number, all diverging from the same centre; and let us suppose that they are each made to undulate by a disturbing action at that centre, acting in a similar manner, and in the same degree, on all. It is obvious, then, that an undulation will be propagated along all the strings; and that these undulations will be equal in magnitude, and will be propagated with the same velocity, provided the strings be equal in tension, elasticity, and other respects. In this case, then, similar waves will be propagated to points equally distant from the origin of disturbance in the same time; and all the points which are in a similar phase of vibration will be situated on the surface of a sphere, of which that origin is the centre. In the place of the actual strings we have been considering, let us imagine rows of ethereal particles connected by their mutual actions, and all that has been said will apply to the propagation of light, the luminous body being the source of disturbance. The length of the wave is the distance, estimated in any direction from the centre, of two particles which are in similar phases of vibration; and it is therefore the space through which the vibratory movement is propagated in the time of a single vibration. Accordingly, if λ denote the length of the wave, r the time of vibration, and v the velocity of wave-propagation, λ (17) We have hitherto considered the propagation of vibratory movement without reference to any diversity in its nature. It is obvious, however, that vibrations may differ from one another in two particulars,-namely, in the space of vibration, and in the time. In the aerial pulses the amplitude of the vibration determines the loudness of the sound; and the frequency of the pulses, or the time of vibration, determines its note. In like manner, the amplitude of the ethereal vibrations determines the intensity of the light; and their frequency, or the period of vibration, determines the colour. Thus, two lights may differ from one another in intensity and colour, the former depending (according to the wave-theory) on the space of vibration, and the latter on the time. But though the intensity of the light is obviously dependent on the amplitude of the vibration, yet it does not appear, à priori, by what power of the amplitude it is to be represented. In fact, we must define what we mean by a double, triple, &c. quantity of light, before we can know how that quantity is to be mathematically measured. If then we say that a double light is the sum of the lights produced by two luminous origins of equal intensity, placed close together, it is easy to prove that the quantity of light, in general, is measured by the square of the amplitude of the vibration. From this it follows that the intensity of the light diverging from any luminous origin must decrease inversely as the square of the distance; for, from the laws of wave propagation it appears that the space of vibration diminishes in the inverse simple ratio of the distance. Thus the known law of the variation of the intensity of light is deduced from the principles of undulatory propagation. (18) The colour of the light (it has been said) depends on the number of impulses which the nerves of the eye receive, in a given time, from the vibrating particles of the ether,— the sensation of violet being produced by the most frequent vibrations, and that of red by the least frequent. But the number of vibrations performed in a given time varies inversely as the time of a single vibration; the colour of the light, therefore, varies with the time of vibration, or with the length of the wave in a given medium. By experiments, which will be described hereafter, it has been found that the length of a wave, in air, corresponding to the extreme red of the spectrum, is 266 ten-millionths of an inch, and that corresponding to the extreme violet 167 ten-millionths. The length of the wave corresponding to the ray of mean refrangibility is nearly 200 ten-millionths, or th of an inch. It appears, then, that the sensibility of the eye is confined within much narrower limits than that of the ear; the ratio of the times of the extreme vibrations which affect the eye being only that of 1:58 to 1, which is less than the ratio of the times of vibration of a fundamental note and its octave. There is no reason for supposing, however, that the vibrations themselves are confined within these limits. In fact, we know that there are invisible rays beyond the two extremities of the spectrum, whose periods of vibration (and lengths of wave) must fall without the limits now stated to belong to the visible rays. (19) The aberration of light, it has been said, results from the movement of the Earth in its orbit, combined with the movement of light. Nothing can be simpler than its explanation in the theory of emission. In fact, we have only to combine the two coexisting motions according to the known mechanical law, and the apparent direction of the star is that of their resultant. The angle between this direction, and that of the principal component, is called the aberration. In order to explain this phenomenon, in accordance with the principles of the wave-theory, it seemed necessary to suppose that the ether which encompasses the Earth does not participate in its motion, so that the ethereal current produced by their relative motion pervades the solid mass of the Earth as freely," to use the words of Young, "as the wind passes through a grove of trees." Fresnel has developed this hypothesis, and has shown that it suffices to explain other phenomena also, in which the Earth's motion is concerned. Professor Stokes has lately shown that the same results may be deduced from a more plausible hypothesis relative to the mutual dependence of the ether and the Earth. CHAPTER II. REFLEXION AND REFRACTION. (20) WHEN light meets the surface of a new medium, a portion of it is always turned back, or reflected. The reflexion of light is twofold. Thus, when a beam of solar light is admitted into a darkened chamber through an aperture in the window, and is allowed to fall upon a metallic mirror, a reflected beam is seen pursuing a determinate direction after leaving the mirror; and if the eye be placed in this direction, it will perceive a brilliant image of the sun. This beam is said to be regularly reflected, and its intensity increases with the polish of the mirror. But it is observed also, that in whatever part of the room the eye is placed, it can always distinguish the portion of the mirror which reflects the light; some of the rays, consequently, are reflected in all directions. This portion of the light is said to be irregularly reflected, and its intensity decreases with the polish of the mirror. Irregular reflexion is due, mainly, to the inequalities of the reflecting surface, which is composed of an indefinite number of reflecting surfaces in various positions, and which therefore reflect the light in various directions. (21) The angles of incidence and reflexion (or the angles which the incident and reflected rays make with the perpendicular to the reflecting surface at the point of incidence) are in the same plane, and are equal. This law is universally true, whatever be the nature of the light itself, or that of the body which reflects it. (22) The intensity of the reflected light, on the other hand, C is found to vary greatly with the medium. The following leading facts have been established experimentally. I. The quantity of light regularly reflected increases with the angle of incidence, the increase being very slow at moderate incidences, and becoming very rapid at great ones. Thus, water at a perpendicular incidence, according to the experiments of Bouguer, reflects only 18 rays out of 1000; at an incidence of 40° it reflects 22 rays; at 60°, 65 rays; at 80°, 333 rays; and at 8940, 721 rays. II. The quantity of light reflected at the same incidence varies both with the medium upon which the light falls, and with that from which it is incident. Thus, at a perpendicular incidence, the number of rays reflected by water, glass, and mercury, are 18, 25, and 666, respectively, the number of incident rays being 1000. The dependence of the quantity of the reflected light upon the medium from which it is incident is easily shown by immersing a plate of glass in water or oil. III. The differences in the reflective powers of different substances are much more marked at small, than at great incidences. Thus, water and mercury-the first of which reflects but the one-fiftieth part of the incident light at a perpendicular incidence, while the latter reflects two-thirds -are equally reflective at an incidence of 8940, the number of rays reflected at this angle being, in both cases, 721 out of 1000. (23) When light is incident upon the surface of a transparent medium, a portion enters the medium, pursuing there an altered direction. This portion is said to be refracted. When the ray passes from a rarer into a denser medium, the angle of incidence is, in general, greater than the angle of refraction, and the deviation takes place towards the perpendicular to the bounding surface. On the contrary, when the ray passes from a denser into a rarer medium, the angle of |