44 THE POPULAR SCIENCE MONTHLY. 



feet. There seems to be considerable evidence that very primitive 

 peoples do not count above four or five, all quantity above that 

 being simply an indefinite many. Mr. Galton has given so strik- 

 ing and graphic an account of a Damara's conflict with matters 

 mathematical, that one can not forbear citing it in detail : " In 

 practice, whatever they may possess in their language, they cer- 

 tainly use no numeral greater than three. When they wish to 

 express four, they take to their fingers, which are to them as 

 formidable instruments of calculation as a sliding rule is to an 

 English school-boy. They puzzle very much after five, because 

 no spare hand remains to grasp and secure the fingers that are 

 required for units. Yet they seldom lose oxen ; the way in which 

 they discover the loss of one is not by the number of the herd 

 being diminished, but by the absence of a face they know. When 

 bartering is going on each sheep must be paid for separately. 

 Thus, suppose two sticks of 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. I have done so, and seen a man put two of 

 the sticks apart, and take a sight over them at one of the sheep 

 he was about to sell. Having satisfied himself that one was hon- 

 estly paid for, and finding to his surprise that exactly two sticks 

 remained in hand to settle the account for the other sheep, he 

 would be afflicted with doubts ; the transaction seemed to come 

 out too ' pat ' to be correct, and he would refer back to the first 

 couple of sticks; and then his mind got hazy and confused, 

 and wandered from one sheep to the other, and he broke off the 

 transaction until two sticks were put into his hand and one sheep 

 driven away, and then the other two sticks given him, and the 

 second sheep driven away. . . . 



" Once while I watched a Damara floundering hopelessly in a 

 calculation on one side of me, I observed Dinah, my spaniel, 

 equally embarrassed on the other. She was overlooking half a 

 dozen of her new-born puppies which had been removed two or 

 three times from her, and her anxiety was excessive as she tried 

 to find out if they were all present, or if any were still missing. 

 She kept puzzling and running her eyes over them backward and 

 forward, but could not satisfy herself. She evidently had a vague 

 notion of counting, but the figure was too large for her brain. 

 Taking the two as they stood, dog and Damara, the comparison 

 reflected no great honor on the man." 



Of corresponding difficulties in children it would doubtless be 

 possible to collect considerable evidence. Prof. Preyer, in his 

 painstaking study of his infant son, found that the child would 

 miss one of his set of nine-pins when ten months old, but so late 

 as the twenty-seventh month he failed to teach the child the dif- 

 ference between numbers from one to five : and two months later 



