168 THE QUANTITATIVE METHOD IN BIOLOGY 



above-mentioned factors are continually varying ; their vari- 

 able values are combined in an unlimited number of ways : 



they are the COMPONENTS OF 

 CHANCE. The prevailing com- 

 bination is different for all the 

 specimens of a given species. 



I take the influence of tempera- 

 ture upon a given primordium (for 

 instance, the length A of the spike 

 of a given subspecies of rye) as 

 example . We know from experience 

 that the growth of any living object 

 whatever is possible only within two 

 limits of temperature. I call the 

 lowest Umit t° and the highest hmit 

 T°. Let us suppose that, in the 

 case of the spike, t° = -{- 5° C. and 

 J° = 35° C. (or thereabout). Be- 

 tween t° and T° every variation of 

 temperature results in a variation 

 of the intensity of growth and 

 therefore of the value A. Starting 

 from t°, every increase of tempera- 

 ture brings about an increase of A 

 tiU a certain temperature 0° (I 

 „ suppose 15° C.) is reached. Every 

 ■l2 CD further increase from 6° to T° re- 

 sults on the contrary in a decrease 

 of A. The temperature 6° (inter- 

 mediate between t° and T°) is the 

 optimal temperature, which coin- 

 cides with the maximal effect. 



The relation between cause and 

 effect is roughly represented by Fig. 

 25. Below i° and above r° the length 

 A = o, for the simple reason that no 

 spike may come into existence. 



The limits t° and T° are, of course, 

 critical temperatures. Therefore I 

 Fig. 25.— The curve is an ap- take, in Fig. 25, Umits which are a 

 proximate expression of the rela- i-..i i i ,o j Tij.i i_ '7-0 



tion between temperature (f-T) httle below ^ and a little above T . 

 and length \ of the spike ; x^. Suppose that a Series of speci- 

 maximai length of the spike ; e\ mens have been cultivated at all 

 optimal temperature. (See text.) p^^^-^^j^ temperatures between f^ 

 and T°, the other conditions of development being the same 

 for each and all. The adult spikes being measured, a series 



of values A A„ A, 



A;«, is obtained. The highest value 



