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surface of the reflector is in this instance supposed to be perfectly polished.*
Let A B, Fig. 1, be the plane surface of a plate of glass or metal. Let A C, inclined to A B, represent a part of a wave of light, whose centre is so remote that A C may be considered a straight line. The point C of the wave A C will, in a certain time, advance to the point B of the plane A B, by the rectilinear path C B, perpendicular to A C. But in the same time the point À of the same wave, which is prevented from communicating its motion beyond the plane A B, at least in part, ought to have continued its motion in the etherial matter which is above this plane, and through an extent equal to CB, forming its particular spherical wave, whose radius is A N, equal to C B. This particular wave is here represented by the circumference SNR, whose centre is A. In like manner, every other point HH of the wave AC will, after its arrival at the points K K of the reflecting surface, form a similar particular wave represented by the circumference of circles, whose centres are K K, and whose radii are L B, LB successively. But all these circumferences have for their common tangent the straight line B N, which is a tangent to the first circle S N R. The line BN, therefore, contained between the points B and N, where the perpendicular from the point A falls, being formed by all the cir. cumferences, and terminating the motion which is made by the reflection of the wave A C, is the point where this motion is also in greater quantity than any where else. It is, therefore, the propagation of the wave A C, at the instant that the point Chas arrived in B, for there is no other line which like B N is the common tangent to all these circles, excepting B G below the reflecting plane A B, which would be the propagation of the wave, if the
* Brewster: Art. Optics.
motion had been able to extend itself in a substance homogeneous to that which is above the plane. In order to understand how the wave A C has arrived at BN successively, let the straight lines KO, K O be drawn parallel to B N; and KL, K L parallel to A C, and it will be evident that the rectilineal wave A C has been bent in all the lines O K L successively, and has become rectilinear again in BN. The principal law of catoptics may now be easily demonstrated :—For the triangles A CB, B N A, being rectangular, the sides A B common, we have C B equal to NA, the angle CAB equal to ABN, and A B C equal to B A N. But as C B perpendicular to C A is the direction of the incident ray, A N perpendicular to the wave B N, will be the direction of the reflected ray, consequently the angle of incidence is equal to the angle of reflection.
Although the motion of the etherial matter be partly communicated to that of the reflecting body, yet this will in no respect alter the velocity of the waves, upon which the equality of the angles of incidence and reflection depend : for a slight percussion generates in the same medium waves with as great velocity as a stronger percussion, in the same manner as elastic bodies recover their shape in equal times, whether their compression be great or small. The angles of incidence and reflection will therefore be equal, although the reflectimg body may take away part of the motion of the incident light.
In the transmission of light from a rarer to a denser medium, it is always observed that the ray does not continue through the latter in the same rectilinear course, but is refracted towards the perpendicular in a greater or less degree according to the nature of the transparent medium. The cause of this phenomenon has excited many conjectures. Formerly it was generally considered to depend upon the law of gravitation; but Sir Isaac Newton has shown that this is not the case, upon the following reasoning. He demonstrated, that as all bodies attract one another by the force of gravitation, therefore the attractive forces of two homogeneous spheres upon particles of matter, placed near their surfaces, are in the ratio of the diameters of the spheres.* For example, if a refracting medium of the same density as the earth be spherical, the attractive force excited by the earth near its surface, will surpass that of the medium near its surface, as much as the diameter of the earth surpasses the diameter of the medium, or almost infinitely. When we consider, however, that gravity acts upon all bodies alike, and that a ball impelled from the mouth of a cannon is at first scarcely deflected towards the earth in virtue of its attraction, it follows that the least particle of the ball, if separated from the rest of the mass, would be no more deflected than the whole. Wherefore it follows, that a particle of light, which moves with an infinitely greater velocity than a cannon ball, would be much less deflected from its path by the attractive force of the whole earth, and therefore infinitely less by the attractive force of the medium, as it is infinitely weaker than that of the earth. But as the ray of
* Principia, lib. i. prop. 71, cor. 2.
light is actually deflected in a very considerable degree from its path by the small spherical medium, it must be acted upon by some other power residing in the medium than the force of gravity. Sir Isaac having found, from various optical facts, that light appeared to be attracted, or repelled, by bodies near which it passed, he concluded that the phenomena of refraction were produced by an attractive force residing in all bodies, and extending to some distance beyond their surface. This was Newton's idea, and by its means he has explained the laws of refraction according to the corpuscular theory
Huygens and his followers adopt a different supposition. As formerly mentioned in the general view of the undulatory doctrine, the ether still. exists in the interior of refracting media, but, on account of the attraction of matter, in a state of less elasticity, compared with its density, than when in vacuo, and therefore the elasticity of the ether in the interior of media is less, relatively speaking, in proportion to their refractive powers. Wherefore it follows, that vibrations communicated to the ether in free space are propagated through refractive media by means of the ether in their interior, but with a velocity corresponding to its inferior degree of elasticity. Upon these data, we may proceed, in the following manner, to explain the principal phenomena of refraction. We have thought it better to put the diagrams of reflection and refraction together, in order that those two phenomena may be more readily compared, although we almost fear it will add to the intricacy of the subject.
Let A B, (fig. 1,) represent a plane surface separating two transparent media, and AC a part of a wave of light, whose centre is so remote, that the part A C of the wave may be considered as a straight line. The part C of this wave will in a certain space of time reach the refracting surface A B, in the direction CB, which, as it comes from the luminous centre will be at right angles with A C. But in the same time that C moves from C to B the point A will have arrived at G in the rectilineal direction AG, which is equal and parallel to CB.. And for the same reason, every point of the wave A C will have reached G B provided the transparent medium, whose surface is A B, transmitted the motion of the wave as quickly as that of the ether. But we have supposed, that it transmits it slower. Let us suppose that the motion is transmitted one third slower, for example :—then the point A will only have advanced two-thirds of C B in the medium A B, and will therefore form a particular spherical wave whose circumference TV W has A for its centre, and A V equal to of A G or of CB for its radius. By the same reasoning it may be shown, that the other points H H H of the wave A C, will, during the time that C arrives at B, have not only arrived at the points KKK in the surface of the medium A B, but will have advanced into it by a space KV, KV, equal to i of K M, KM, and will have created round the centres KK K, particular waves represented by circumferences, whose radii KV, KV, KV, are respectively t of KM, KM, K M, that is of the continuation of H K, HK, H K to the straight line BG;
for these radii would bave been equal to the whole of K M, KM, KM, if the two transparent media had the same penetrability. But all these circumferences have for their common tangent the straight line BV, which is the tangent to the first circumference TV W at the point V. The line B V therefore formed by the small arcs of these circumferences, terminates the motion which the wave AC has communicated to the transparent medium ; and where this motion is found in greater quantity than anywhere else. Hence, as may be understood by what was said about the propagation of light in straight lines, this line B V is the propagation of the wave AC at the moment that C arrives at B; for there is no other line below the refracting plane A B, which, like BN, is the common tangent of all the particular waves. In order to understand how the wave A C has come successively into B V we have only to draw the straight lines KP, KP, parallel to B V, and KL, KL, parallel to A C. In this manner it will be seen, that the wave AC has been bent from a straight line, and has again become a straight line at B V. If we now draw E AF, cutting the plane A B at right angles at the point A, and DA perpendicular to the wave AC, D A will be incident ray of light, and A V perpendicular to BV the refracted ray, since the rays are only straight lines, along which the points of the waves are propagated.
By a similar process of reasoning, it may be shown how the luminous waves are separated from the perpendicular in passing from a dense to a rarer medium, and also why the phenomenon of total reflection takes place at great angles of incidence. All these are explained in the most beautiful and satisfactory manner by the undulatory theory, but they would occupy a far greater space than we can allot to them in this elementary sketch.
It would be as well to conclude the subject of refraction, with the explanation which Huygens has given of the refraction of light in media of variable density. The atmosphere of the earth is of this kind, as it is well known that towards the surface of the globe it is much more dense than above. The waves which issue from a luminous point, such as the top of a steeple, A, fig. 2. are propa
gated from it in every direction, and ought, according to the laws of refraction, to extend themselves more widely above, as represented in the diagram, and less widely below, and in other directions more or less in proportion as these directions coincide more or less with the two extremes. Let B C be the wave which conveys to the eye of the spectator at B the impression of the light which emanates from A ; and let B D be the straight line which cuts this wave perpendicularly. Then because the ray, or the straight line, by which we judge of the place where an object appears to us, is nothing more than the perpendicular to the wave which arrives at our eye, it is obvious that the point A will be seen as if it were in the straight line BD or higher than it is in reality. The light issu. ing from the point B has therefore moved through the atmosphere in a direction A E B, which is necessarily perpendicular to all the waves propagated from A as a centre.
(To be continued.)
Nick SOBER, Hon. Sec. “ 'Twas the morning after the fray," said the Major, musingly.“ What fray, my dear Major ?" inquired Manlove, whose deepest affections were immediately awakened. “Ay,—I forgot,” answered the other, with the air of a man suddenly entrapped into the necessity to tell a story," You never heard it.” “I doubt it," whispered Balance to Dick Careless. “But you shall hear it now :-'Twas a sad affair, that murder! though it was all done by the articles of war, and in the enforcement of military discipline : and discipline must be enforced," said the Major, in a higher and firmer tone, and planting his foot abruptly on the floor. “'Tis a pity,” ejaculated Manlove, innocently. « 'l'o enforce discipline, Sir ?” inquired the Major, while a slight Aush of anger stained his cheeks. 5. O no! my dear Major; but that the man was murdered."
" It was a pity,--so it was. I thought so too, the morning after the quarrel. He was a fine fellow : his heart was a jewel, and his body was a case fit to keep it in. I sha'nt forget him, Manlove. He had a fault or two, as we all have ; but that only made me love him the more, with a touch of pity for his weakness. His temper was hot, and, with a little chafing, would flash like gunpowder. But if his fist, now and then, closed sooner than another man's, it opened also more readily, and a wide palm finished the matter. Then, too, - God forgive him, for the laws did not,- he loved liquor; and that -saving the murder—was the death of him. Tis a bad propensity, my friends," said the Major, shaking his head. “ I've known many a man bring disgrace upon himself-(Balance smiled covertly)—and make a bad soldier into the bargain.
“ Well, as I was going to tell you, I was sitting in my quarters, over an egg and coffee, and watching the gambols of a young kitten,