i9o8.] JENNINGS— HEREDITY IN PROTOZOA. 457 



growth curve, the correlation rises to .7132. In this larger collection 

 the short specimens are much the narrower, the large specimens much 

 broader — giving high positive correlation. Slight changes in one 

 dimension may not be accompanied by notable changes in the other, 

 while great changes in one are always accompanied by changes in ihe 

 other. This is a relation which we shall meet again. 



While thus growth has a very great effect on the correlation to 

 be computed from the measurements of a collection of Parainecia, 

 it is important to bear in mind the fact that it is by no means the 

 only factor concerned in correlation. This becomes evident as soon 

 as we take a collection in which the specimens are all in nearly the 

 same stage of growth ; the coefficient of correlation is then high. 

 This is perhaps best realized by considering specimens in the begin- 

 ning of fission. As we have before noticed, in the collection of 131 

 specimens beginning fission, from lot i, great pains were taken to 

 include only a single stage in the process. This collection gives a 

 high positive correlation of .6546. This correlation can be due only 

 to the fact that in specimens at a single grow^th stage the length and 

 breadth tend to bear a certain proportion to each other. The eft'ects 

 of this are clearly seen in many other collections of Table X. Thus, 

 in rows 8, 9 and 15 the specimens all fall in the period when length 

 is increasing while breadth is decreasing ; yet there is in each case a 

 small positive correlation. This is due to the fact that the period of 

 grow'th over which each collection extended was small, so that the 

 negative correlation due to growth was more than counterbalanced 

 by the inherent proportionality of length to breadth. A collection 

 including only specimens that were all in the same stage of growth 

 would undoubtedly (other things begin equal) show a high corre- 

 lation between length and breadth, no matter what point on the 

 growth curves they represented. This signifies, of course, that in 

 any given stage of growth the relation of length to breadth tends to 

 be the same in all specimens — although in different stages of growth 

 this is often not the case. Other factors which modify the correla- 

 tion will be considered in the later sections of this paper; a summary 

 of all these factors will be presented in a special section. 



With this we conclude our study of growth in Paramecium; 



PROC. AMER. PHIL. SOC. XLVH. I90 DD, PRINTED JANUARY II, I9O9. 



