igoS] JENNINGS— HEREDITY IN PROTOZOA. 519 



throwing together ten each of the different lines of Table XXV. 

 (page 494), giving the individuals of each line the mean dimensions 

 of its line (thus nearly excluding variations due to growth and 

 environment), then calculate the coefficient of correlation in the 

 same way as for our other collections, we find it to have the high 

 value of .9735. 



(b) The inclusion of dift'erent stages of growth in a collection 

 reduces the correlation below i.ooo, since different growth stages 

 have different ratios of breadth to length. A detailed summary of 

 the effects of growth on correlation is found on pages 455 to 457; 

 here we can notice only the main points. In the earliest stages of 

 growth the length is increasing while the breadth is decreasing; 

 hence if we take a collection including various stages within this 

 period, the correlation between length and breadth becomes negative ; 

 it may fall to a value of — -3138 (see Table X.). The inclusion of 

 various early stages in a collection of adults decreases the positive 

 correlation shown by the adults. In later growth, length and breadth 

 increase together; the inclusion of various stages at this period has 

 little effect on the correlation ; it does, however, tend to reduce it 

 slightly, since length and breadth do not increase at the same ratio. 

 In old specimens, beginning fission, the length decreases while the 

 breadth increases ; a collection including dift'erent stages in this 

 process tends again to give negative correlation, or to reduce the 

 positive correlation due to other causes. In a collection from the 

 same pure line, in which all specimens are in the same stage of 

 growth, the correlation between length and breadth is high ; this 

 would be true no matter what stage of growth is the one represented. 

 Random samples from any culture usually contain many stages of 

 growth ; this lowers the correlation between length and breadth. 



(c) Environmental dift'erences, like growth, affect length and 

 breadth differently or in different proportions; if individuals thus 

 diversely affected are included in a sample, this tends to decrease the 

 correlation between length and breadth. A detailed analysis of the 

 many and important effects of environmental action on the corre- 

 lation will be found on pages 481 to 484; here, again, we can but 

 summarize the important points. 



I. Certain environmental a2:ents increase the breadth while decreas- 



