as those projected by the lungs.  Consequently if the two sets of waves start together the crest of every third wave of the rapid series of short waves will coincide with the crest of one of the long waves of the slower series, while the intermediate short waves will coincide with the depression of one of the long waves.  Now the effect of the crest of one wave overtaking that of another going in the same direction, is to raise the two together at that point into a single wave of greater amplitude or height than the original waves had by themselves; if the reader has the opportunity of studying the inflowing of waves on the seabeach he can verify this for himself.  Consequently when the more rapid etheric waves overtake the slower ones they combine to form a larger wave, and it is at these points that the zones of sensation occur.  If the reader will draw a diagram of two waved lines travelling along the same horizontal line and so proportioned that the crest of each of the large waves coincides with the crest of every third wave of the small ones, he will see what I mean:  and if he then recollects that the fall in the larger waves neutralizes the rise in the smaller ones, and that because this double series starts from the interior of the body the surface of the body comes just at one of these neutralized points, he will see why sensation is neutralized there; and he will also see why the succeeding zones of sensation are double the distance from each other that the first one is from the surface of the body; it is simply because the surface of the body cuts the first long wave exactly in the middle, and therefore only half that wave occurs outside the body.  This is the explanation given by De Rochas, and it affords another example of that principle of mathematical sequence of which I have spoken.  It would appear that under normal conditions the double series of vibrations is spread all over the body, and so all parts are alike sensitive to touch.

I think, then, we may assume on the basis of De Rochas’ experiments and others that there are such things as etheric vibrations proceeding from human personality, and in the next chapter I will give some examples showing that the psychic personality extends still further than these experiments, taken by themselves, would indicate—­in fact that we possess an additional range of faculties far exceeding those which we ordinarily exercise through the physical body, and which must therefore be included in our conception of ourselves if we are to have an adequate idea of what we really are.

CHAPTER II

SOME PSYCHIC EXPERIENCES