hypothesis that two small particles of matter attracted each other, in the direction of the line joining them, with a force varying inversely as the square of the distance between them. This law is an "action at a distance" law and so is opposed to the idea (a). We have tacitly supposed that the space in which we make our measurements is that made familiar to us by the study of Euclid's elements. The characteristic property of this space is that stated by the theorem of Pythagoras that the distance between two points is found by extracting the square root of the sum of the squares of the differences of the Cartesian coordinates of the two points. Mathematicians have long recognized the possibility of other types of space and Einstein has followed their lead. He abandons the empiricist method and when asked what he means by a point in space replies that to him a point in space is equivalent to four numbers how obtained it is unnecessary to know a priori; in certain special cases they may be the three Cartesian coordinates of the experimenter (measured with reference to a definite material framework) together with the time. Accordingly he says his space is of four dimensions. Between any two "points" we may insert a sequence of sets of four numbers, varying continuously from the first set to the second, thus forming what we call a curve joining the two points. Now we define the "length" of this curve in a manner which involves all the points on it and stipulate that this length has a physical reality, i.e., according to our idea (b) its value is independent of the particular choice of coordinates we make in describing the space. Among all the joining curves there will be one with the property of having the smallest length; this is called a geodesic and corresponds to the straight line in Euclidean space. We must now, for lack of an a priori description of the actual significance of our coordinates, extend the idea of vector so that we may speak of the components of a vector no matter what our coordinates may actually signify. In this way are introduced what are known as tensors; if two tensors are equal, i.e., have all their components equal, in any one set of coordinates they are equal in any other and the fundamental demand of the new physics is that all physical equations which are not merely the expression of equality of magnitudes must state the equality of tensors. In this way no one system of coordinates is privileged above any other and the laws of physics are expressed in a form independent of the actual coordinates chosen; they are written, as we may say, in an absolute form. THE GRAVITATIONAL HYPOTHESIS