244 GEOEGE JOHN EOMANBS 1888- 



tobacco to be the rate of exchange for one sheep, it 

 would sorely puzzle a Damara to take two sheep and 

 give him four sticks.' (F. Galton, ' Tropical South 

 Africa,' p. 213.) But if the savage had to deal with 

 a larger number of pigs the insufficiency of his sensu- 

 ous estimation would increase with the increase of 

 numbers, until a point would be reached at which, if 

 he were to keep count at all, he would be obliged to 

 resort to some system of notation, i.e. to mark off 

 each separate unit with a separate 7iota, whether by 

 fingers, notches, or words. Similarly vdth the sense 

 of hearing and the so-called muscular sense. We 

 can tell whether a clock strikes 1,2, 3, 4, or 5 without 

 naming each stroke, and whether we have walked 1, 

 2, 3, 4, or 5 paces without naming each pace, but we 

 caniiot in this way be sure whether a clock has struck 

 11 or 12, or we ourselves have, walked as many yards. 

 Thus there is counting and counting, distinguish- 

 ing between low numbers by directly appreciating 

 the difference between two quantities of sensuous 

 perceptions, and distinguishing between numbers of 

 any amount by marking each sensuous perception 

 with a separate sign. Of course, in the above in- 

 stance of animals counting it must be the former 

 method alone that is employed, and, therefore, I have 

 not sought to carry the ape beyond the number 5 

 lest I should spoil the results already gained. But a 

 careful research has been made to find how far this 

 method can be carried in the case of m9.n. The 

 experiments consisted in ascertaining the number of 

 objects (such as dots on a piece of paper) which admit 

 of being simultaneously estimated with accuracy. It 



