370 Report of the Committee for conducting Inquiries [Feb. 28, 



shaded area of the figure. The population after such destruction is 

 ktf-z </TT in number, and the shaded area represents a number of in- 

 dividuals equal to ki</ir(ci c 2 ), so that the ratio of animals selec- 

 tively destroyed to animals which survive all unselective destruction 



is l ~" 2 , a quantity which can be experimentally determined. 



GI 

 From the data given in Table III, this ratio, for frontal breadths 



10'79 _ 9'96 

 of Plymouth crabs, becomes - - or about 0'077, so that 



-L \J /t/ 



the hypothesis of selective destruction involves a death-rate of about 

 77 per thousand between the age corresponding to 12*5 mm. in cara- 

 pace-length and maturity, as a consequence of deviation in frontal 

 breadths, and in the group of structures, whatever these may be, 

 which are directly correlated with it. 



This total death-rate does not affect individuals of all deviations 

 alike ; an inspection of the figure will show that the death-rate is a 

 function of the deviation, and that function is quite simply deter- 

 mined. Consider any ordinate E</ of the curve ABEC, and let its 

 abscissa, DGr, be of magnitude x ; then the length of E</ is A^e"^ 2 /^ 2 

 and the number of individuals of deviation between x and x + dx is 

 ^e"* 2 /* 2 . dx. In the same way, the height of the ordinate F# is 



and the number of individuals of abnormality within unit distance 

 of x after selection is 



k 2 e-*W . dx. 



The ratio between the number of animals of abnormality x which 

 survive the unselective destruction and those which are selectively 

 destroyed is therefore 





So that if g is the selective death-rate among animals of abnor- 

 mality x, then that death-rate increases as x increases according to 

 the equation 



g = l e~ hx \ 



'where h is the numerical value of GI c 2 2 /Cj 2 c 2 2 , GI and c 2 being the 

 values of the modulus at the time of its maximum value and at 

 maturity respectively. 



For the frontal breadth of Plymouth crabs, the value of h is about 

 0'015 ; so that of the whole number of animals which attain the size 

 12-5 mm., having an abnormality x of their frontal breadth, the 



