4 



Scientific Proceedings (109). 



2 (1584) 



Formulae for the determination of the correlations of size and of 

 growth increments in the developing organism. 



By J. Arthur Harris. 



[From the Station for Experimental Evolution, Cold Spring 

 Harbor, L. I.] 



In the analysis of the growth of the higher organism it is 

 essential to obtain definite measures of the interrelationship 

 between certain measured magnitudes. Those which require 

 consideration are the following: 



(1) The correlations between the actual size of the organism 

 at the various stages 1 of growth. (2) The correlations between 

 growth increments of the organism during the several growth 

 periods. (3) The correlations between the size of the organism 

 at any stage and any or all subsequent growth increments. 



The labor of determining these correlations by ordinary 

 methods is excessive. If the first set of correlations (1) be deter- 

 mined by taking all moments about o as origin, 2 we may solve 

 problems (2)-(3) as follows. 



Problem 2. — To determine the correlations between growth 

 increments from the moments and product moments of size at 

 the several growth stages. 



Let Wy x, y, z be the dimensions of the organism at growth 

 stages p, q, r, s. The growth increment during the intervals 

 q-p, r-q, s-r will then be i pq = x-w, i qr = y-x, i rs = z-y. 



The moments 2(V), 2(x 2 ), 2(;y 2 ),---, and the product 



moments 2(wx), 2(wy) f - • •, are available for the correlations 



between size, which are required on their own account (Problem 1). 



The constants for growth increments are given by well-known 

 formulae 



1 Growth stage denotes any given moment of time at which series of organisms 

 of the same age are measured. During development it is, therefore, synonymous 

 with age. The absolute size of the organism or any of its parts at a given growth 

 stage is the only character of the organism available for consideration. 



Growth period denotes the period of time elapsing between the 5th and the 

 s + nth growth stage, where s is any growth stage. Growth increment denotes the 

 increase in size during any such period. 



2 Harris, J. Arthur, Amer. Nat., 1910, xliv, 693-699. 



