, therefore, that distance be denoted by a, the velocity of light will be

V = 2a × 2np.

Ifn be the number of revolutions in a second corresponding to the mth eclipse, the velocity of light will be given by the formula,

The apparatus devised by M. Fizeau for this experiment is ingenious and effective. It consists of two telescopes, directed towards each other, and so adjusted that an image of the object-glass of each is formed in the focus of the other. The light from the source is introduced laterally into the first telescope, through an aperture near the eye-piece. It is then received on a transparent plate, placed between the focus and the eye-glass, and inclined at an angle of 45° to the axis of the instrument. It is thus reflected along the axis of the first

telescope, having passed through one of the apertures in the revolving wheel, and is received perpendicularly on the mirror in the focus of the second. It then returns by the same route, and is received by the eye at the eye-glass of the first telescope. The distance of the two telescopes in M. Fizeau's experiments was 9440 yards. The revolving disc had 720 teeth, and was connected with a counting apparatus which measured its velocity of rotation. The first eclipse took place when the wheel made 12.6 revolutions in a second. With double the velocity, the light was again visible; with treble the velocity, there was a second eclipse, and so on. The mean result of the experiments gave 196,000 miles, nearly, for the velocity of light.

(12) Let us now proceed to the physical explanation of the foregoing facts.

We have seen that light travels from one point of space to another in time, and with a prodigious velocity. Now, there are two distinct and intelligible ways of conceiving such a propagated movement. Either it is the same individual body which is found in different times in distant parts of space;-or there are a multitude of moving bodies, occupying the entire interval, each of which vibrates continually within certain limits, while the vibratory motion itself is communicated in succession from one to another, and so advances uniformly. These two modes of propagated movement may be distinguished by the names of the motion of translation and the motion of vibration. The former is more familiar to our thoughts, and is that which we observe, when with the eye we follow the path of a projectile in the air; or about which we reason, when we determine the course of a planet in its orbit. Motions of the latter kind, too, are everywhere taking place around us. When the surface of stagnant water is agitated by any external cause, the particles of the fluid next the origin of the disturbance are set vibrating up and down, and this vibratory motion is communicated to the adjacent particles,