Obviously, we ought not to apply the term "special case" to a case that never occurs. Nevertheless, this case is of extreme value to us in our mental processes. Many of the motions with which we are concerned are so nearly at constant velocity that we find it convenient to treat them as though they were uniform, either ignoring the resulting error or correcting for it at the end of our work. In many other cases we are able to learn what actually occurs under accelerated motion by considering what would have occurred under uniform motion were such a thing possible. Science is full of complications which we unravel in this fashion. The physicist deals with gas pressures by assuming temperatures to be constant, though he knows temperature never is constant; and in turn he deals with temperatures by assuming pressures to be constant. After this, he is able to predict what will happen when, as in nature, pressures and temperatures are varying simultaneously. By using as a channel of attack the artificially simple case that never occurs, we get a grip on the complex case that gives us a true picture of the phenomenon. And because in actual nature we can come as close as we please to this artificial case, by supposing the variable factor to approach constancy, so when we assume it to be absolutely constant we speak of the result as the limiting case. This situation does not occur, but is the limiting case for those that do occur. When, in the matter of motion, we abandon the artificial, limiting case of uniform velocity and look into the general, natural one of unrestricted motion, we find that the structure which we have built up to deal with the limiting case provides us with many of the necessary ideas and viewpoints. This is what we expect--in it lies the value of the limiting case. We shall see that the relativity of time and space, established for the limiting case, holds good in the general one. We shall see that the idea of the four-dimensional space-time continuum as representing the external world persists, forming the whole background of the General Theory much more definitely than in the Special Theory. Incidentally we shall see that the greater generality of the case under consideration will demand a greater degree of generality in the geometry of this continuum, a non-Euclideanism of a much more whole-hearted type than that of the Special Theory. But all the revisions of fundamental concepts which we have been at such pains to make for the sake of the Special Theory will remain with us in the General. With this we may consider our preliminary background as established, and give our attention to the essayists, who will try to take us more deeply into the subject than we have yet gone, without losing us in its intricacies. VII RELATIVITY The Winning Essay in the Contest for the Eugene Higgins $5,000 Prize BY LYNDON BOLTON SENIOR EXAMINER, BRITISH PATENT OFFICE LONDON