lotka: efficiency in organic evolution 367 



We have obtained this result by lumping together in a sta- 

 tistical way errors committed by the individual, and dealing not 

 directly with variations in these errors but with corresponding 

 variations in the productive efficiency E^. There is now no 

 difficulty in carrying our analysis farther, so as to make it corre- 

 spond in matter of detail more nearly with the qualitative 

 analysis from -sYhich we started. We may proceed as follows: 



Let I be some suitable parameter which can serve as an index 

 of the imprecision of a particular type of observation or oper- 

 ation. (Thus / may be the .mean error made in a particular 

 type of observation or operation; or it may be, for example, the 

 strength of the correcting lens worn by a short-sighted person; 

 or yet again it may be a suitable index measuring the acuity of 

 the logical faculties of the type under consideration, say, some- 

 thing of the nature of a refined Binet test).i° 



Then if i is the value of the parameter /, we have 



E; = ^ (i) (10) 



8r= — di (11) 



^^ ^^^8i (12) 



^ bEj bi 



the summation being carried over all those parameters X, for 

 which the productive efficiency is affected by the imprecision /. 



Hence, by (9) 



5r = y vj Lj ^ bi (13) 



^^ bi 



or 



which we interpret, in view of (7) as 



/ 



V, = V ., Lj ^ (15) 



^^^ bi 



" Compare C. B. Davenport, Heredity in Relation to Eugenics, 1911, p. 9. 



