520 THE POPULAR SCIENCE MONTHLY. 



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 accu- 

 mulating, just as any conscientious statistician would, before I began 

 to form conclusions. I was soon convinced of its substantial trust- 

 worthiness, and that conviction has in no way been shaken by subse- 

 quent 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 men- 

 tal 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 there- 

 fore 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 any- 

 thing 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 di- 

 visions 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 



