Fig. 19. 20. These difficulties are removed by means of an instrument invented by S'Gravesande. It is called a heliostat, because it enables us to direct and fix the rays of the sun in any manner we please. This instrument is composed of two principal parts, a plane metallic mirror MM, and clock-work by which the mirror is continually changing its position so as to keep the reflected beam always in the same direction. The mirror is made of metal instead of glass, to avoid the inconvenience of a double reflection. That it may take freely every possible position, it is so mounted as to have two motions of rotation perpendicular to each other, one about a horizontal axis AA, and the other about a vertical axis CP, which serves also as a support. The clock-work is connected with the mirror by means of a shaft CQ, attached perpendicularly to its posterior surface, and of which the extremity Q is carried by the hand C'R of the dial, by means of the piece FF, separately represented in figure 20. This piece, which is made in the form of a fork, has a cylindrical shaft 99, which enters freely into a hole made near the extremity R of the dial hand, perpendicular to its direction, by which arrangement the fork is capable of turning about its axis q q. Between the branches of this fork is a small cylindrical tube tt, which turns freely about an axis of rotation a a, perpendicular to the direction of the fork. Combining this motion with that of the fork itself about its axis q q, it will be seen that the little tube may take in space all imaginable directions. Now if we wish to attach the shaft of the mirror to the clock-work, we take off the fork FF, and introduce the extremity Q into the tube tt, which has precisely the same diameter; the axis of the fork is then replaced in the extremity of the dial-hand, the motion of which is thus communicated to the mirror. But in order that the motion of the mirror may be such as to keep the reflected beam in the same direction, the dial must have a position parallel to the plane of the equator; and there must be a certain relation between the distance and the positions of the mirror which cannot be determined or even explained without the aid of the calculus.t † For a full account of the principle of this adjustment, see Biot's Traité de Physique. Tom. iii, p. 176. A more simple form of the heliostat is sometimes used. Let Of the Forces which produce the Reflection of Light at the Surfaces of Bodies. 21. WHEN We have found by experiment the actual laws of reflection, we must next endeavour to refer them to mechanical causes, that is, to assign systems of forces capable of producing the same effects. For if we can discover such forces, we are carried at once to the source of the phenomena, we know all their natural and necessary relations; and instead of involving ourselves in details we have only to examine them in their principles, which is far more simple. Let us endeavour then to assign the cause of the phenomena of reflection. Since we consider light as matter sent forth by the luminous body, we shall seek the conditions to which its particles must be subjected, in order that the phenomena may be such as observation indicates. If we proceed with rigor in this inquiry, the conditions which we shall obtain will be so many properties belonging to light, or to the bodies which act upon it, and which will thus serve to characterize its nature, and the kind of action it experiences from these bodies. If we would afterwards consider light as the effect of pulsations, impressed upon a very elastic medium, these results will not lose any of their value, for they will become so many characteristic conditions, which it is necessary to apply to these pulsations, and the mode of transmission which bodies admit of their possessing. It is thus that physical hypotheses are useful when we regard them simply as the means of connecting, temporarily, phenomena, the cause of the dial plate SS be placed parallel to the plane of the equator, and be made to turn uniformly once in 24 hours by clock-work; and suppose a mirror attached to its under surface, and moveable on an axis coinciding with this surface, and capable of being so adjusted as to reflect the sun's rays perpendicularly through an aperture in the centre of the dial plate. The uniform motion of the dial plate and mirror will preserve the reflected beam constantly in a direction parallel to the axis of the earth. Then, by means of a fixed mirror, this beam may be brought into a horizontal or any other position that may be required. which is not known to us; and such is the nature of the understanding, that we cannot without this aid, follow the connexion of a series of facts, the principle of which is not discovered. It is thus that the astronomer, who is unable to comprehend generally in his formulas the course of a heavenly body, when it is very complicated, calculates successively the different parts of its path adapted to different orbits, which are not respectively applicable, except through a small extent, and which are changed according as it is found that they become erroneous. When we consider light as an actual emission from the luminous body, the phenomena of specular reflection seem, at first sight, to be simple results of the elasticity, which causes the luminous particles to be reflected from the surface of polished bodies, as an ivory ball rebounds from a marble table, making the angle of reflection equal to the angle of incidence. But this idea which first presents itself, and which was also first adopted, will not bear examination. 22. Without being acquainted with the absolute dimensions of the particles of light, it will be readily understood that they must be exceedingly small, so small that the most powerful microscopes cannot magnify them to a perceptible size; if it were otherwise, how could they pass, as they do, through large masses of glass, water, and other transparent substances, not only without any retardation, but, as we shall presently show, with an accelerated motion. And finally, when with their incredible velocity, they fall by millions every instant upon the delicate membranes of the eye, how happens it that the organ is not torn in pieces, and that we do not suffer a thousand pangs, unless it be true that the particles are so minute as to render their impulse almost insensible? Now I ask what proportion there can be between the particles of light and the inequalities which still remain upon bodies, polished by processes of art? And considered in relation to light, what difference is there between bodies polished and unpolished? For in polishing bodies we only rub them, as it were, with small and hard particles of dust, which indeed remove their greater inequalities, but leave them furrowed in every direction. But these particles of dust, which we can recognise with a microscope and even discover with the naked eye, are vast masses, and the furrows which they leave upon bodies are of immense depth, compared with the particles of light. If light, therefore, coming in actual contact with the surface of bodies, were reflected by the mere force of elasticity, the little particles of which it is composed would be dispersed in every direction by the elevations, or lost in the deep cavities, of these bodies; and reflection from the most carefully polished would be hardly more perfect than that from the most rough. But, since reflection from polished bodies is much more abundant, more perfect and regular, we infer that it is not the mere mechanical effect of elasticity, and that the particles of light do not come in actual contact with the polished surface. 23. The force by which the rays are repelled, acts therefore at a distance from the solid surface. It acts, moreover, in general, unequally upon the different particles of the same ray. For in most cases, in which reflection takes place, one part of the incident light is reflected and another transmitted, either because the repulsive force is variable in its action, being at one moment more active and feeble than at another; or, as seems most probable, because all the luminous particles which follow each other successively in the same ray, are not, at the moment of their incidence, in the same physical state, and equally susceptible of being repelled. 24. As to the nature of the reflecting force, we are entirely unacquainted with it. We do not know whether it belongs to the particles of the reflecting body or to those of light; whether it acts by repulsion or attraction; and, considering only its general effects, we might represent it by numberless mechanical But without attempting to determine its nature, we may always compare it to a repulsive force acting at the points of incidence, and tending to repel a certain number of the particles which compose the incident rays. causes. Let us suppose that the waving line AB represents the plane Fig. 21. surface of a body covered with natural asperities, or those which art cannot remove, and let us imagine that all the points of this surface, or more generally, that all the particles of the two contiguous media which compose it, exert at a certain distance a repulsive force upon the luminous particles which approach it. This force must be very powerful at the distance where reflection takes place, since it is then sufficient to destroy the prodigious velocity with which the particles of light are impelled, and to turn them back in the opposite direction; but it must diminish rapidly as the distance increases. For, if it were otherwise, the direction of the reflected rays would be affected by the parts of the reflecting body, which are at a sensible distance from the point of incidence, and then this direction would depend upon the general form of the reflecting surface, whereas it is determined solely by the direction of the superficial element, which the ray strikes upon; and it really takes place as if all the rest of the reflecting surface did not exist. Moreover, if the thickness of the reflecting body be gradually reduced by grinding away the second surface A'B', without altering the first, the regularity and amount of the reflection are not at all effected, at least till the body is brought to an extreme degree of thinness, scarcely attainable by art. Thus the particles situated at a greater depth than this limit, cannot extend their influence to the reflecting surface, or at least to the distance from it at which reflection takes place; and since their force, which is so great at very small distances, is diminished to such a degree as to become insensible at a little depth, it follows that it decreases as the distance varies with very great rapidity. This will, therefore, be one of the characters which we ought to recognise. 25. Let us now suppose that a beam of parallel rays of light Fig. 22. SM, S'M', falls at any angle upon the reflecting surface AB of indefinite extent, and let us consider what takes place with respect to the luminous particles M, M', when they are near enough to begin to feel the repulsive action of the particles of the body. If the surface is perfectly plane, as AB, or which is the same thing, if its inequalities are insensible compared with the distance to which the repulsive force extends, the activity of this force will be the same at every point of the surface, and consequently, the effect upon all the particles of light M, M' ̧ whose directions, velocities, and dispositions are the same, will be equal. This is the case with polished bodies; but if the Fig. 23. reflecting surface is broken up with large elevations E, E', E", separated by deep cavities, F, F', the reflecting force cannot be equal at all these points. It is evident, for example, that the luminous particles which enter the cavities will not be reflected in the same direction with those which fall upon the inclined sides of the elevations, nor those which fall upon the sides like those which fall upon the summits. It may even happen that |