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



lem of great importance is that of the causes which bring about 

 the differences in size observable at any stage of development, or 

 after growth has entirely ceased. Are individuals which are 

 found to be small at maturity those which were small initially and 

 have remained so from the beginning, or may the growth rate of 

 an individual change during the course of its development to such 

 an extent that it may vary its position in the series under investi 

 gation from time to time? That the latter is to some extent the 

 case we know from general observations on human children. The 

 problem to be solved is that of the quantitative magnitude of the 

 relationship between the size of the individual at different stages 

 of development. 



The nature of the biological problems to be investigated has 

 been stated in earlier work, and an attempt has been made to 

 solve them by grouping plants according to quintile (Pearl and 

 Surface, 1915) or quartile (Reed, 1919) position in the culture 

 to which they belong and ascertaining the quartile or quintile in 

 which they fall at different stages of growth. 



This method has the disadvantage that all the individuals, 

 whatever their size, are lumped together in four or five groups. 

 In this method of treatment, small differences between two indi 

 viduals are, therefore, given as much significance as large ones, 

 providing they are large enough to throw the two individuals into 

 different quartiles or quintiles. 



An alternative method, which will completely obviate this dif 

 ficulty, is to determine the correlation between the sizes of the 

 individual at different periods of growth. The possible correla 

 tions between the absolute size of the individuals in the u dif 

 ferent stages of growth of the Helianthus plants are shown in 

 Table III. 



The coefficients in this table can be best understood by first ex 

 amining those for the relationships between the sizes of the plants 

 near the period of maturity, and then passing to the relationships 

 between the sizes of the plants at earlier stages. 



Considering first of all the coefficients in the lower right-hand 

 corner of the table, we note that all the coefficients are very high, 

 denoting practically perfect correlation. This is the relationship 

 which w r ould be expected for a period when the organism has 



