MEASUREMENT OF VARIABLE PROPERTIES 171 



about the data. The figures which I have taken are more or 

 less approaching to reality ; they are, however, arbitrary. In 

 any case, the arithmetical mean is here, for the biologist, an 

 empirical value. 



Second Eventuality ; The limits of temperature are supposed 

 to be 11° and 2i°C. (^° = i5°). The frequencies of temperature 

 are given by the following curve (according to (| + 1)^") :■ — 



Temperature 

 Frequency ^ 

 Groups . 



Temperature 

 Frequency ^ 

 Groups . 



The variation curve of the primordium A is given by the 

 following Table (the relation between A and temperature being 

 the same as in the first contingency, and the length of the 

 spike at 21° being ^^5 = 9 cm.) : — 



The curve is asymmetrical, yet distinctly different from the 

 preceding one. Arithmetical mean of A. = 13-52 cm. 



The remarks about the mean value in the first eventuality 

 are also applicable here. 



It is easUy seen that an unlimited number of eventualities 

 are possible, since the most frequent temperature and the 

 extremes may coincide, in each peculiar case, with various 

 temperatures between the limits t° and T°. The form of the 

 variation curve of A, (hump, mean value, etc.) depends, in each 

 series of measurements, on the prevailing conditions. ^ The 

 observed figures (values of A), and also the mean value, are an 

 indirect expression of the conditions of development (tempera- 

 ture). One single figure is invariable : this is the maximal 

 value of A (I have supposed A;u = i5 cm.).' This value will be 



' Number of specimens (total 1024). 



' In certain cases a unilateral curve might be obtained. 



' About the minimal value of A, see below. 



