the difference-tone of 101 vibrations and the primary tone of 100 vibrations. By the beats to which they thus give rise, resultant tɔnes exercise an influence on consonance and dissonance.

Resultant tones, when sufficiently loud, are themselves capable of performing the part of primaries, and yielding what are called resultant tones of the second order, by their combination with other primaries. Several higher orders of resultant tones can, under peculiarly favourable circumstances, be sometimes detected.

OPTICS.

CHAPTER LXVII.

PROPAGATION OF LIGHT.

936. Light.-Light is the immediate external cause of our visual impressions. Objects, except such as are styled self-luminous, become invisible when brought into a dark room. The presence of something additional is necessary to render them visible, and that mysterious agent, whatever its real nature may be, we call light.

Light, like sound, is believed to consist in vibration; but it does not, like sound, require the presence of air or other gross matter to enable its vibrations to be propagated from the source to the percipient. When we exhaust a receiver, objects in its interior do not become less visible; and the light of the heavenly bodies is not prevented from reaching us by the highly vacuous spaces which lie between.

It seems necessary to assume the existence of a medium far more subtle than ordinary matter; a medium which pervades alike the most vacuous spaces and the interior of all bodies, whether solid, liquid, or gaseous; and which is so highly elastic, in proportion to its density, that it is capable of transmitting vibrations with a velocity enormously transcending that of sound.

This hypothetical medium is called æther. From the extreme facility with which bodies move about in it, we might be disposed to call it a subtle fluid; but the undulations which it serves to propagate are not such as can be propagated by fluids. Its elastic properties are rather those of a solid; and its waves are analogous to the pulses which travel along the wires of a piano rather than to the waves of extension and compression by which sound is propagated through air. Luminous vibrations are transverse, while those of sound are longitudinal.

A self-luminous body, such as a red-hot poker or the flame of a

candle, is in a peculiar state of vibration. This vibration is communicated to the surrounding æther, and is thus propagated to the eye, enabling us to see the body. In the majority of cases, however, we see bodies not by their own but by reflected light; and we are enabled to recognize the various kinds of bodies by the different modifications which light undergoes in reflection from their surfaces.

As all bodies can become sonorous, so also all bodies can become self-luminous. To render them so, it is only necessary to raise them to a sufficiently high temperature, whether by the communication of heat from a furnace, or by the passage of an electric current, or by causing them to enter into chemical combination. It is to chemical combination, in the active form of combustion, that we are indebted for all the sources of artificial light in ordinary use.

The vibrations of the æther are capable of producing other effects besides illumination. They constitute what is called radiant heat, and they are also capable of producing chemical effects, as in photography. Vibrations of high frequency, or short period, are the most active chemically. Those of low frequency or long period have usually the most powerful heating effects; while those which affect the eye with the sense of light are of moderate frequency.

937. Rectilinear Propagation of Light.-All the remarks which have been made respecting the relations between period, frequency, and wave-length, in the case of sound, are equally applicable to light, inasmuch as all kinds of luminous waves (like all kinds of sonorous waves) have sensibly the same velocity in air; but this velocity is many hundreds of thousands of times greater for light than for sound, and the wave-lengths of light are at the same time very much shorter than those of sound. Frequency, being the quotient of velocity by wave-length, is accordingly about a million of millions of times greater for light than for sound. The colour of lowest pitch is deep red, its frequency being about 400 million million vibrations per second, and its wave-length in air 760 millionths of a millimetre. The colour of highest pitch is deep violet; its frequency is about 760 million million vibrations per second, and its wave-length in air 400 millionths of a millimetre. It thus appears that the range of seeing is much smaller than that of hearing, being only about one octave.

The excessive shortness of luminous as compared with sonorous waves is closely connected with the strength of the shadows cast by a light, as compared with the very moderate loss of intensity produced by interposing an obstacle in the case of sound. Sound may,

RECTILINEAR PROPAGATION.

949

for ordinary purposes, be said to be capable of turning a corner, and light to be only capable of travelling in straight lines. The latter fact may be established by such an arrangement as is represented in Fig. 641. Two screens,

each pierced with a
hole, are arranged so
that these holes are in

a line with the flame
of a candle.
An eye
placed in this line, be-
hind the screens, is then
able to see the flame;
but a slight lateral dis-
placement, either of the
eye, the candle, or either
of the screens, puts
the flame out of sight.
It is to be noted that,

in this experiment, the same medium (air) extends from the eye to the candle. We shall hereafter find that, when light has to pass from one medium to another, it is often bent out of a straight line.

We have said that the strength of light-shadows as compared with sound-shadows is connected with the shortness of luminous waves. Theory shows that, if light is transmitted through a hole or slit, whose diameter is a very large multiple of the length of a lightwave, a strong shadow should be cast in all oblique directions; but that, if the hole or slit is so narrow that its diameter is comparable to the length of a wave, a large area not in the direct path of the beam will be illuminated. The experiment is easily performed in a dark room, by admitting sunlight through an exceedingly fine slit, and receiving it on a screen of white paper. The illuminated area will be marked with coloured bands, called diffraction-fringes; and if the slit is made narrower, these bands become wider.

On the other hand, Colladon, in his experiments on the transmission of sound through the water of the Lake of Geneva, established the presence of a very sharply defined sound-shadow in the water, behind the end of a projecting wall.

For the present we shall ignore diffraction,1 and confine our atten1 See Chap. lxxiv.

tion to the numerous phenomena which result from the rectilinear propagation of light.

938. Images produced by Small Apertures.-If a white screen is placed opposite a hole in the shutter of a room otherwise quite dark,

an inverted picture of the external landscape will be formed upon it, in the natural colours. The outlines will be sharper in proportion as the hole is smaller, and distant objects will be more distinctly represented than those which are very near.

M

B'

A

A

These results are easily explained. Consider, in fact, an external object A B (Fig. 643), and let O be the hole in the shutter. The point A sends rays in all directions into space, and among B them a small pencil, which, after passing through the opening O, falls upon the screen at A'. A' receives light from no other point but A, and A sends light to no part of the screen except A'. The colour and brightness of the spot A' will accordingly depend upon the colour and brightness of A; in other words, A' will be the

N

Fig. 643.-Explanation.