139 



„who succeed in overcoming the first difficulty then begin 

 „to grow very rapidly indeed, the rapidity increasing till 

 „the size 27 is reached. After that the growth begins to 

 „diminish; it gradually decreases, to only half of the 

 ..maximum growth for the individual of size 100 and to 

 „one eighth of the maximum growth for individuals of 

 „size 170. 



„À11 this proves to be in good agreement with what 

 „has been really observed. Dr. Tammes writes: „„the 

 „„case I sent you is as follows: the quantities communi- 

 „„cated are stalk-lengths of Linum crepitans, a variety 

 „„of the ordinary flax. They were measured, at a moment 

 „„in which the growth had not yet ceased, by Miss 

 „„A. Haga. The seeds were sown in a great deep 

 „„flower-pot. Their number was purposely taken very 

 „„high, so that they were extremely croivded. At starting, 

 „„therefore, the difficulty for each seed was to get a 

 „„root into the soil. It seems allowable to assume that 

 „„all seeds germinated. This has necessarily entailed an 

 „„intense struggle and many individuals must not hâve 

 „„succeeded or not sufficiently succeeded. For those who 

 „„really got their root in the soil there now came a good 

 „„time. There was plenty of food for a good many of 

 „„very small plants. The case however changed when the 

 „„plants, becoming greater, required more room. Then a 

 „„second struggle ensued, viz the struggle for the available 

 „„food in the too narrow room. The plants now became 

 „„more and more impeded in their growth. 



„„It seems to me that the conclusions from your curve 

 „„are well in accordance with the facts."" 



16. Proportional curves. 



What becomes of the frequency curve: 



a. if for any one cause the reaction becomes /• fold; 



b. if — the average reaction or déviation remaining 

 equal — the number of causes grows in the proportion of 1 : /? 



