252 J. ARTHUR HARRIS AND H. S. REED. 



widely separated in time the correlations are in part positive and 

 in part negative in sign. 



Thus from the results as a whole it appears that the incre- 

 ments of successive periods are generally positive and fairly 

 highly correlated when the periods show actual growth incre- 

 ments. Thus the zone of coefficients lying along the diagonal 

 cell are positive and generally fairly high. When the periods are 

 separated by any considerable length of time the coefficients are 

 generally insignificant in magnitude and may, as a matter of fact, 

 be either positive or negative in sign. 



The relationship may be brought out by determining the aver- 

 ages of the correlation coefficients, with regard to sign, for the 

 increments of periods separated by various lengths of time. The 

 results are as follows. 



Period of Separation Number of Correlations Average 



(Weeks). Averaged. Correlation. 



9 + -5009 



1 8 + .2240 



2 7 .0334 



3 6 .1236 



4 5 -.1640 



5 4 .1033 



6 3 .0077 



7 2 .0585 



8 i .1360 



If we disregard the cases in which there are less than five co- 

 efficients to be averaged, we note a steady decrease in the magni- 

 tude of the correlation coefficient. Periods of growth which are 

 successive or separated by only one week have positively corre- 

 lated growth increments. Periods which are more widely separ- 

 ated show negative correlations of the increments. 



The relationship between the coefficients in Table IV. may be 

 clarified by diagram 3 which shows the relationship between four 

 of the ten growth increments and each of the other ten incre- 

 ments. The increments selected as a " first variable " in the cor- 

 relation are the first, fourth, seventh, and tenth. This has the 

 advantage of representing the first and the last growth incre- 

 ment, and of leaving undrawn no more than two successive incre- 

 ments. The figures are aligned according to the ten increments 

 representing the " second variable " of the correlation. 



