Chapter V. goes back again to general ground. Among the ideas which the competing essayists were forced to introduce into their text on a liberal scale is that of non-Euclidean geometry. The entire formulation of the General Theory of Relativity is in fact an exercise in this. The essayists--good, bad and indifferent alike--were quite unanimous in their decision that this was one thing which the reader would have to assume the responsibility of acquiring for himself. Certainly they were justified in this; for the Editor has been able to explain what non-Euclidean geometry is only by using up considerably more space than the contestants had for an entire essay. No effort has been made to set forth any of the details of any of the various non-Euclidean geometries; it has simply been the aim to draw the dividing line between Euclidean and non-Euclidean, and to make the existence of the latter appear reasonable, so that when the essayists come to talk about it the reader will not feel hopelessly at sea. In other words, this is another case of providing the mental background, but on such a scale that it has seemed necessary to give a separate chapter to it. Chapter VI. completes the preliminary course in the fundamentals of relativity by tying up together the findings of Chapter V. and those of Chapters III. and IV. It represents more or less of a last-minute change of plan; for while it had been the Editor's intent from the beginning to place the material of Chapters II.-V. in its present position, his preliminary impression would have been that the work of the present Chapter VI. would be adequately done by the essayists themselves. His reading of the essays, however, convinced him that it had not so been done--that with the possible exception of Mr. Francis, the essayists did not make either a serious or a successful effort to show the organic connection between the Special Theory of Relativity and the Minkowski space-time structure, or the utter futility of trying to reconcile ourselves to the results of the former without employing the ideas of the latter. So Chapter VI. was supplied to make good this deficiency, and to complete the mental equipment which the reader requires for his battle with the General Theory.