MEASUREMENT OF VARIABLE PROPERTIES 173 



We know that when a large number of causes (factors) are 

 combined under the influence of chance, the intensity of each 

 factor being variable according to the law of chance (see tem- 

 perature, p. 170),! and when no cause is predominant, the fre- 

 quency of the combinations is, when all is said and done, 

 governed by the law of chance which also governs the errors 

 of observation and finds its expression in the curve of errors 

 (Fig. 18, p. 146). 



When a certain primordium is measured in a number of 

 specimens of a given species taken at random in the state of 

 nature, each figure is the expression (the measure, as it were) 

 of a certain combination (resultant) of ALL the factors which 

 are the components of the conditions of development. It may 

 therefore be expected that the observed variation would be 

 expressed by a one-humped symmetrical curve similar to a 

 curve of errors (or the variation of the prisms. Fig. 24, p. 161). 

 This is actually often (not always) the case.^ 



In a biological variation curve (whatever its form may be) 

 the arithmetical mean is not a constant of the species. It is, 

 just as any of the observed individual values, a physiological 

 measure of a certain combination of factors. It is not the 

 expression of a simple something. It is impossible to decom- 

 pose each observed value into a constant ± an error. The very 

 same causes which produce variation bring the measured pri- 

 mordium into existence. (Compare § 108, p. 147, and § 116, 

 p. 162.) 



It is, moreover, impossible to determine exactly the MEAN 

 VALUE of a variable property of a species. I take as example 

 Poa annua and suppose that I wish to determine the mean 

 length of the axis of its panicle. If a number of specimens are 

 collected from a dry, waste place, a wood (shadow), the banks 

 of a stream (humid and sunny), walls or rocks, etc., a different 

 mean value is obtained from each series. A comparison 

 between the mean values is simply a comparison between the 

 conditions of existence in the mentioned localities. If an 

 arithmetical mean were calculated from all the series con- 

 sidered as a whole, the obtained figure would depend, of course, 

 on the number of specimens of each series ; it would be an 

 arbitrary and undecipherable something which would be modi- 

 fied by each new observation. 



The MAXIMAL VALUE is, on the contrary, a strictly deter- 



^ In the case of living beings each factor is not only variable from one 

 specimen to another, but also continually varying through the whole period 

 of development of each specimen. 



^ Asymmetrical curves in which the mean does not coincide at all with the 

 hump arc common. When certain values of the measured primordium are 

 more easily realized than others because of a certain specific energy, the varia- 

 tion curve deviates from the typical form. (Sec Part VII., variation steps.) 



