forms as are shown in Figs. 13, 15, and 16. Nevertheless, it is probable that all strongly eye-minded people, if they do not visualize the alphabet in any other way, visualize it as they do other things, in the form in which they had usually seen it.

Concerning the stability of number forms, any one may have his doubts removed by a few tests separated by months or years. In almost every case it will be found that, no matter how complicatedFig. 7. the form may be, the subject, after one, two, or three years, will draw from his mental picture of it a copy differing in no essential respect from the original copy. The number form represented in Fig. 3 was given to me in 1889. In October, 1892, I requested of the young man by letter a second copy, and in reply received one precisely like the first. Other tests gave similar results. Galton testifies to the unchangeable character of number forms in all cases where they are well defined. It is true, however, that they sometimes disappear entirely. They are found to be more common among children than adults. It is probable that in children who are not naturally vivid visualizers, or in cases where it does not serve any useful purpose, the form fails to survive. One case of such a lapse I have found in an adult.

The general character of number form is such that a person having one can not think of the related numbers without seeing them in a definite visual picture. A form or outline rises involuntarily before his mind. In some cases the seer can describe it as definitely located in space in relation to his own body. It is two feet long or six inches long. It stares him in the face or lies at his feet. It recedes to the right or left, or into the distance. Others can not answer the question as to the location. In most cases, though not in all, no individual number can be thought of without seeing it in its appropriate place in the usual outline. Sometimes the form seems to be useful to its possessor in computations, Fig. 8. particularly in addition and subtraction. In other cases it seems to have no use at all further than that of all mental imagery, which will be considered below. It has been suggested that it is by means of a number form, or at least by a clear visualization of numbers, that the arithmetical prodigies accomplish their remarkable computations. Though it has been shown that many of them do visualize the numbers, and mentally see the different steps of their problem, yet this alone offers