6 W. E. Alkins — Variation of Sphceria 



(c) Correlation of Length and Thickness. The correla- 

 tion table for length and thickness is shewn in full in 

 Table III. The correlaton here is not quite so high as in the 

 case of length and width ; the coefficient of correlation has the 

 value + 0906. 



The equations of regression are: — 



(a) L = 130 + i*2i t, 



with a standard error of ± 0302 ; 



(b) t = - 014 + 068 L, 



with the standard error ±0226. (t = thickness 

 in mm.) 



(d) Correlation of Width and Thickness. The correlation 

 table for width and thickness is shewn in Table IV. The 

 coefficient of correlation has the value + 0925, while the 

 equations of regression are : — 



(a) W = 126 + 1519 t, 



with a standard error of + 0*334; 



(b) t = - 010 + 0563 W, 



standard error + 0203. 



Thus, the correlation of each pair of dimensions is high. 



/L\ n •*-.-!. *■ 1 4.-L x- Width j Thickness* 



(e) Distribution of the ratios ^ r and — ^ i — 



v ' Length Length 



Data shewing the distribution of the ratios -t -r and 



Thickness 



-j 77— respectively are shewn in Tables V and VI. The 



range covered by each ratio is somewhat surprisingly small : 



the -z -r ratio varies from 113 to 129, only 2 per cent, of 



the specimens lying outside the limits 114 and 1*25; the 



thickness 



— j r— ratio varies from 057 to 074, and in this case 93*5 



per cent, of the total number of specimens fall between the 

 limits 0*62 and 070. This very restricted variation is reflected 

 in the values of the standard deviations and the coefficients of 

 variation of the two ratios, which are shown at the foot of 

 Tables V and VI. 



