Page:Eddington A. Space Time and Gravitation. 1920.djvu/170

154 the earth's—rotation the protuberance of its equator, the phenomena of the gyrocompass, etc. are due to a rotation relative to any matter we can recognise. The philosopher who persists that a rotation which is not relative to matter is unthinkable, will no doubt reply that the rotation must then be relative to some matter which we have not yet recognised. We have hitherto been greatly indebted to the suggestions of philosophy in evolving this theory, because the suggestions related to the things we know about; and, as it turned out, they were confirmed by experiment. But as physicists we cannot take the same interest in the new demand; we do not necessarily challenge it, but it is outside our concern. Physics demands of its scheme of nature something else besides truth, namely a certain quality that we may call convergence. The law of conservation of energy is only strictly true when the whole universe is taken into account; but its value in physics lies in the fact that it is approximately true for a very limited system. Physics is an exact science because the chief essentials of a problem are limited to a few conditions; and it draws near to the truth with ever-increasing approximation as it widens its purview. The approximations of physics form a convergent series. History, on the other hand, is very often like a divergent series; no approximation to its course is reached until the last term of the infinite series has been included in the data of prediction. Physics, if it wishes to retain its advantage, must take its own course, formulating those laws which are approximately true for the limited data of sense, and extending them into the unknown. The relativity of rotation is not approximately true for the data of sense, although it may possibly be true when the unknown as well as the known are included.

The same considerations that apply to rotation apply to acceleration, although the difficulty is less striking. We can if we like attribute to the sun some arbitrary acceleration, balancing it by introducing a uniform gravitational field. Owing to this field the rest of the stars will move with the same acceleration and no phenomena will be altered. But then it seems necessary to find a cause for this field. It is not produced by the gravitation of the stars. Our only course is to pursue the cause further and further towards infinity; the further we put it away, the greater