Einstein’s law is just as exact as Newton’s for the slower planets. For faster bodies, the motion of which can be observed with a higher degree of precision, Newton’s law is wrong, and Einstein’s triumphs once more. * * * * * This improvement of what had been considered perfect—the work of Newton—is a great victory for the human mind. Astronomy and celestial mechanics derive additional precision and power of forecast from it. We can now follow the golden orbs, on the triumphal wings of calculation, better than we could before, or antedate their movements by centuries. But there is another test of Einstein’s law of gravitation. If it is sound, the duration of a phenomenon increases, according to Einstein, when the gravitational field becomes more intense. It follows that the duration of the vibration of a given atom must be longer on the sun than on the earth. The wave-lengths of the spectral lines of the same chemical element ought to be a little greater in sunlight than in light which originates on the earth. Recent observations tend to confirm this, but the verification is less satisfactory than in the case of Mercury because other causes may intervene to modify the wave-lengths. On the whole, the powerful synthesis which Einstein calls the theory of General Relativity, which we have here rapidly outlined, is a lofty and beautiful mental construction as well as a superb instrument of exploration. To know is to forecast. This theory forecasts, and better than its predecessors did. For the first time it combines gravitation and mechanics. It shows how matter imposes upon the external world a curvature or warping of which gravitation is but a symptom: just as the weeds one sees floating on the sea are but indications of the current which bears them along. Whatever modifications it may undergo in the future—for everything in science is open to improvement—it has shown us a little more of the harmony that is born of unity in the laws of nature. But I have sufficiently shown that if I have succeeded in enabling the reader to understand—to feel, at least—these matters without invoking the aid of the pure light which geometry pours upon the invisible. CHAPTER VII IS THE UNIVERSE INFINITE? _Kant and the number of the stars—Extinct stars and dark nebulæ—Extent and aspect of the astronomical universe—Different kinds of universes—Poincaré’s calculation—Physical definition of the infinite—The infinite and the unlimited—Stability and curvature of cosmic space-time—Real and virtual stars—Diameter of the Einsteinian universe—The hypothesis of globes of ether._ Is the universe infinite? It is a question that men have asked in all ages, though they have not defined its meaning very accurately. The theory of Relativity enables us to approach it from a new and subtle point of view.