Popular scientific lectures. Ernst Mach

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СКАЧАТЬ his life, then, the efforts of Galileo to determine the velocity of light remained uncrowned with success. But the subsequent history of the measurement of the velocity of light is intimately associated with his name, for with the telescope which he constructed he discovered the four satellites of Jupiter, and these furnished the next occasion for the determination of the velocity of light.

      The terrestrial spaces were too small for Galileo's experiment. The measurement was first executed when the spaces of the planetary system were employed. Olaf Römer, (born at Aarhuus in 1644, died at Copenhagen in 1710) accomplished the feat (1675–1676), while watching with Cassini at the observatory of Paris the revolutions of Jupiter's moons.

      

Fig. 14.

      Let AB (Fig. 14) be Jupiter's orbit. Let S stand for the sun, E for the earth, J for Jupiter, and T for Jupiter's first satellite. When the earth is at E₁ we see the satellite enter regularly into Jupiter's shadow, and by watching the time between two successive eclipses, can calculate its time of revolution. The time which Römer noted was forty-two hours, twenty-eight minutes, and thirty-five seconds. Now, as the earth passes along in its orbit towards E₂, the revolutions of the satellite grow apparently longer and longer: the eclipses take place later and later. The greatest retardation of the eclipse, which occurs when the earth is at E₂, amounts to sixteen minutes and twenty-six seconds. As the earth passes back again to E₁, the revolutions grow apparently shorter, and they occur in exactly the time that they first did when the earth arrives at E₁. It is to be remarked that Jupiter changes only very slightly its position during one revolution of the earth. Römer guessed at once that these periodical changes of the time of revolution of Jupiter's satellite were not actual, but apparent changes, which were in some way connected with the velocity of light.

      Let us make this matter clear to ourselves by a simile. We receive regularly by the post, news of the political status at our capital. However far away we may be from the capital, we hear the news of every event, later it is true, but of all equally late. The events reach us in the same succession of time as that in which they took place. But if we are travelling away from the capital, every successive post will have a greater distance to pass over, and the events will reach us more slowly than they took place. The reverse will be the case if we are approaching the capital.

      At rest, we hear a piece of music played in the same tempo at all distances. But the tempo will be seemingly accelerated if we are carried rapidly towards the band, or retarded if we are carried rapidly away from it.[14]

      

Fig. 15.

      Picture to yourself a cross, say the sails of a wind-mill (Fig. 15), in uniform rotation about its centre. Clearly, the rotation of the cross will appear to you more slowly executed if you are carried very rapidly away from it. For the post which in this case conveys to you the light and brings to you the news of the successive positions of the cross will have to travel in each successive instant over a longer path.

      Now this must also be the case with the rotation (the revolution) of the satellite of Jupiter. The greatest retardation of the eclipse (16–½ minutes), due to the passage of the earth from E₁ to E₂, or to its removal from Jupiter by a distance equal to the diameter of the orbit of the earth, plainly corresponds to the time which it takes light to traverse a distance equal to the diameter of the earth's orbit. The velocity of light, that is, the distance described by light in a second, as determined by this calculation, is 311,000 kilometres,[15] or 193,000 miles. A subsequent correction of the diameter of the earth's orbit, gives, by the same method, the velocity of light as approximately 186,000 miles a second.

      The method is exactly that of Galileo; only better conditions are selected. Instead of a short terrestrial distance we have the diameter of the earth's orbit, three hundred and seven 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.

      

Fig. 16.

      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 СКАЧАТЬ