igos.] JENNINGS— HEREDITY IN PROTOZOA. 481 



are very precisely defined. If all conditions of environment and 

 growth were made absolutely the same, there is reason to believe (as 

 we shall see farther) that for a given line (descended from a single 

 individual) the coefficient of variation would be very close to zero. 

 Its actually observed value in a given lot then depends almost entirely 

 on environmental and growth differences. 



Effect of Enmronment on Correlation. — The observed correlation 

 between length and breadth varies greatly under different environ- 

 mental conditions. In the D line the coefficient which measures 

 correlation varies in different cultures from .3906 to .8463 ; in the 

 c line from 4141 to .8500 (see Table XVIII.). Such differences 

 are easily and quickly produced by environmental changes ; thus the 

 two extremes just mentioned for the D race were found in samples 

 of the same lot of Paramecia taken twenty-four hours apart — one 

 before, the other after, the addition of a nutritive fluid. 



The correlation between length and breadth expresses the accu- 

 racy with which length and breadth vary proportionately. The 

 actual proportion of one to the other, in a given lot, is, of course, of 

 no consequence ; length and breadth might be the same, or one might 

 be 50 per cent, or i per cent, of the other; the correlation would 

 still be complete (i.ooo) provided this same proportion were main- 

 tained throughout the particular lot examined. Any factor which 

 causes the proportion of breadth to length to vary in a given lot, of 

 course causes the correlation to fall below i.ooo. If in a given lot 

 many different ratios of breadth to length are represented, the cor- 

 relation is, of course, lowered. In such a lot, any factor which tends 

 to make the proportion of breadth to length more constant, of course, 

 increases the correlation. 



Examining the various factors which have the effects just men- 

 tioned, we find that the observed correlation depends upon many 

 things. 



(a) In considering the effects of growth (page 455), we saw 

 that the proportion of breadth to length differs in different stages. 

 Some of the effects of the environment on correlation are due to its 

 eff'ect on multiplication and growth. 



(b) Certain environmental agents (as increased nutrition) increase 

 the breadth while decreasing the length. Now, if this happens at 



