May, 1908.] Annual Wood-Increment of Acer rubrum L. 



347 



extracted. The result as corrected by a number representing 

 the probable error is the standard deviation. We thus arrive 

 at a value 1.87 mm. for the bog habitat, and 0.56 mm. for the 

 woodlot habitat, which stands as a definite measure of varia- 

 bility. It enables comparisons from year to year and between 

 different localities, advantages which are too obvious to require 

 elaboration. 



To compare variability on an abstract basis an expression 

 combining the idea both of standard deviation and type is added 

 here. -It is found by dividing the standard deviation by the 

 mean as a base. The result is an excellent index of variability 

 in the form of a rate percent usually known as the coefficient 

 of variability. The value of the coefficient of variation will 

 change directly with changes of the standard deviation, and 

 inversely with changes of the mean. For the case at hand the 

 coefficient of variability is 54.60 and 33.28 for the bog con- 

 ditions and the woodlots respectively. 



The mode and the three important variations constants, 

 together with the probable errors of the determination, which 

 were deduced from the frequency curves in the manner described 

 above, are as follows: 



Habitat. 



Mode 



Mean 



Standard Deviation 



Coefficient of Variability. 



Bog 



3 mm. 



3.425 ±0.098 

 1.870 ±0.069 

 54.60 +2.55 



Woodlots 



2 mm. 

 1.701 ±0.038 

 0.566 ±0.027 

 33.28 + 2.46 



Difference 



1 mm. 

 1.72 mm 

 1.31 mm. 

 21.32 



The amount of variation is, as we should expect it to be, 

 sensibly different in each of the localities selected. The ex- 

 treme values for - the coefficients are 54.60 and 33.28 giving 

 a difference of 21.32. We may accept these differences in the 

 coefficients of variability as additional proof that when organ- 

 isms are introduced in changed or unusual conditions they be- 

 come more or less variable. It can safely be granted that the 

 conditions of variability which are here a function of place, are 

 ■masked but little by others. In the case at hand, variability 

 is not due to chance but is an inevitable accompaniment of the 

 differences in the habitat. .The evidence for this statement is 

 ■found especially in a forthcoming paper on the response of plants 

 to toxic bodies, and in the methods and results of experimental 

 physiology (2). Here, however, the results appear to be of 



