lotka: objective standard of value 457 



this case indeterminate, unless the " path " of the change is defined. 

 On the other hand, as soon as the path is defined, say by the condi- 

 tion that certain parameters P are to be kept constant in forming 



the partial derivative , which latter we may accordingly write 



( ), then the value of 



CO: = 



becomes definite, and we have a definite value for 



Vdmi I V 



With a path thus prescribed we can apply exactly the same 

 reasoning as before, and we shall have a precisely analogous 

 set of equations, with only this difference, that everywhere for 



-^ we must write ( ), ( ), and similarly, tor , 



dWi d/i \b7nj p \ dfi / p dWi 



br 4. -i. / br \ /dr\ 

 — we must write ( , ( — ) 



Thus, for a given prescribed path (order) or production and con- 

 sumption we obtain a perfectly definite set of "true" or objective 

 values: Both subjective and objective values are in this case 

 dependent on the "path" of production and consumption. 



Finally, it may be remarked that in general, among the various 

 possible paths there is one which makes the rate of increase r of 

 the species an absolute maximum.- In a specially restricted 

 sense we might speak of the objective values corresponding to 

 this path as the "true" values of the several conamodities pro- 

 duced and consumed. But the more general interpretation pre- 

 viously indicated will probably be found more serviceable for the 

 purposes for which the development here given has been worked 

 out — that is to say, for the treatment of certain problems in the 

 theory of evolution, as indicated by the writer elsewhere.^ 



2 Compare Pareto, Manuel d'economie politique, 1909, 547. 



3 Jl. Washington Acad. Sci., 2: 2. 49. 66. 1912; Ann. Naturphil. 1911, 59; 

 Phys. Review, 1912, 235; Am. Jl.Sci., 24: 199.375. 1907. 



