366 lotka: efficiency in organic evolution 



While we have thus lost something of the detail of our first 

 analysis, we have gained this point, that the quantities with 

 which we are now dealing are clear cut, measurable and, in 

 principle at least, determinable by statistical methods. By 

 their aid we can attack the problem before us by analytical 

 methods; and furthermore, when we have taken the first steps 

 in this direction, we can, if we wish, restore to our analysis 

 some of the detail which we had temporarily sacrificed. 



ERRORS OF observation, OPERATION, AND MENTATION 



We shall deal with these three types of error under one gen- 

 eral head, since they have this in common: that they all exert 

 their, influence upon r through the productivity or productive 

 efficiency of the individual. 



We have, quite generally, 



r = r {xi, X2, ■ ■ ■ ■ Xj, ' • •) (5) 



so that 



dE.^bxj' bEj 



In the particular case that the parameter X, is of the nature 

 of mass produced (and consumed) per unit of time (e.g. the 



br 

 annual production and consumption of wheat), — - is the objec- 



dXj 



tive value ** v, per unit mass of the commodity Xj. In any case, 



we can, with obvious economic significance, write 



Also, from (4) we have 



so that (6) becomes 



(7) 



(8) 



(9) 

 dEj ' ' 



9 This Journal, 1914, loc. cit. 



