119 



The effect of the various causes of growth can be 

 independent, therefore, only in the case that the growth 

 due to any one of thèse causes is the same for individuals 

 of ail sizes. — If we assume this to be the case for the 

 diameters, then and then only, will the frequency-curve 

 of thèse diameters become normal. 



If however any causes hâve the same effect on the 

 diameters of large and small individuals, then this same 

 cause will hâve a différent effect on the volumes of thèse 

 same individuals. 



Take for instance two berries of diameter 5mm and two 

 of diameter 10mm. 



Let the effect of a certain cause be to make them grow 

 as follows: 



mm mm mm 



Ist berry from diam. 5.00 to 5.01; growth 0.01 

 2nd „ „ „ 5.00 „ 5.02; „ 0.02 



3d „ „ „ 10.00 „ 10.01; „ 0.01 

 4th „ „ „ 10.00 „ 10.02; „ 0.02 



the effect on the diameters of the large and small berries 



being the same hère. 



Àssuming the berries to be spherical, the growth in 



volume will be; 

 Ist berry from vol.,";- {5m)Holr. (5.01)^; growth 0.75 X iTrmm^ 

 2nd „ „ „ Xt: (5.00)'^,, i" (5.02)'^; ,. 1.51Xi7Tmm^ 

 3th „ „ „ ^,-(10.00)=^, 177(10.01)3; „ 3.00 Xi-mm3. 

 4th „ „ „ J - (10.00)3 „ 177(10.02)3; „ 6.01Xi77mm3. 



the growth of the large berries in volume is thus found 



to be practically ^) 4 times as large as that of the small ones. 



After what has been said we thus fînd, that if the 

 various causes of growth may be considered to be inde- 



') Practically; it would be rigorously so only for a growth in 

 diameter infinitely small. 



