25O J. ARTHUR HARRIS AND H. S. REED. 



findings of Webber (1920) in regard to the growth of Citrus 

 stock. 



PROBLEM 2. The correlation between the growth increments 

 of the organism during the several growth periods. 



Our second problem is to determine whether there is a corre- 

 lation in growth increments as well as in actual size of the or- 

 ganism. We shall thus answer the question whether the organism 

 which grows more rapidly than the average during one growth 

 period will grow more rapidly than the average in other growth 

 periods and whether the organism which lags behind the average 

 in its rate of growth during one growth period will also lag be- 

 hind during other growth periods. 



Little has heretofore been done towards the statistical treat- 

 ment of growth increments. This is probably in part due to the 

 arithmetical difficulties of computing the constants for incre- 

 ments, but if the moments and product moments be taken about 

 zero as origin in computing the coefficients required under Prob- 

 lem i above, the calculations for growth increments are easily 

 made by the use of formulae given elsewhere (Harris, 1920). 



The symmetrical table showing the relationship between the 

 actual growth increments for all of the combinations of growth 

 periods appears as Table IV. This table shows positive and sta- 

 tistically significant correlation coefficients for closely associated 

 periods throughout the season up to and including the period for 

 the 63d to the /oth day. The coefficients for the period from 

 the 7Oth to the 7/th day cannot in general be considered statis- 

 tically significant in comparison with their probable errors. 



Examining these results in a little greater detail, we note that 

 the nine coefficients showing the relationship between the growth 

 increments of successive weeks (the constants bordering the diag- 

 onal cell of the symmetrical table of constants) are all positive in 

 sign and with the exception of the last (showing the relationship 

 between the growth of the period from the 63d to /oth and that 

 between the /oth to 7/th day) all are statistically significant. The 

 eight coefficients measuring the correlations between the growth 

 increments of weekly periods which are separated by one week 

 are also without exception positive, but are lower in magnitude 

 and less certainly statistically significant. For periods more 



