"The examination of the spectra of coloured flames has accordingly acquired a new and high interest; I will carry it out in conjunction with Bunsen as far as our means allow. In connexion therewith we will investigate the weakening of rays of light in flames that has been established by my observations. In the course of the experiments which have at present been instituted by us in this direction, a fact has already shown itself which seems to us to be of great importance. The Drummond light requires, in order that the lines D should come out in it dark, a salt-flame of lower temperature. The flame of alcohol containing water is fitted for this, but the flame of Bunsen's gas-lamp is not. With the latter the smallest mixture of common salt, as soon as it makes itself generally perceptible, causes the bright lines of sodium to show themselves. We reserve to ourselves to develope the consequences which may be connected with this fact." EINSTEIN, MINKOWSKI, EDDINGTON RELATIVITY LIGHT has the properties of wave motion, and hence there has been imagined a medium or aether to carry it. Even if we suppose the solar system at rest in the aether of space, the earth in its daily and annual path must move through the aether. Astronomical observation indicates that it does not drag aether with it, and therefore we must imagine the aether to stream through a laboratory as wind through a grove of trees. We should expect that light reflected back by a mirror would travel with different speeds in different directions, according as its path was up and down or across and across the aether stream. But an experiment made in America by Michelson and Morley in 1887 gave the surprising result that no such difference could be detected. However measured, and in whatever direction, the speed of light always appears to be 186,000 miles a second. If we try to explain this constancy in terms of our old conceptions of the world, we are driven to suppose compensating changes in the scales and clocks with which the measurements are made. The electrical theory of matter gives reasons for this assumption, and it probably represents one aspect of the truth. But in 1905 Einstein founded the modern theory of relativity by pointing out that absolute space and time are figments of the imagination, and that real or observed space and time as measured depend on the motion of the observer and his instruments. In 1908 Minkowski showed that if we cease to think of space and time as separate entities, and bring the length, breadth and thickness of space into relation with time, we get a four-dimensional continuum which is the same for all observers. In the old concept of the world, the distance between two points was an absolute quantity however measured. In the new four-dimensional world that distance will depend on the observer, but there is an absolute quantity, an extension in space and time combined, or “interval," which is the same for all observers, though they may divide it into space and time in different manners and with different results. The natural connection between time and space is given by the fact that light travels 186,000 miles in a second. Hence, in the four-dimensional world, one second is equivalent to 186,000 miles, and the discrepancies in our old conceptions of the world only become apparent when great velocities are involved. There is still a difference—one of sign-between time and the three space dimensions. The mathematical consequence is that the spacetime continuum of our new world does not give the geometry made familiar by Euclid. It is subject to something analogous to curvature, and, if a groove or pleat is started, it can only run in one direction through the continuum. Thus there are natural paths in this space-time which, on the theory, are the tracks of freely moving particles. In 1911 Einstein showed the bearing of these conceptions on gravitation. The extra weight we feel as a lift starts, or the centrifugal force of a whirling stone, are forces of the same nature as that of gravity. It is impossible to draw a distinction in kind between their effects-they are equivalent. Thus the effects of gravity may be imitated exactly by an acceleration or a change of path. A curvature of space, taking bodies out of their free paths, may therefore be the cause of the phenomenon we call gravitation. Gravity affects not only material bodies, but light as well. If light passes near a heavy body such as the Sun, it is deflected from its straight path, and the deflection should be twice as great on Einstein's theory as on Newton's. Professor Eddington, who has done much to extend and expound Einstein's theory, working with other observers, carried out the delicate astronomical measurements needed to test this crucial point, and found that the facts conformed to Einstein's view and not to Newton's. SPACE, TIME AND GRAVITATION An Outline of the General Relativity Theory By A. S. EDDINGTON, M.A., M.Sc., F.R.S. CHAP. VI. The New Law of Gravitation and the Old Law I don't know what I may seem to the world, but, as to myself, WAS there any reason to feel dissatisfied with Newton's law of gravitation? Observationally it had been subjected to the most stringent tests, and had come to be regarded as the perfect model of an exact law of nature. The cases, where a possible failure could be alleged, were almost insignificant. There are certain unexplained irregularities in the moon's motion; but astronomers generally looked-and must still look-in other directions for the cause of these discrepancies. One failure only had led to a serious questioning of the law; this was the discordance of motion of the perihelion of Mercury. How small was this discrepancy may be judged from the fact that, to meet it, it was proposed to amend square of the distance to the 2.00000016 power of the distance. Further it seemed possible, though unlikely, that the matter causing the zodiacal light might be of sufficient mass to be responsible for this effect. The most serious objection against the Newtonian law as an exact law was that it had become ambiguous. The law refers to the product of the masses of the two bodies; but the mass depends on the velocity—a fact unknown in Newton's day. Are we to take the variable mass, or the mass reduced to rest? Perhaps a learned judge, interpreting Newton's statement like a last will and testament, could give a decision; but that is scarcely the way to settle an important point in scientific theory. Further distance, also referred to in the law, is something relative to an observer. Are we to take the observer travelling with the sun or with the other body concerned, or at rest in the aether or in some gravitational medium?...... It is often urged that Newton's law of gravitation is much simpler than Einstein's new law. That depends on the point of view; and from the point of view of the four-dimensional world Newton's law is far more complicated. Moreover, it will be seen that if the ambiguities are to be cleared up, the statement of Newton's law must be greatly expanded. Some attempts have been made to expand Newton's law on the basis of the restricted principle of relativity alone. This was insufficient to determine a definite amendment. Using the principle of equivalence, or relativity of force, we have arrived at a definite law proposed in the last chapter. Probably the question has arisen in the reader's mind, why should it be called the law of gravitation? It may be plausible as a law of nature; but what has the degree of curvature of space-time to do with attractive forces, whether real or apparent? A race of flat-fish once lived in an ocean in which there were only two dimensions. It was noticed that in general fishes swam in straight lines, unless there was something obviously interfering with their free courses. This seemed a very natural behaviour. But there was a certain region where all the fish seemed to be bewitched; some passed through the region but changed the direction of their swim, others swam round and round indefinitely. One fish invented a theory of vortices, and said that there were whirlpools in that region which carried everything round in curves. By-and-by a far better theory was proposed; it was said that the fishes were all attracted towards a particularly large fish-a sun-fish-which was lying asleep in the middle of the region; and that was what caused the deviation of their paths. The theory might not have sounded particularly plausible at first; but it was confirmed by marvellous exactitude by all kinds of experimental tests. All fish were found to possess this attractive power in proportion to their sizes; the law of attraction was extremely simple, and yet it was found to explain all the motions with an accuracy never approached before in any scientific investigations. Some fish grumbled that they did not see how there could be such an influence at a distance; but it was generally agreed that the influence was communicated through the ocean and might be better understood when more was known about the nature of water. Accordingly, nearly every fish who wanted to explain the attraction started by proposing some kind of mechanism for transmitting it through the water. But there was one fish who thought of quite another plan. He was impressed by the fact that whether the fish were big or little they always took the same course, although it would naturally take a bigger force to deflect the bigger fish. He therefore concentrated on the courses rather than on the forces. And then he arrived at a striking explanation of the whole thing. There was a mound in the world round about where the sun-fish lay. Flat-fish could not appreciate it directly because they were two-dimensional; but whenever a fish went swimming over the slopes of the mound, although he did his best to swim straight on, he got turned round a bit. (If a traveller goes over the left slope of a mountain, he must consciously keep bearing away to the left if he wishes to keep to his original direction relative to the points of the compass.) This was the secret of the mysterious attraction, or bending of the paths, which was experienced in the region. The parable is not perfect, because it refers to a hummock in space alone, whereas we have to deal with hummocks in space-time. But it illustrates how a curvature of the world we live in may give an illusion of attractive force, and indeed can only be discovered through some such effect. How this works out in detail must now be considered. In the form Gur = 0, Einstein's law expresses conditions to be satisfied in a gravitational field produced by any arbitrary distribution of attracting matter. An analogous form of Newton's law was given by Laplace in his celebrated expression V2 = 0. A more illuminating form of the law is obtained if, instead of putting the question what kinds of space-time can exist under the most general conditions in an empty region, we ask what kind of space-time exists in the region round a single attracting particle? We separate out the effect of a single particle, just as Newton did.... We need only consider space of two dimensions-sufficient for the so-called plane orbit of a planet-time being added as |