Popular scientific lectures. Ernst Mach
million kilometres; in place of the uncovered and covered lanterns we have the satellite of Jupiter, which alternately appears and disappears. Galileo, therefore, although he could not carry out himself the proposed measurement, found the lantern by which it was ultimately executed.
Physicists did not long remain satisfied with this beautiful discovery. They sought after easier methods of measuring the velocity of light, such as might be performed on the earth. This was possible after the difficulties of the problem were clearly exposed. A measurement of the kind referred to was executed in 1849 by Fizeau (born at Paris in 1819).
I shall endeavor to make the principle of Fizeau's apparatus clear to you. Let s (Fig. 16) be a disk free to rotate about its centre, and perforated at its rim with a series of holes. Let l be a luminous point casting its light on an unsilvered glass, a, inclined at an angle of forty-five degrees to the axis of the disk. The ray of light, reflected at this point, passes through one of the holes of the disk and falls at right angles upon a mirror b, erected at a point about five miles distant. From the mirror b the light is again reflected, passes once more through the hole in s, and, penetrating the glass plate, finally strikes the eye, o, of the observer. The eye, o, thus, sees the image of the luminous point l through the glass plate and the hole of the disk in the mirror b.
If, now, the disk be set in rotation, the unpierced spaces between the apertures will alternately take the place of the apertures, and the eye o will now see the image of the luminous point in b only at interrupted intervals. On increasing the rapidity of the rotation, however, the interruptions for the eye become again unnoticeable, and the eye sees the mirror b uniformly illuminated.
But all this holds true only for relatively small velocities of the disk, when the light sent through an aperture in s to b on its return strikes the aperture at almost the same place and passes through it a second time. Conceive, now, the speed of the disk to be so increased that the light on its return finds before it an unpierced space instead of an aperture, it will then no longer be able to reach the eye. We then see the mirror b only when no light is emitted from it, but only when light is sent to it; it is covered when light comes from it. In this case, accordingly, the mirror will always appear dark.
If the velocity of rotation at this point were still further increased, the light sent through one aperture could not, of course, on its return pass through the same aperture but might strike the next and reach the eye by that. Hence, by constantly increasing the velocity of the rotation, the mirror b may be made to appear alternately bright and dark. Plainly, now, if we know the number of apertures of the disk, the number of rotations per second, and the distance sb, we can calculate the velocity of light. The result agrees with that obtained by Römer.
The experiment is not quite as simple as my exposition might lead you to believe. Care must be taken that the light shall travel back and forth over the miles of distance sb and bs undispersed. This difficulty is obviated by means of telescopes.
If we examine Fizeau's apparatus closely, we shall recognise in it an old acquaintance: the arrangement of Galileo's experiment. The luminous point l is the lantern A, while the rotation of the perforated disk performs mechanically the uncovering and covering of the lantern. Instead of the unskilful observer B we have the mirror b, which is unfailingly illuminated the instant the light arrives from s. The disk s, by alternately transmitting and intercepting the reflected light, assists the observer o. Galileo's experiment is here executed, so to speak, countless times in a second, yet the total result admits of actual observation. If I might be pardoned the use of a phrase of Darwin's in this field, I should say that Fizeau's apparatus was the descendant of Galileo's lantern.
A still more refined and delicate method for the measurement of the velocity of light was employed by Foucault, but a description of it here would lead us too far from our subject.
The measurement of the velocity of sound is easily executed by the method of Galileo. It was unnecessary, therefore, for physicists to rack their brains further about the matter; but the idea which with light grew out of necessity was applied also in this field. Koenig of Paris constructs an apparatus for the measurement of the velocity of sound which is closely allied to the method of Fizeau.
The apparatus is very simple. It consists of two electrical clock-works which strike simultaneously, with perfect precision, tenths of seconds. If we place the two clock-works directly side by side, we hear their strokes simultaneously, wherever we stand. But if we take our stand by the side of one of the works and place the other at some distance from us, in general a coincidence of the strokes will now not be heard. The companion strokes of the remote clock-work arrive, as sound, later. The first stroke of the remote work is heard, for example, immediately after the first of the adjacent work, and so on. But by increasing the distance we may produce again a coincidence of the strokes. For example, the first stroke of the remote work coincides with the second of the near work, the second of the remote work with the third of the near work, and so on. If, now, the works strike tenths of seconds and the distance between them is increased until the first coincidence is noted, plainly that distance is travelled over by the sound in a tenth of a second.
We meet frequently the phenomenon here presented, that a thought which centuries of slow and painful endeavor are necessary to produce, when once developed, fairly thrives. It spreads and runs everywhere, even entering minds in which it could never have arisen. It simply cannot be eradicated.
The determination of the velocity of light is not the only case in which the direct perception of the senses is too slow and clumsy for use. The usual method of studying events too fleet for direct observation consists in putting into reciprocal action with them other events already known, the velocities of all of which are capable of comparison. The result is usually unmistakable, and susceptible of direct inference respecting the character of the event which is unknown. The velocity of electricity cannot be determined by direct observation. But it was ascertained by Wheatstone, simply by the expedient of watching an electric spark in a mirror rotating with tremendous known velocity.
If we wave a staff irregularly hither and thither, simple observation cannot determine how quickly it moves at each point of its course. But let us look at the staff through holes in the rim of a rapidly rotating disk (Fig. 17). We shall then see the moving staff only in certain positions, namely, when a hole passes in front of the eye. The single pictures of the staff remain for a time impressed upon the eye; we think we see several staffs, having some such disposition as that represented in Fig. 18. If, now, the holes of the disk are equally far apart, and the disk is rotated with uniform velocity, we see clearly that the staff has moved slowly from a to b, more quickly from b to c, still more quickly from c to d, and with its greatest velocity from d to e.
A jet of water flowing from an orifice in the bottom of a vessel has the appearance of perfect quiet and uniformity, but if we illuminate it for a second, in a dark room, by means of an electric flash we shall see that the jet is composed of separate drops. By their quick descent the images of the drops are obliterated and the jet appears uniform. Let us look at the jet through the rotating disk. The disk is supposed to be rotated so rapidly that while the second aperture passes into the place of the first, drop 1 falls into the place of 2, 2 into the place of 3, and so on. We see drops then always in the same places. The jet appears to be at rest. If we turn the disk a trifle more slowly, then while the second aperture passes into the place of the first, drop 1 will have fallen somewhat lower than 2, 2 somewhat lower than 3, etc. Through every successive aperture we shall see drops in successively lower positions. The jet will