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520 appear to me to bear internal marks of scrupulous truthfulness. A third part has been collected for me by many kind friends in many countries, each of whom has made himself or herself an independent center of inquiry; and the last, and much the most numerous portion, consists of brief replies by strangers to a series of questions contained in a circular that I drew up. I have gone over all this matter with great care, and have cross-tested it in many ways while it was accumulating, just as any conscientious statistician would, before I began to form conclusions. I was soon convinced of its substantial trustworthiness, and that conviction has in no way been shaken by subsequent experience. In short, the evidence of the four groups I have just mentioned is quite as consistent as could have been reasonably desired.

The lowest order of phenomena that admit of being classed as visions are the "Number forms" to which I have drawn attention on more than one occasion, but to which I must again very briefly allude. They are an abiding mental peculiarity in a certain proportion of persons (say five per cent.), who are unable as adults, and who have been ever unable as far back as they can recollect, to think of any number without referring it to its own particular habitat in their mental field of view. It there lies latent, but is instantly evoked by the thought or mention of it, or by any mental operation in which it is concerned. The thought of a series of consecutive numbers is therefore attended by a vision of them arranged in a perfectly defined and constant position, and this I have called a "Number form." Its origin can rarely be referred to any nursery diagram, to the clock-face, or to any incident of childhood. Nay, the form is frequently unlike anything the child could possibly have seen, reaching in long vistas and perspectives, and in curves of double curvature. I have even had to get wire models made by some of my informants in explanation of what they wished to convey. The only feature that all the forms have in common is their dependence in some way or other upon the method of verbal counting, as shown by their angles and other divisions occurring at such points as those where the 'teens begin, at the twenty's, thirty's and so on. The forms are in each case absolutely unchangeable, except through a gradual development in complexity. Their diversity is endless, and the Number forms of different men are mutually unintelligible.

These strange "visions," which are extremely vivid in some cases, are almost incredible to the vast majority of mankind, who would set them down as fastastic nonsense, but they are familiar parts of the mental furniture of the rest, where they have grown naturally, and where they remain unmodified and unmodifiable by teaching. I have received many touching accounts of their childish experiences from persons who see the Number forms, and the other curious visions of which I shall speak. As is the case with the color-blind, so with these