Suppose we were to take a series of cinematograph pictures of the two-dimensional world, from the direction of the third dimension. We should obtain a succession of pictures each representing the precise state of affairs at some given moment in the two space world. Every thing in it would be represented in each. There would be no question of one thing being hidden by another because we are regarding them all from the direction of the third dimension in which they have an inappreciable extension. If we imagine the two space world to be very small or our camera to be very large there is no difficulty in supposing that each of our pictures includes the whole of the two space universe,--plane beings, earth, sun, planets, etc., all complete. Imagine further that these pictures are reproduced, as cinematograph films actually are, on a transparent substance and then let us superimpose these successive pictures on one another in order so as to form a block. By this means we can represent the disposition of all the objects in a two space system at a number of successive instants in one single three space figure. For instance, the motion of a two space planet round its sun would become a part of a helix or spiral. If we now cut away from our block all the blank material which intervenes between the representations of the various two space objects we shall have a complete synthesis in three space of a succession of two space arrangements. If we were now to pass this three space object through a penetrable two space surface, _e.g._, a soap film, we should exactly reproduce for the two space beings in it the changes which we had originally recorded. By analogy we can see that it would be possible to account for all the changes in our three-dimensional space by supposing them to be due to the passage through it of suitably shaped and arranged four-dimensional solids, of which we only perceive at any moment a section whose extension in the fourth dimension is imperceptibly small. It will appear later that I do not think that this is literally the case. The point I want to make here is that the phenomena of change or successive arrangement in space of a given dimensionality are capable of explanation in terms of forms in the next space higher, which latter do not change within themselves. The precise import of this will appear when we come to consider the bearing of the higher space theory on the problem of the nature of Time. CHAPTER II THE SCOPE OF APPLICATION AND PROBABLE IMPORTANCE OF THE HIGHER-SPACE CONCEPTS. In the preceding chapter I have tried to explain what is meant by the term "four-dimensional space" and to demonstrate some of its more important properties from the point of view of ourselves who live in space of three dimensions. I am now in a position to state the basic hypothesis which I propose to discuss in the pages which follow. Briefly stated it is this:--