368 Report of the Committee for conducting Inquiries [Feb. 28 y 



error diminishes, and the parallel between the behaviour of the 

 frontal breadth in Plymouth crabs and that seen by Bowditch in the 

 stature of civilised human beings ceases to hold. The obvious sug- 

 gestion by which to account for this seems to be that in the United 

 States, where Bowditch made his observations, human beings are 

 under conditions of such civilisation that there is considerable pro- 

 tection of the physically unfit ; and that here, as in other civilised 

 countries, any influences which might in a savage race produce selec- 

 tive destruction are reduced to a minimum, whereas in the case of 

 the crabs such selective influences are active. 



It is, of course, possible that the deviation of " abnormal " young 

 may in each individual case first attain a maximum and then 

 diminish with advancing age ; if this is the case, we cannot know 

 without experiment. In the absence of such experiment, the hypo- 

 thesis may be provisionally adopted that the diminution in the fre- 

 quency of individuals of given deviation is due to a selective destruc- 

 tion, and the consequences of this hypothesis will be examined. 



Consider a population of crabs, measured at the time of their 

 maximum variability, and suppose the distribution of deviations 

 among the population to be accurately represented, for a particular 

 organ, by a probability equation of modulus Ci. Now, let the number 

 of individuals of deviation lying between a be represented by the 

 area dbgd (fig. 4) ; then, if gd = 2a be small, compared with the ob- 

 served range of variation, and ki = - ^ , in other words, if ki 



aQi 



be the height of the median ordinate BD of the generalised curve, 

 then the whole number of individuals in the population will be 

 fcrftv^ 



Now, suppose any destruction, which acts unselectively with re- 

 gard to the organ in question, to reduce the number of individuals 



whose deviation lies between db a, to cdef, and let the - - = 



& 2 , or the height of the median ordinate BD 1 . Since this destruction 

 is unselective, it will destroy an equal percentage of animals of every 

 deviation, and will therefore not alter the modulus. The population 

 will therefore be reduced to k z Ci */TT in number. This unselective de- 

 struction cannot be directly measured. 



The selective destruction is most simply conceived as follows : 

 In fig. 4 let AD X HE represent a curve of modulus Ci, and let BD 1 

 = k z , so that the area of the whole curve AD^E = J^CK/IT represents 

 the population left after unselective destruction has occurred. Then 

 suppose the modulus to be reduced during growth to c 2 , where c 2 is 

 less than Ci, and let AD*KE be a curve of modulus c 2 . The minimum 

 number of individuals which it is necessary to destroy, in order to 

 affect this reduction in the modulus, is evidently represented by the^ 



