150 
BIOLOGY: A. J. LOTKA 
Proc. N. a. S. 
as compared with plants, and, to make Professor Johnstone's argument 
conclusive, it would seem necessary to show, not merely that the animal 
organism evolves in that direction, but that the system of coupled 
transformers, plant and animal, as a whole has so evolved. 
Professor Johnstone's conclusion is, however, not essentially incompati- 
ble with the one developed in this paper Where the supply of available 
energy is limited, the advantage will go to that organism which is most 
efficient, most economical, in applying to preservative uses such energy as 
it captures. Where the energy supply is capable of expansion, efficiency 
or economy, though still an advantage, is only one way of meeting the sit- 
uation, and, so long as there remains an unutilized margin of available 
energy, sooner or later the battle, presumably, will be between two groups 
or species equally efficient, equally economical, but the one more apt than 
the other in tapping previously unutilized sources of available energy. 
There is here a problem that will call for further investigation. In par- 
ticular, it remains to be established just what is the significance of the 
phrase "compatible with the constraints" which, in the presentation here 
given, modifies the maximum principle enunciated. The present commu- 
nication is intended rather a preliminary than as an attempt to say the 
last word on the subject. More detailed discussion is planned for another 
occasion. 
* Papers from the Department of Biometry and Vital Statistics, School of Hygiene 
and Public Health, Johns Hopkins University, No. 59. 
^ Der zweite Hauptsatz der mechanischen Wdrmeiheorie, 1886 (Gerold, Vienna), p. 21; 
Populdre Schriften, No. 3, Leipsic, 1905; Nernst, Theoretische Chemie, 1913, p. 819; 
Burns and Paton, Biophysics, 1921, p. 8, H. F. Osborn, The Origin and Evolution of 
Life, 1918, p. XV. 
2 Compare also Sir Oliver Lodge, Life and Matter, 1906, pp. 139, 140. 
3 Lotka, A. J., Ann. Naturphil, 1910, pp. 67, 68; Proc. Nat. Acad., Sci., 1921, pp. 194, 
195. 
4 Lotka, A. J., Proc. Washington Acad., 5, 1915, pp. 360, 397. 
^ The term energy flux is here used to denote the available energy absorbed by and 
dissipated within the system per unit of time. 
^ As, for example, if the total mass of the system is capable of accretion, but only at 
a limited velocity, in which case the phenomenon of a moving equilibrium may present 
itself. Compare Lotka, A. J., Proc. Nat. Acad. Sci., 7, 1921, p. 168. 
7 Pearl, R., The Nation's Food, 1920, pp. 218, 203, 258, 80, 245; Amer. J. Hygiene, 1, 
1921, p. 598. 
8 Owing to the fact that in existing organisms the anabiotic and catabiotic functions 
are very largely segregated in different types (plants and animals), evolution will here 
operate upon systems or groups of at least two species, one species of autotrophic ana 
bions, and one of heterotrophic catabions. 
9 Compare Lotka, A. J., Amer. J. Sci., 24, 1907, pp. 204, 216. 
" Lotka, A. J., Proc. Nat. Acad. Sci., 7, 1921, p. 172. 
11 Idem., Ann. Naturphil., 1910, p. 70. It is there suggested that the continuous 
energy transformations associated with the maintenance of a steady state would prob- 
ably be found to play the dominant role, while any "latent heat" effect associated 
