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DETERMINATION OF PROPER MOTION OF STARS.

[114.

engine, the puffs of steam appear to succeed one another rapidly, and on receding, the time between the puffs is appreciably increased, so much so, indeed, that it is difficult to believe that the engine has not suddenly slackened its speed.

Now, since the effects of light are produced by waves caused by the vibrations of the luminous body, it follows that supposing the source of light to be moving towards the observer with a velocity not insensibly small compared with the velocity of light, the light waves will be more crowded together or the wave length will be shortened and the refrangibility increased. Conversely, if the source of light is receding from the observer the waves will be lengthened and the refrangibility diminished. Dr. Huggins found that the spectra of some stars, like that of the sun, contained dark absorption lines, and that the light from Sirius exhibited the two dark lines c and r due to the presence of an absorbing atmosphere containing hydrogen; but in the spectrum of the light from this star the F line did not agree exactly in position with the green line, obtained by passing electric sparks through hydrogen at low pressure, but was a little less refrangible. This increase of the wave length can only be explained by assuming that the earth and Sirius were at the time of the observation receding from one another. The alteration of refrangibility to the observed extent would be caused by a movement of 414 miles a second, and of this motion 12 miles a second was attributable to the orbital motion of the earth, leaving 29'4 miles a second as the motion of Sirius from the solar system. (Phil. Trans. 1868, 529.) It must be observed, however, that this is not the whole of the motion of the star, for it exhibits an angular movement which obviously would not affect the character of the light.

Dr. Huggins (Proc. Roy. Soc. 1872, xx. 386) has since corrected the number obtained for the motion of Sirius, and has calculated the velocity of the movements of several other stars from and towards the sun, with the following results :

The combination of the observations of the change of refrangibility of light and of the angular motion of stars will doubt

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INTERFERENCES OF UNDULATION.

225

less be of great service to the astronomer in determining the motion of stars in space.

Interference.

(115) Illustrations of Interference of Undulations.-One of the simplest, and at the same time most beautiful proofs of the analogy in the mechanism by which sound and light are produced, is exhibited in the phenomena included under the term interference.

It is well known that when two stretched strings, not quite in unison with each other, are struck simultaneously, each gives its own note, and the compound sound produced, instead of dying away gradually and uniformly, is subject to a succession of alternate maxima and minima of intensity; the sound alternately dies away and revives several times in succession before it becomes finally inaudible; it thus produces what are termed beats in the notes. These beats are due to the interference with each other of the waves produced by the two strings. As one string is vibrating a little faster than the other, it must happen that the direction of the vibrations in the two strings at certain moments must coincide; at this point we have the maximum of sound; the periods of vibration will then gradually recede, and ultimately oppose each other, when they produce a momentary silence.

Again, when two equal impulses are given at a little distance from each other upon the surface of a sheet of still water, each becomes the centre of a system of waves, which ultimately cross each other, and alternately increase and diminish the effect of each other. For example, if in

fig. 92 the concentric circles represent two equal systems of waves in water, setting out simultaneously, they will intersect each other; the length of the wave in each system is the same where the crests of the waves coincide, the elevation will be doubled: but where the crest of one wave

FIG. 92.

coincides with the depression of the other, the water will retain its level surface. These points will occur in regular succession, and form lines of double disturbance and no disturbance.' The lines of double disturbance, indicated in the diagram by the points where the circles touch or cut each other, occur at distances

226

INTERFERENCE-COLOURED BANDS.

[115.

which differ by the entire width of one or more waves, or by an even number of half waves. The intermediate points, or points of no disturbance, are situated at distances from the centres differing by an odd number of half waves: the first will occur at the distance of half a wave; the second at a wave and a half; the third at two waves and a half, and so on. Now these phenomena of undulation in air and in water have an exact counterpart in the case of light.

If a beam of light of a single colour be admitted into a darkened room by two small apertures in a thin sheet of metal, such as pin-holes, placed very near each other, and the light which enters be allowed to fall upon a screen just beyond the point where the outermost rays of the two cones intersect each other, a spot of increased brightness is seen where the screen is intersected by a line at right angles to it, which line also bisects at right angles the line joining the two pin-holes; on either side of this bright spot will be a series of bands, alternately dark and bright, although the dark bands as well as the bright ones are receiving the rays from both apertures. The addition of light to light has here produced darkness. Let o, q, fig. 93, represent the two pin-holes, and A B C D, a section of the screen; let P A bisect the distance between the apertures at right angles, and fall vertically on the screen. If the spots A, B, C, D, each represent the centre of a bright band, o A, QA, will be formed of rays the paths of which are equal; o B, Q B, will differ by the length of one wave; o c, qc, by two waves; O D, Q D, by three waves; and the black bands between the bright ones will be formed by the interfering of rays, the paths of which differ in length successively by half a wave, a wave and a half, two waves and a half, &c.—(Lloyd's Lectures on the Wave Theory of Light, 3rd Edit. 1873, 85.)

с

PDRA

B

FIG. 93.

0

P

The length of the paths traversed by the rays from each aperture is equal in the central spot A, and the intensity of the light is therefore increased; but since the path of the rays on either side of this becomes more or less oblique by regular increase or decrease, the lengths of those paths must necessarily be gradually and progressively either augmented or diminished; consequently the number of undulations in each will as gradually be proportionately increased or diminished. When the lengths of the paths of the two rays differ by an even number of half undulations, that is to say, by entire undulations, a bright band is the result; when they differ by an odd number of half undulations, darkness

115.]

ensues.

INTERFERENCE OF UNDULATIONS.

227

Now as the inclination is progressive, there is necessarily a progressive passage from the brightest light to the most complete darkness. By intercepting the light from one aperture, all the dark bands disappear. The measurement of the breadth of one of these bands affords one means of determining the length of a wave of light of that particular colour, if the length of A P be known. Further, since the length of a wave of light differs in lights of different colour and refrangibility, being longest in the red or least refrangible, and shortest in the violet or most refrangible ones, the coloured bands are broadest in the red and narrowest in the violet ; and if the experiment illustrated by fig. 93 be performed with white light instead of with monochromatic light, the overlapping of the bands of the different colours will produce a succession of iridescent or coloured bands, instead of mere alternations of light and darkness.

The phenomenon of interference is one of the fundamental properties of light: indeed it takes place with common light under all circumstances; but the disturbing causes in ordinary cases exactly compensate each other, and it is only by intercepting part of a pencil of rays, so as to remove the compensating system, that the disturbance produced by the remainder becomes manifest; if in the experiment just described the holes are very much enlarged interference will still occur, but the overlapping of the coloured bands will reproduce white light and the interference will be inappreciable. If upon a brilliant plane reflecting surface, such as a polished plate of steel, a number of very fine lines or grooves be traced at equal intervals, so that there may be from 40 to 800 per millimetre, a surface is obtained which reflects a multitude of diverging cones of light, in consequence of the absence of reflection at regular intervals corresponding to the grooves: these cones of rays interfere at their edges without compensation, and a series of colours of the most brilliant tints is perceptible. A variety of natural objects owe the beautiful iridescent play of colours which they exhibit, to a structure of this kind; instances of this occur in the feathers of many birds. The hues of mother of pearl and other shelly structures are also due to their mode of formation in successive extremely thin laminæ, the edges of which form a series of grooves upon their surfaces, and thus produce the phenomenon; impressions of these grooves may often be taken in sealing-wax or in fusible metal, and the same play of colours is then obtained in the impressions.

When fine lines are ruled on a transparent plate, such as a

228

COLOURS OF THIN PLATES-NEWTON'S RINGS.

[115. piece of glass, the iridescent colours are observed on looking through the plate at a luminous object. If the luminous object be an illuminated slit placed parallel to the lines on the plate, a series of spectra will be observed, which may be projected on a screen or viewed through a telescope. By measuring the angular distance between the different rays of the spectrum and the distances between the lines on the plate, it is possible to determine the length of the waves producing the coloured rays constituting white light. By a process of this kind, Angström has made the most complete map of the black lines in the solar spectrum, in which the wave lengths are measured to fractions of the tenmillionth part of a millimetre.

(116) Colours of Thin Plates.-A different set of colours, also dependent for their origin upon interference, are those termed the colours of thin plates. By dipping the mouth of a wine-glass into a solution of soap in water, or what is better still, into gum-water, a bubble may be formed across it; if the glass be laid upon its side, the film becomes gradually thinner and thinner from the action of gravity, and, if viewed by reflected light, a series of iridescent tints is developed, increasing in brilliancy until the bubble becomes reduced to a state of extreme tenuity; it then appears to become black at the thinnest point, and speedily bursts. These colours are due to the interference of a part of the light which is reflected from the second surface of the film, with that which is reflected from the first surface. Any transparent object, such as glass, thin films of metallic oxides, mica, &c., if reduced to laminæ of sufficient thinness, will produce the same effect. The particular colour is dependent on the thickness of the film. In tempering steel, its surface becomes covered with a film of oxide, and the workmen judge of the heat by the colour produced; the higher the temperature which is applied, the thicker does the film become. The laws which regulate this phenomenon were traced with great success by Newton. He placed a convex lens, of a very long radius of curvature, upon the flat surface of a planoconvex lens. Fig. 94 shows a section of both lenses, the curvature of which is much exag

FIG. 94.

gerated. Around the point of contact the rings developed themselves with a black spot in the centre, in an order dependent upon the thickness of the film of air included between the two plates (fig. 95). Knowing the convexity of the upper lens, he was able to calculate the thickness of the film required