Now since an acceleration in a gravitational field is identical with that due to centrifugal force produced by rotation, we concluded that the geometry in a gravitational field must also be non-Euclidean. That is, space in the neighborhood of matter is distorted or curved. The curvature of space bears the same relation to three dimensions that the curvature of a spherical surface bears to two dimensions, and that is why we do not perceive it, any more than the intelligent two-dimensional being would be aware of the distortion of his space (or surface). Furthermore, like this being, we have assumed the existence of a gravitational force to account for discrepancies in our geometrical measurements. The identification in this manner of gravitational effects with geometrical curvature of space enables Einstein to derive a general law for the path of any particle in a gravitational field, with respect both to space and to time. Furthermore, the law expresses this motion in terms which are independent of the relative motion and position of the observer, and satisfies the condition that the fundamental laws of physics be equally valid for all observers. The solution of the problem involved the use of a new kind of higher calculus, elaborated by two Italian mathematicians, Ricci and Levi-Civita. The result is a law of motion which is extremely general in its validity. For low velocities it approximates to Newton's solution, and in the absence of a gravitational field it leads to the same conclusions as the special theory of relativity. There are three deductions from this law which have aroused a great deal of interest, and the confirmation of two of these by actual observation must be regarded as striking proof of Einstein's theory. XIII AN INTRODUCTION TO RELATIVITY A Treatment in Which the Mathematical Connections of Einstein's Work are Brought Out More Strongly and More Successfully Than Usual in a Popular Explanation BY HAROLD T. DAVIS, UNIVERSITY OF WISCONSIN, Madison, Wis. One of the first questions which appears in philosophy is this: What is the great reality that underlies space and time and the phenomena of the physical universe? Kant, the philosopher, dismissed it as a subjective problem, affirming that space and time are "a priori" concepts beyond which we can say no more.