ORGANIC VARIABILITY 



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masses. So long as we know absolutely nothing (in the 

 physical sense) of the causes of organic variability, so long 

 must the expression f(a, b, c, . . . x) remain a quite general 

 one really concealing our ignorance. 



The mathematical description of organic variability must 

 therefore be approached from another point of view. Let the 

 following two series of values represent a series of observations 

 of organic variation : 



The independent variable X represents a series of values of 

 the measurable character X of an organism. These values 

 have their mean between 2 and 3. The dependent variable 

 y represents the number of times, or frequency, with which 

 the values o, 1,2 ... 9, 10 were observed : that is, there 

 were 5 individuals giving a value of the character X equal to 

 o, 42 which gave a value = 1, 63 which gave the value 2, and 

 so on. The whole series is called a frequency distribution, 

 expressing the observed frequency of occurrence of the various 

 values of the variable character X. Suppose now that we 

 had an indefinitely great number of individuals which we can 

 measure, and suppose that we measured 50, then 100, then 

 200, then 400, and so on. In each case we should obtain a 

 rather different frequency distribution, but as the number of 

 individuals measured became greater, we should find that the 

 form of the distribution would tend to become " steady." It 

 is sometimes said that when the number of measurements 

 made is " infinite " the distribution takes a definite form — 

 which is rather to be regarded as nonsense. As the number of 

 individuals becomes greater and greater the form of the distribu- 

 tion tends towards a limit. In this particular case the limit is : 



neglecting the decimal figures after the second one. This is 

 an evaluation of the series represented by y = f (a, b, c, . . x) 



