518 JENNINGS— HEREDITY IN PROTOZOA. [April 24, 



form of the body), of course, varies in dependence upon all the three 

 sets of factors with which we have dealt — difference of race, growth 

 and environmental conditions. The smaller races are found to show, 

 under the same conditions, a slightly greater ratio of breadth to 

 length (see Table XXVL). Within the same race different stages 

 of growth show different ratios ; in general, the proportion of breadth 

 to length is greatest in the young, and gradually decreases with age ; 

 it increases again very rapidly in preparation for fission. Environ- 

 mental agents affect in most marked and varied ways the proportion 

 of breadth to length ; this is connected with the fact that such agents 

 act more upon the breadth than upon the length. A detailed sum- 

 mary of the different effects of the environment on the proportion 

 of breadth to length is found on pages 478 and 479. The most im- 

 portant general relation is, that increase of nutriment increases the 

 proportional breadth ; decrease of nutriment produces the opposite 

 effect. Any agent which suddenly increases the breadth likewise, as 

 a rule, increases the ratio of breadth to length. 



5. The coefficient of correlation between length and breadth is 

 the measure of the accuracy with which breadth and length vary 

 proportionately. If the proportion of breadth to length is the same 

 in all individuals of a collection, then the coefficient of correlation 

 of that collection is 1.000.^° Since, as we have just seen, the pro- 

 portion of breadth to length is altered by many factors, it follows 

 that all these factors modify the correlation, tending to reduce it 

 below 1.000. The correlation is affected by all the three categories 

 of factors that affect the dimensions in essentially the following ways : 



(a) The inclusion of different races in a collection, particularly 

 if some of the smaller and some of the larger races occur, makes the 

 correlation less than i.ooo, because the proportion of breadth to 

 length is greater in the smaller races. The reduction in correlation 

 produced by this alone is very slight. If we make a collection by 



" It is perhaps not necessary to point out that the "coefficient of correla- 

 tion " is descriptive; it shows the observed condition in a given set of meas- 

 urements. The cause of this condition is a matter to be determined. Corre- 

 lation is often conceived physiologically as an underlying something that 

 binds two things together, so that ihey must change correspondingly. The 

 descriptive correlation of the statistician may be the resultant of many 

 factors. 



