The fourth dimension

16 THE FOURTH DIMENSION

theory of mechanics—motions would take place which he could not explain by his theory of motion. Hence, to determine if we are in a four-dimensional world, we must examine the phenomena of motion in our space. If movements occur which are not explicable on the suppositions of our three-dimensional mechanics, we should have an indication of a possible four-dimensional motion, and if, moreover, it could be shown that such movements would be a consequence of a four-dimensional motion in the minute particles of bodies or of the ether, we should have a strong presumption in favour of the reality of the fourth dimension.

By proceeding in the direction of finer and finer subdivision, we come to forms of matter possessing properties different to those of the larger masses. It is probable that at some stage in this process we should come to a form of matter of such minute subdivision that its particles possess a freedom of movement in four dimensions. This form of matter I speak of as four-dimensional ether, and attribute to it properties approximating to those of a perfect liquid.

Deferring the detailed discussion of this form of matter to Chapter VI, we will now examine the means by which a plane being would come to the conclusion that threedimensional movements existed in his world, and point out the analogy by which we can conclude the existence of four-dimensional movements in our world. Since the dimensions of the matter in his world are small in the third direction, the phenomena in which he would detect the motion would be those of the small particles of matter.

Suppose that there is a ring in his plane. We can imagine currents flowing round the ring in either of two opposite directions. These would produce unlike effects, and give rise to two different fields of influence. If the