452 THE POPULAR SCIENCE MONTHLY 



We have : 



Mathematics 



History 3 



Literature 



Science 3 



Music 2 



Drawing 1 



Other hand-work 1 



Sum of the seven differences 10 



These facts are repeated in the first column of Table 3. 



Table 3 



Computing the other differences as shown in the second and third 

 column of Table 3, we have for this individual the means of answering 

 question 1, concerning the permanence of interests. If the individual 

 had remained unchanged in his interests from any one period to any 

 other the appropriate seven differences of Table 3 would obviously have 

 been all zeros and the sum of that column would have been zero. If, 

 on the other hand, he had from one to another period, changed as com- 

 pletely as possible, the sum of the appropriate column of Table 3 would 

 have been 24 (7-1, 6-2, 5-3, 4-4, 3-5, 2-6, 1-7 giving 24). If the 

 individual's interests had been due to mere caprice, changing their 

 relative strength at random, the sum of any column of Table 3 would 

 approximate 16. For, if a 1 is equally likely to become a 1, 2, 3, 4, 5, 6 

 or 7, and so also of a 2, a 3, a 4, etc., the average result will be 16. 2 



Any quantity below 16 as the sum of a column then means some 

 permanence of interests in the individual in question, and the degree of 

 permanence is measured by the divergence from 16 toward 0. 



For the permanence from the elementary-school period to the junior 



2 1 becoming 1, 2, 3, 4, 5, 6, 7 gives as differences 0, 1, 2, 3, 4, 5, 6; 



2 becoming 1, 2, 3, 4, 5, 6, 7 gives as differences 1, 0, 1, 2, 3, 4, 5; 



3 becoming 1, 2, 3, 4, 5, 6, 7 gives as differences 2, 1, 0, 1, 2, 3, 4. 

 Continuing and dividing the sum of the 49 differences by 49 we get 2 2/7 for 

 the average difference by mere chance shifting and 7X2 2/7 or 16, as the 

 average sum of a column in Table 3 by mere chance shifting. 



