Manchester Memoirs, Vol. lx-v. (192 1), No. 10 3 



(c) Correlation of Length and Thickness. In Table III 

 are given the data for the correlation of length and thickness. 

 The coefficient of correlation has the value - o"g288, which is 

 rather less than that for length and width ; the equations of 

 regression are : — 



(a) L = 1722 + 1145 T, 



with the standard error ± o'2i84; 



(6) T = - 0779 - 07532, 



with the standard error ± 01 771. 



(L = length; W = width; and T = thickness, all in millimetres.) 



(d) Correlation of Width and Thickness. Table IV gives 

 the correlation of width and thickness. The value of the 

 coefficient of correlation is + 0*9420, which is intermediate 

 between those of the other two pairs of dimensions studied. 

 Thus the three coefficients are in the same order in each of the 

 three species that have been examined up to the present. The 

 equations of regression are : — 



(a) W = 1 705 + 1-815 T, 



with the standard error ± 0309; 



(0) T = - 041 1 + 0489 W, 



with the standard error ± 0160. 



i \ n- * -u ■*- / #l d *■ Width , Thickness 



(e) Distribution of the Ratios ; -r and —^ it— . 



v J J Length Length 



-ru j- j. u • r i_ • width , thickness . . . 



Ihe distribution of the ratios -, r and — ; 77— is given in 



length length 



Tables V and VI below. 



