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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.

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