334 



Variation and Con'elation in Arcella 



A fourfold table was formed from Table VII. and is exhibited in Table VIII. 

 The divisions were taken between the outer dianieter classes centoring at 

 55 mikrous and 57 mikrons, and between the coloiir classes C and D. These 

 seemed on the whole the best divisions to choose. They lie near the medians 

 and satisfy the requirements of niaking a-'roh + d and of also making ad>bc, 

 although they do not niake a + b> c + d. It is impossible to fulfil this condition 

 without making our horizontal division soniewhcre within cülour class D. As 

 a consequence of c + d being greater thaii a + b, k is, of course, negative. 



TABLE VIII. 

 Fourfold Gorrelation between Colour and Outer Diameter. 



/( = -78704, 



A- = - 07778. 

 The equation in r is 



•018179 ?•' - -003044 ?-'' + -030008 r- -r + -012046 = 0. 



Solving for r by Horner's method, we get 



r= -01205. 



The probable error of this very low coefficient with such a comparatively small 

 number of observations is of cduiso large as compared with the coefficient itself. 

 The value of the probable error in case this r had been comptited by the product- 

 niomcnt method would bc appro.ximately + -035. The value of the probable error 

 for the method here used has not been coinputed, but it is of course still larger. 



Making all (lue allDwance for the size of the probable error it is clearly seen 

 that there is an c.xtreniely small degree of correlation between colour and size 

 in the .shell of Arcella within the limits of size in the series here discussed. It 

 niay even be said that practically there is no correlation between these two 

 characters. 



