Vol. XL. May, 1921. No. 5 



BIOLOGICAL BULLETIN 



INTER-PERIODIC CORRELATION IN THE ANALYSIS 



OF GROWTH. 



J. ARTHUR HARRIS AND H. S. REED, 

 STATION FOR EXPERIMENTAL EVOLUTION, COLD SPRING HARBOR, LONG ISLAND. 



I. INTRODUCTORY. 



In the literature of growth, mathematical equations to describe 

 changes in the actual size of the organism, or changes in the 

 growth rate, are finding continuously widening applications. One 

 has merely to refer to the papers by Robertson, Miyake, Moeser, 

 Ostwald, Reed and Holland (1919), and Reed (I92O) 1 for illus- 

 trations. 



The criticism usually directed against such work is that in the 

 higher organism, growth is a highly complex process, and that in 

 consequence it cannot be represented mathematically. It is be- 

 cause of the very fact that growth is a complex process that 

 mathematical analysis of the experimental data is necessary. 

 Corollary to this must be the recognition of the fact that since 

 growth is not a simple process, no one mathematical formula will 

 be adequate for full description 2 and no one method adequate for 

 complete analysis. 



Our purpose in the present note is to illustrate on a series of 

 data collected by one of us (1919) the application of inter-periodic 

 correlation coefficients to certain phases of the problem of growth. 



Before passing to the analysis, which is the special purpose of 

 this paper, definition of the terms which will be used and a note 



1 Citations of literature may be traced from Reed's paper. 



2 Those who consider the possible adequacy of a single equation take the 

 ground that if it be possible to represent the growth of an organism by a 

 simple equation, it may be by virtue of the fact that during growth the various 

 (often conflicting external) factors which affect the living substance are inte- 

 grated by the organism. 



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