176 THE QUANTITATIVE METHOD IN BIOLOGY 



annua, Phleum arenarium, etc.) behave in the same way, the 

 minimal value of h converges towards the same limit (practic- 

 ally o) in each and all, just as in the above example of the 

 leaves. Therefore the terms minimal height of the stem, without 

 more, represent an indeterminate notion. 



Remark : The facts alluded to may be actually observed as often as a limited 

 area is crowded with seeds of the same species. The growth of the young 

 plants is stopped when their stems are still very short (and sterile). The same 

 experiment being carried out with several species (each of them separately), 

 no perceptible difference is observed with regard to the minimal value of h. 

 I have carried out the experiment with rye, Poa annua and Phleum arenarium. 



Certain CONVENTIONS (restrictions) being made, however, 

 the minimal value of a primordium may be looked upon as 

 being a characteristic specific constant. 



The aspect of the question is changed, indeed, if we take a 

 given primordium under certain definite conditions ; for in- 

 stance, the height hf of the fertile stem of a grass. The exis- 

 tence of 2i fertile stem is only possible when the variation of the 

 conditions of existence (combined factors) is included within 

 certain limits which are different according to the species, and 

 narrower than the limits between which the development of a 

 stem in general is possible. Therefore the minimum of hf is 

 not the minimal height of a stem in general, but the peculiar 

 minimum which may occur when the conditions of fertility of 

 the species are prevailing. Therefore the minimum of hf is a 

 specific constant. 



In a similar way the minimal values of various primordia of 

 animals and plants are specific constants. 



Examples : The length, breadth and other primordia of the longest leaf of 

 a fertile stem of an acrocarpic moss ; the length and other primordia of the 

 longest petal of a flower ; the number of flowers of an inflorescence ; the length 

 of an antenna, a wing and other parts (segments) of an insect ; the primordia 

 of an animal or a vegetable embryo in a state of development coinciding with 

 a given value of the leading property (see § 49), etc, 



§ 120b.— RELATION BETWEEN MEAN VALUE AND 

 VARIATION STEPS.— The arithmetical mean of a series of 

 measurements has, in general, only an empirical significance. 

 It may happen, however, that a mean value coincides with one 

 of the terms of a series of variation steps. In this case the 

 mean value is the expression of a characteristic state of equi- 

 librium, and is really a constant of a peculiar kind. (See Part 

 VII., especially § 127.) 



§ 121.— USEFULNESS OF MEAN VALUES FOR COM- 

 PARING TWO OR MORE SERIES OF MEASUREMENTS.— 

 One single mean value, taken alone, is a rather vague piece of 

 information; if we ascribe to it a definite significance we 



