Manchester Memoirs, Vol. Jxvi. (1922), No. 2 7 



mistake in the century when suddenly called upon to give a 

 date, and also bv a year or two, as I have to work by the 

 diagram." 



This fact, that the vividness of the diagram depends upon 

 the use made of it, is brought out by another of my contribu- 

 tors, a business man, who tells me that numbers which he 

 habituallv uses, e.g., 15 (for i/sd. per yard), stand out more 

 brightlv than the others. An absence from business through 

 illness caused the numbers to become dim. 



Their Utility. 



The supposition is erroneous that all possessors of number- 

 forms necessarily use them whenever they think of a number 

 or set of numbers. Galton's original statement (3, 82),^ 

 " (the peculiarity) consists in the sudden and automatic appear- 

 ance of a vivid and invariable ' Form ' in the mental field of 

 view whenever a numeral is thought of, ..." would naturally 

 tend to deepen such a belief. But the number-form described 

 on pp. 3-5 is not used when the day of the month or degrees of 

 latitude and longitude are thought of ; in these cases there 

 appear visual images of a wall calendar or of a map, on 

 Mercator's projection. And as Flournoy has shown, a number- 

 form may be used by a person for one kind of operation {e.g., 

 writing down a series of figures) but not for another, such as 

 thinking of a date. Moreover, the answers to questions 

 concerning the utility of these forms show that many persons 

 who possess them consider them to be useless. Calkins found 

 that of 67 persons so questioned concerning the usefulness 

 of number-forms both in mathematical operations and in 

 remembering dates, 29 were sure they were useful, while 21 

 were sure that they were not. Of Phillips's 211 subjects, 

 97 declared that their number-form was useful in reckoning, 

 113 that it was neither useful nor harmful, and one that he 

 was disturbed by it. 



In this connection it is interesting to note that one of the 

 examples in my own collection is an algehra-iorm. It consists 

 of a vertical line with a horizontal line crossing it, the zero 

 being at the point of intersection. Positive quantities are 

 visualized as proceeding vertically upwards and negative ones 

 downwards. There are no gradations on the lines other than 

 those actually in use at the time. In thinking oi a - b the 

 subject feels that the h is pulling the a down, and the a pulling 

 the h up. Frequently a circle appears round the zero point ; 



]. Italics mine. 



