II. Pkarl and f. J. Di'nkar 



33:^ 



pi-obublc .sizu in niikroiis ut' llie inner diaiiicter and JJ„ tlu; probable sizu in 

 iiiikrons of the oute7' diameter, we get for the regrcssion eiiuations : 



A-15'9107= •817(0-55-7<S97), or 7),; = -317 - 1-775 (i), 



A,-.'5.r7897 = 2-204 (/■- 15-9107). or /)„ = 20723 + 2-204 / (ii), 



whcre stauds fm- t.ho observed outer, ainl / fm- llio observed inner diameter. 



The probable error in determining the valuc of the inner diameter from that of 

 tiie outer by equation (i) i.s given by the expression + -0740 er, Vi —/•'-. In the 

 present case thi.s expre.ssion e(iuals + -S04 mikrons. 



The probable error in determining the outer diameter from the inner by 

 equation (ii) is 2120 mikron.s. The expre.ssion for this probable error is the .same 

 as that for equation (i) except that er, is written instead of er,. 



2. Correlation between outer diameter and colonr. 



The methods used in mea.suring and clas.sifying the colonr of Arcella .shells have 

 been fully de.scribed in another section. It will be rccalled that the shells were 

 divided into four colour cla.sses, designated A, B, C, and D. Clas.s A includes the 

 shells lightest in colour and D those darkest. 



In Table VII. is shown the frequency of the occurrence of the different combi- 

 nations of colour and size of shells. 



TABLE VII. 



Gorrelation hetween Colour and Outer Diameter in Arcella. 

 Outer diameter in mikrons. 



The colour classes are not quantitatively defined in this table, but they may 

 be considered each as including a definite though unknown portion of the colour 

 Scale of some one pigment in the Arcella shell. The intensity of this colour niay 

 also be considered to increase regularly and gradually from the lower limit of 

 class A to the upper limit of cla.ss D. 



The method we have used in obtaining the coctficient of correlation between 

 colour and diameter of shell is that described by Pearson*. 



* Pearson, K., Pkil. Trans., Vol. 19.5, A, pp. 1-47. 



