what matter a velocity is measured with respect to. This is largely a question of how much accuracy is needed in specifying velocities and rotations, respectively. If in stating the speed of a β particle we do not mind an error of 10,000 kilometres a second, we need not specify precisely what star or planet its velocity is referred to. The moon's (local) angular velocity is sometimes given to fourteen significant figures; I doubt if any universal frame is well-defined enough for this accuracy. There is no doubt much greater continuity in the geodesic structure in different parts of the world than in the material structure; but the difference is in degree rather than in principle.
It is probable that here we part company from many of the continental relativists, who give prominent place to a principle known as the law of causality—that only those things are to be regarded as being in causal connection which are capable of being actually observed. This seems to be interpreted as placing matter on a plane above geodesic structure in regard to the formulation of physical laws, though it is not easy to see in what sense a distribution of matter can be regarded as more observable than the field of influence in surrounding space which makes us aware of its existence. The principle itself is debateable; that which is observable to us is determined by the accident of our own structure, and the law of causality seems to impose our own limitations on the free interplay of entities in the world outside us. In this book the tradition of Faraday and Maxwell still rules our outlook; and for us matter and electricity are but incidental points of complexity, the activity of nature being primarily in the so-called empty spaces between.
The vague universal frame to which rotation is referred is called the inertial frame. It is definite in the flat space-time far away from all matter. In the undulating country corresponding to the stellar universe it is not a precise conception; it is rather a rude outline, arbitrary within reasonable limits, but with the general course indicated. The reason for the term inertial frame is of interest. We can quite freely use a mesh-system deviating widely from the inertial frame (e.g. rotating axes); but we have seen that there is a postponed debt to pay in the shape of an
