way, we say that by a judicious use of Two Directions only, he can get from any one place to any other.

When we look a little closer, we see that this being fills up the whole of his Space from side to side. If therefore he wishes to pass another being in his Space he can only do it by jumping or climbing over his head, or crawling under his feet. He cannot turn round, he can only see what is before him. And of course he cannot see anything which lies outside the plates which enclose him. His senses are only adapted for the Space in which he dwells, he cannot by means of any of them perceive anything outside of it.

But at the same time we observe that he is infinitely better off than a being in the Lower Space of only One Direction, he is not compelled to confine himself to the utterly monotonous existence in the tube, his ideas are of a higher order than those of the lower being; compared to them his powers are of an infinitely

extended nature, he can think of what the lower being could not conceive, he is in the enjoyment of a Greater Freedom, although to our notions even that is sadly limited.

Although this Space is to our perceptions very limited, still as before it is not possible to know all about it. There is no limit beyond which we can say that farther motion is impossible. Our friend may take his journey with an acquaintance behind him, and travel to any distance, and then it will always be possible to think of going farther. He can never be said to know the conditions of any part of his Space which he has not visited. And even we who can look down upon his Space, and see through the plate of glass what is going on in it, cannot know all about that Space; for beyond the small extent of it in our own immediate neighbourhood, we can only depend upon the principles of Analogy and Continuity in our speculations as to the conditions

prevailing at different points of the Space.

The idea of infinity comes in, to warn us of the existence of the Mystery of Space, and to remind us that what we know outside the very narrow limits of our own observation, we can know only by a process of reasoning or deduction or inference, although we are content consider them as being trustworthy guides.

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There are two observations to be made in this place which are of great importance to the developing of our future argument. This is the first. That we perceive that an infinite number of tubes such as represented the Lowest Space may be laid side. by side in the Space of Two Directions, this means that the Space of Two Directions is of an infinitely greater extent than the Space of one Direction. That is that the infinity of the Lower Space is swallowed up in the infinity of the Higher; so that this latter though it includes the former may be regarded as practically

independent of it. So small a portion of it is occupied by the comparatively insignificant tube, that from the lower point of view, the whole of the Higher Space. may be regarded as lying outside the Inferior Space, and beyond it. At the same time the Higher Space is in absolute contact with every point of the Lower Space, at the two sides at the Right and Left. Not at an infinite distance from it.

Already then there appears a faint glimmering of the answer to the question, Where is there any room for the Higher Space?

The second observation is this. In passing from the Lower Space of One Direction to the next Higher Space of Two Directions there is an enormous increase in the power of the mind, proportional to the increase of the Space in which it works. At once it becomes emancipated from the very narrow limits imposed upon it while it was confined in its operations to Space of One Direction,

and it revels in the sense of comparatively very much Greater Freedom.

4. We are now ready to take another step. We will introduce the idea of a Third Direction, that is we will no longer confine ourselves to the plane Space shut in between the two glass plates; but, removing them, permit ourselves to rise above or sink below it. This brings in the conception of thickness, or of what we call solid things.

Up to the present we have only been able to think of flat things. Everything has been perfectly flat, possessing only length and breadth, with the minimum of thickness which is required for any physical perception of them at all. Now beside length and breadth things may have the property of thickness.

This Space to which we have come is known as Space of Three Dimensions, or in the same way as before we may call it Space of Three Directions; for now we