of the same configuration as the molecules of the other, save that those of one are right-handed and the other left-handed.
These two varieties change one into the other apparently without any chemical resolution and reconstitution. If such were certainly the case, it would be a proof of the fourth dimension, because only in four-dimensional space can a right-handed shape become a left-handed shape by simple movement.
Case 3.—In the proceedings of the Washington Philosophical Society, November, 1902, the writer argues as follows: It is not at all certain that the mechanics which is found capable of explaining the processes of nature that occur on a large scale is capable of explaining what occurs in the minute. Right and left handed shapes never occur in any phenomenon on a large scale, such as rocks, clouds, configurations of continents, but do frequently occur as results of processes which take place in the minute, such as the vital processes, crystallization, etc. Now to produce figures symmetrical about a line the simplest way is to use a three-dimensional process. This is exemplified in Fig. 6, which was produced by folding over a piece of blotted paper, and in this folding over the third dimension was used.
Thus symmetry in two dimensions is produced by a three-dimensional process.
Similarly, it is not unnatural to expect shapes symmetrical about a plane as the result of a four-dimensional process. Thus it is worth while to form a complete system of four-dimensional mechanics, and it is only when such a system has been elaborated that we shall be in a position to determine whether the obscurities found in the domain of molecular physics are to be attributed to the complexity of the three-dimensional conditions or to the presence of four-dimensional motions. For example, no satisfactory explanation has been given on mechanical principles of an electric current.
To take the most familiar type, an electric current involves the existence of a wire or other conductor. The action is not conveyed through the wire, but, as Professor Poynting has shown, through the medium in which the wire is situated. It is therefore not incorrect to say that a continuous electric current is a disturbance in a medium which demands for its existence a continuous boundary (the conductor) in that medium.
Now in three-dimensional mechanics a certain type of disturbance is known which demands for its continuous existence in a medium that its opposite ends shall impinge on a boundary of the medium. Of such a kind is a vortex, which may be thought of as an eddy. A smoke ring is an instance of a vortex with its ends joined together. In a perfect fluid a smoke ring could exist with ends free from one another if these ends impinged on a boundary of the fluid.
Here we have the phenomenon of a disturbance involving as the condition of its continuous existence that its ends impinge on two opposite boundaries of the medium in which it takes place. This differs from the electric current because only two ends necessarily impinge on a boundary of the medium, while in the electric current a whole contour must impinge on a boundary.
Now examining into the nature of a four-dimensional vortex it is found that in such a disturbance of a medium the condition of its continuous existence is that it impinges on a boundary by a whole contour. Where a three-dimensional vortex requires two opposing boundaries a four-dimensional vortex requires a complete circuit of boundary. Thus a four-dimensional vortex has a striking analogy with an electric current.
It is in the examination of questions such as these that the physical inquiry as to the existence of the fourth dimension consists in asking, namely, whether the types of action which occur can be explained on the principles of three-dimensional mechanics, or whether they demand for their explanation the assumption of a four-dimensional motion.
