8 T. H. Pear, Number- Forms 



the result of his addition and subtraction must then He within 

 that circle. He cannot do algebra without this form, and he 

 possesses no number-form. 



The tendency to visualize connected series of entities 

 spread out in space is not confined to numbers. Calkins 

 mentions " forms for piano-notes (squares) with lines for 

 violin notes : and an interesting- prayer-form, well remembered 

 from the time ^\ hen the progress from one part to another was 

 always the passage from one part to another of the form."^ 



One of Lemaitre's subjects (4) possessed 30 diagram-forms 

 of different kinds ; one of ■Nliiller's saw, in the part of his year- 

 diagram corresponding- to the beginning of spring, a fair 

 youth holding a staff decked with apple-blossom, and with, 

 apple-blossom in his hair. 



The alleged heredity of number-forms. 



, Upon this question there appears to have been not a 

 little confused thinking and generalization from insufficient 

 evidence ; even occasionally from evidence which is opposed 

 to some of the conclusions drawn from it. It is therefore 

 necessary to distinguish different senses in which number- 

 forms might at anv rate be conceived as transmissible bv 

 heredity. There might be handed down a general tendency 

 to visualize, a more specific tendency to visualize numbers in 

 space or an even more specific tendency to visualize a 

 particular kind of number-form. 



Galton believed in transmission not onlv in the second but 

 also in the third sense mentioned above. He writes : — 



I have the strongest evidence of its (the peculiarity's) 

 hereditary character after allowing, and over-allowing, for 

 all conceivable influences of education and family tradition 

 (3, 82). I give four instances in which the hereditary 

 tendency is found, not only in having a Form at all, but 

 also to some degree in the shape of the Form " (3, 100). 



These tendencies which he conceives to be hereditary, 

 he compares to the instincts of animals. He likens the 

 '^ natural fancies for different lines and curves" of 

 different persons to the universal tendency of each species 

 -of animal " to pursue their work according- to certain definite 

 lines and shapes, which are to them instinctive, and in no 



1. The writer remembers, though unfortunately he has no written record 

 of it, that a ' commandment-form ' of a curious kind was once mentioned by a 

 correspondent to the Westminster Gazette. Each of the ten Commandments 

 was localized at some part of the correspondent's native village, e.g., one mifrht 

 be thought of as localized at the bridge, another as at the school door. 



