The point arises in the following way. Consider the two triangles ABC and DEF in Fig. 9. If these were cut out and laid on a smooth surface exactly as shown, no amount of sliding about would enable us to fit one exactly over the other. In order to do this it would be necessary to pick one up out of the plane of the paper and turn it over. In a precisely similar manner two asymmetrical three-dimensional objects such as a right and left hand, each of which is the mirror image of the other, could not be made to coincide unless one of them were to be turned over in four-dimensional space. The point made by Mr. Hinton and other writers who attach importance to the phenomena of symmetry, is that there seems to be a general tendency in nature towards a right and left handed symmetry in which the whole organism is symmetrical about a central plane, each half being the mirror image of the other and that this symmetry is unlikely to have arisen through equal increments on either side of the central plane. They suppose as an alternative that "the ultimate elements of living matter" are not right and left handed _ab initio_, but become so by virtue of some of them being "folded over" in four-dimensional space. This view seems to me to lack foundation especially in view of the fact that the work of Le Bel and Van't Hoff fully cleared up the analogous phenomena in the case of crystals without introducing the concept of higher space at all. In general therefore I agree with Schubert who says:-- " ... the only inference we can here make is that the idea of a four-dimensioned space is competent, from a mathematical point of view, to throw some light on the phenomena of symmetry." (Mathematical Essays, p. 91.) None the less Bragdon is right in his contention that "Could it be shown that the two-dimensional symmetry in nature is the result of a three dimensional movement, the right and left-handed symmetry of solids would by analogy be the result of a four-dimensional movement." I need hardly say that if we could experimentally obtain the changing of an asymmetrical right-handed object into the corresponding left-handed one it would be of the very first importance as a proof of the reality of higher space. Far more important than any of the foregoing, however, are the considerations arising from what is known as the Principle of Relativity. This subject, which has received much attention at the hands of mathematical physicists in recent years, is far too abstruse to be dealt with in detail here and a partial and popularised account would almost certainly fail to satisfy those who are not wholly ignorant of mathematical physics and would weary those who are. I propose, therefore, to dismiss it in very few words in spite of its great importance and relevance.