3:32 Variation and Correlation in Arcella 



•421 + •055. The higlicr value für the correlation coefficient of the characters 

 studied in the Arcella shell over the vuUie for length aiul hreadth of Parama'cium 

 is what would perhaps be expected froni geueral cousiderations regurdiug the two 

 cases. The shell of Arcella is a very definitely formed, firm structure, which after 

 its production is not easily clianged in its shape by environmental changes. On 

 the other band the body of a Faravicecium is composed of soft, yielding proto- 

 plasni, bouuded externally only by a thin, flexible pellicle. It is well known to 

 every biologist that changes of form in the body of Faramoeciuin are very easily 

 and quickly produced by changes in the surrounding conditions. In this event it 

 would not be expected that there would be so clo.se and definite a relationship 

 between the dimensions of lengtli and breadth in this form as exists between the 

 two dianu'ter.s of tht' firm, unyielding, and definitely formed shell of Arcella*. 



Passing now to the regression equations, we get from the iisual equations for 

 the regressionsf 



6i = r- 

 and b; = r — , 



0-1 



by substituting the values already obtainod for r, er,, and er», the foliowing values 

 for the regression coetficients between outer and inner diameters of Arcella shells, 



ft, = 0'317 (regression of inner on oiiter diameter), 



6j=2'204( „ „ outer „ inner „ ). 



To. express in words the significance of these equations we may say that : 



(1) the mean increase in the diameter of the opening in Arcella shells for every 

 increase of 1 mikron in the whole diameter of the shell is "317 mikrons; and 



(2) the mean increase in the total diameter of Arcella shells for every increase 

 of 1 mikron in tlio opening is 2'204 mikrons. 



The regression lines referred to the means as origin have the form : 



x= •317 y, 

 7/ = 2'204 X. 



Tn thesc equations x Stands for deviatious from the mean inner diameter, and 

 y for deviations from the mean outer diameter. Reducing these to actual values 

 instead of deviations by the method deseribed by Yule^, and Ictting Di denote the 



* Wc may also expoet a difference from Simpson's valuc, becausc in the first place our correlation 

 has not been eorrcctcd for growth, aud in the second place two brcadths expre.ssing generally sUe are 

 a priori more likely to be higlily correlated than a length and breadth which also involve the factor of 

 ehape. Thus the length and breadth of the human skull for most raccs are less highly correlated than 

 two breadtha such as the frontal and bizygomatic brcadths. 



+ Yule, O. U., '■ Ou the Theory of Correlation." Jour. lioy. Slat. Soc. Vol. lx. 1897, p. 818. 



i Luc. cit. p. 8'27. 



