INTER-PERIODIC CORRELATION. 257 



their probable error, and 5 of these are over twice as large as 

 their probable error. 



There is, therefore, clear evidence that the subsequent growth 

 of the higher plant organism is measurably conditioned by its 

 size. In general the larger individuals grow more rapidly in im- 

 mediately subsequent periods, but somewhat more slowly than 

 the average in more distant subsequent periods. 



While a detailed discussion of the relation of these results to 

 the theory that growth may be satisfactorily described by the 

 curve of an autocatylic reaction falls quite outside the scope of 

 this paper, it must be noted that negative correlations between 

 actual size at a given stage and the growth increments of certain 

 subsequent growth periods might be expected. As Reed and 

 Holland (1919) have pointed out the plants attained about half 

 their final height at about the thirty-fourth day. From this time 

 on the increments were decreasing. Plants which had attained 

 more than the average size at this period would, therefore, of 

 necessity, make smaller average increase in size in later periods. 



The number of individuals measured is not sufficiently large to 

 carry the analysis farther. 



III. RECAPITULATION. 



The purpose of this paper has been to illustrate on the basis of 

 a specific series of data the value of the inter-periodic correlation 

 coefficient in the analysis of the phenomena of growth. 



The analysis shows that in the case of a series of Heliantlins 

 plants the actual size of the individual at any stage of develop- 

 ment is closely correlated with its size at other closely associated 

 stages of development. The magnitude of the correlation rapidly 

 diminishes as the growth stages become more widely separated in 

 time. Thus the final size of the organism is but to a slight extent 

 determined by its initial size. 



The correlation between successive growth increments is posi- 

 tive in sign and statistically significant, with the general average 

 of ^=.501. The correlation for increments of weekly periods 

 separated by one week is on the average only about ~r = = .225. 

 For periods more widely separated than this the correlation be- 

 tween growth increments is on the average negative in sign. 



