The Story of the Heavens

principle. The greater the velocity, the more desirable is it that the distance traversed during the experiment shall be as large as possible. In dealing with the measurement of the velocity of light, we therefore choose for our measured distance the greatest length that may be convenient. It is, however, necessary that the two ends of the line shall be visible from each other. A hill a mile or two away will form a suitable site for the distant station, and the distance of the selected point on the hill from the observer must be carefully measured. The problem is now easily stated. A ray of light is to be sent from the observer to the distant station, and the time occupied by that ray in the journey is to be measured. We may suppose that the observer, by a suitable contrivance, has arranged a lantern from which a thin ray of light issues. Let us assume that this travels all the way to the distant station, and there falls upon the surface of a reflecting mirror. Instantly it will be diverted by reflection into a new direction depending upon the inclination of the mirror. By suitable adjustment the latter can be so placed that the light shall fall perpendicularly upon it, in which case the ray will of course return along the direction in which it came. Let the mirror be fixed in this position throughout the course of the experiments. It follows that a ray of light starting from the lantern will be returned to the lantern after it has made the journey to the distant station and back again. Imagine, then, a little shutter placed in front of the lantern. We open the shutter, the ray streams forth to the remote reflector, and back again through the opening. But now, after having allowed the ray to pass through the shutter, suppose we try and close it before the ray has had time to get back again. What fingers could be nimble enough to do this? Even if the distant station were ten miles away, so that the light had a journey of ten miles in going to the mirror and ten miles in coming back, yet the whole course would be accomplished in about the nine-thousandth part of a second—a[Pg 264] period so short that even were it a thousand times as long it would hardly enable manual dexterity to close the aperture. Yet a shutter can be constructed which shall be sufficiently delicate for the purpose. Fig. 63.—Mode of Measuring the Velocity of Light. The principle of this beautiful method will be sufficiently obvious from the diagram on this page (Fig. 63), which has been taken from Newcomb's "Popular Astronomy." The figure exhibits the lantern and the observer, and a large wheel with projecting teeth. Each tooth as it passes round eclipses the beam of light emerging from the lantern, and also the eye, which is of course directed to the mirror at the distant station. In the position of the wheel here shown the ray from the lantern will pass to the mirror and back so as to be visible to the eye; but if the wheel be rotating, it may so happen that the beam after leaving the lantern will not have time to return before the next tooth of the wheel comes in front of the eye and screens it. If the wheel be urged still faster, the next tooth may have passed the eye, so that the ray again becomes visible. The speed at which the wheel is rotating can be measured. We can thus determine the time taken by one of the teeth to pass in front of the eye; we have accordingly a measure of the time occupied by the ray of light in the double journey, and hence we have a measurement of the velocity of light. It thus appears that we can tell the velocity of light either[Pg 265] by the observations of Jupiter's satellites or by experimental enquiry. If we take the latter method, then we are entitled to deduce remarkable astronomical consequences. We can, in fact, employ this method for solving that great problem so often referred to—the distance from the earth to the sun—though it cannot compete in accuracy with some of the other methods. The dimensions of the solar system are so considerable that a sunbeam requires an appreciable interval of time to span the abyss which separates the earth from the sun. Eight minutes is approximately the duration of the journey, so that at any moment we see the sun as it appeared eight minutes earlier to an observer in its immediate neighbourhood. In fact, if the sun were to be suddenly blotted out it would still be seen shining brilliantly for eight minutes after it had really disappeared. We can determine this period from the eclipses of Jupiter's satellites. So long as the satellite is shining it radiates a stream of light across the vast space between Jupiter and the earth. When the eclipse has commenced, the little orb is no longer luminous, but there is, nevertheless, a long stream of light on its way, and until all this has poured into our telescopes we still see the satellite shining as before. If we could calculate the moment when the eclipse really took place, and if we could observe the moment at which the eclipse is seen, the difference between the two gives the time which the light occupies on the journey. This can be found with some accuracy; and, as we already know the velocity of light, we can ascertain the distance of Jupiter from the earth; and hence deduce the scale of the solar system. It must, however, be remarked that at both extremities of the process there are characteristic sources of uncertainty. The occurrence of the eclipse is not an instantaneous phenomenon. The satellite is large enough to require an appreciable time in crossing the boundary which defines the shadow, so that the observation of an eclipse cannot be sufficiently precise to form the basis of an important and accurate measurement.[23] Still[Pg 266] greater difficulties accompany the attempt to define the true moment of the occurrence of the eclipse as it would be seen by an observer in the vicinity of the satellite. For this we should require a far more perfect theory of the movements of Jupiter's satellites than is at present attainable. This method of finding the sun's distance holds out no prospect of a result accurate to the one-thousandth part of its amount, and we may discard it, inasmuch as the other methods available seem to admit of much higher accuracy. The four chief satellites of Jupiter have special interest for the mathematician, who finds in them a most striking instance of the universality of the law of gravitation. These bodies are, of course, mainly controlled in their movements by the attraction of the great planet; but they also attract each other, and certain curious consequences are the result. The mean motion of the first satellite in each day about the centre of Jupiter is 203°·4890. That of the second is 101°·3748, and that of the third is 50°·3177. These quantities are so related that the following law will be found to be observed: The mean motion of the first satellite added to twice the mean motion of the third is exactly equal to three times the mean motion of the second. There is another law of an analogous character, which is thus expressed (the mean longitude being the angle between a fixed line and the radius to the mean place of the satellite): If to the mean longitude of the first satellite we add twice the mean longitude of the third, and subtract three times the mean longitude of the second, the difference is always 180°. It was from observation that these principles were first discovered. Laplace, however, showed that if the satellites revolved nearly in this way, then their mutual perturbations, in accordance with the law of gravitation, would preserve them in this relative position for ever. We shall conclude with the remark, that the discovery of Jupiter's satellites afforded the great confirmation of the[Pg 267] Copernican theory. Copernicus had asked the world to believe that our sun was a great globe, and that the earth and all the other planets were small bodies revolving round the great one. This doctrine, so repugnant to the theories previously held, and to the immediate evidence of our senses, could only be established by a refined course of reasoning. The discovery of Jupiter's satellites was very opportune. Here we had an exquisite ocular demonstration of a system, though, of course, on a much smaller scale, precisely identical with that which Copernicus had proposed. The astronomer who had watched Jupiter's moons circling around their primary, who had noticed their eclipses and all the interesting phenomena attendant on them, saw before his eyes, in a manner wholly unmistakable, that the great planet controlled these small bodies, and forced them to revolve around him, and thus exhibited a miniature of the great solar system itself. "As in the case of the spots on the sun, Galileo's announcement of this discovery was received with incredulity by those philosophers of the day who believed that everything in nature was described in the writings of Aristotle. One eminent astronomer, Clavius, said that to see the satellites one must have a telescope which would produce them; but he changed his mind as soon as he saw them himself. Another philosopher, more prudent, refused to put his eye to the telescope lest he should see them and be convinced. He died shortly afterwards. 'I hope,' said the caustic Galileo, 'that he saw them while on his way to heaven'"[24] [Pg 268]