MEASUREMENT OF VARIABLE PROPERTIES 169 



X[j. coincides with the optimal temperature 0°. It is impossible 

 to obtain a spike longer than A/x, whatever may be the 

 temperature (the other conditions of existence being the same) . 

 Therefore Aji* is a constant. If we compare two or several 

 subspecies of rye, each of them has its own value A/n. 



The maximal value of a primordium is the exact expression of 

 a constant property of each species {specific form), just as the 

 density of a given substance is the exact expression of a con- 

 stant property of that substance. 



REMARK : The influence of temperature upon the pri- 

 mordium under consideration is comparable to the influence 

 of temperature upon the density of water. The existence of 

 liquid water is possible between i° ( = 0° C. ) and T° ( = 100° C). 

 If a series of specimens of water were taken at aU possible 

 temperatures between the limits t° and T°, and if their density 

 were measured, a series of values d^, d^ . . . di^ would be 

 obtained. The highest value dfx would coincide vnth +4° C, 

 which is 6°. This value dfi, has been adopted as a funda- 

 mental physical constant. 



§ 120.— BIOLOGICAL AND INORGANIC VARIATION 

 CURVES {continued). — I suppose that we find, in the state of 

 nature, an unlimited number of specimens which have been 

 developed at all possible temperatures between two limits 

 (which are not necessarily t° and T°) : a large number — for 

 instance, 1024 adult spikes — are measured.^ The temperature 

 of development of each specimen depends on a combination 

 (resultant) of a number of natural accidental causes. The 

 frequencies of these combinations are governed by the laws of 

 chance, and therefore the frequencies of the various observed 

 values of A, (length of the spike) are governed by the same laws. 



The variation curve (curve of frequency) of temperature 

 being represented by (J + \)^° (see Fig. 18, p. 146), what will be 

 the variation curve of A ? 



I take two eventualities as examples and expound the 

 subject by means of figures, supposing that aU other condi- 

 tions of existence are the same for all the specimens. (The 

 following Tables and calculations are merely approximate, 

 owing to the use of the arithmetical method.) 



First Eventuality : The most frequent temperature is 6° 

 (optimum). Suppose the limits of temperature have been 10° 

 and 20°, the optimum {6°) being 15°. The following Table 

 [(« + 6)1"] gives the curve of frequency of temperature expressed 



• In order to eliminate the variation produced by gradation (see Part VIII.) 

 ia each plant only the spike of the first bud generation is measured. This is, 

 in the case of the rye, ordinarily the longest spike of each plant. 



