Manchester Memoirs, Vol. Ixvi. (1922), Ko. 2 5 



" When adding or subtracting numbers like 460 and 780 

 the positions of 46 and 78 are the dominant ones. But if 

 the numbers were 468 and 784, then the positions of 68 and 

 84 would be the dominant ones. 10,000 has the same 

 position as 10, 20,000 as 20, and so on up to 100,000, which 

 has the same position as 100.^ 



" Sums of money are visualized according to their size. 

 Sums between i penny and £1 are usually visualized in 

 pence, but if even shillings then they are visualized accord- 

 ing to the number of shillings. Thus 15/- visualizes as 

 15, but 15/6 as 186. Sums between £1 and ;^5 are 

 invariably visualized in shillings. Above ;^5 they are 

 visualized in pounds, just like ordinary numbers." 



One important feature of this form is that the numbers 

 themselves are not seen, their position onlv being visualized. 

 This mav be connected with the fact that the form carries 

 relative as well as absolute values. The same point in space 

 may represent, in different contexts, 17, the age of adolescence, 

 the XVI Ith Dvnasty or one-and-fivepence. 



The negative values are represented by a mirror-image of 

 the number-form. This extends behind the head. When 

 learning algebra, the use of this form obviated any difficulties 

 in grasping the conception of adding to, or subtracting from, 

 positive numbers, numbers of negative value. 



After making a wire model of his number-form, and dis- 

 cussing it at the meeting of a scientific society. Prof. Tattersall 

 requested me to add a note that closer acquaintance with and 

 analysis of his number-form had persuaded him that the loose 

 term semi-circle should be replaced by '' | circle." He writes : 

 *' Semi-circle is perhaps not strictly accurate. On analysis, 

 the part-circles, on which the groups of ten are arranged, are 

 obviouslv the original clock-face with the portion from 10 to i 

 left out, and are therefore J circles." He also points out the 

 interesting fact that his number-form became unconsciously 

 adapted to increasinglv complex fisfures as they became known 

 to him. But as these notes were made some time after he 

 became scientificallv interested in his own number-form, he 

 requests me to keep them separate from the original description. 



This visual representation in space of the negative numbers 

 is an interesting aspect of the question which seems to have 

 been insufficiently studied. One of my correspondents, whose 

 form, in most respects, is quite a usual one, has " not a 



1. (Added subsequently.) " 1.000.000 has the same position as 10." 



