168 
BIOLOGY: A. J. LOTKA 
Proc. N. A. S. 
"pure lines" which differ among themselves but are per se constant in 
size, but, due to the peculiar way in which rats receive their infections, a 
given infection consists of only a very few of these lines. In fact, a large 
number of "wild" infections are probably actual "pure lines." 
1 Throughout this work the term "pure line infection" is used to designate an 
infection, the trypanosomes of which have all arisen from a single organism. A given 
"pure line" may either have been started from a single trypanosome, or it may have been 
subinoculated from such an infection. The term "wild infection" designates an infec- 
tion as found in nature. 
2 These Proceedings, 7, 1921 (138-143). 
3 The mean sizes in this report are all in microns. 
4 Minchin, B. A., and Thomson, J. D., Quart. J. Microsc. Sci., 60, N. S., 1915 
(463-692). 
5 Gondor, R., Centralbl. BakL, etc., I abt., Originate, 612, 1911 (102-113). 
6 Robertson, M., Proc. Roy. Soc, (B) 85, 1912 (241-248). 
7 Jennings, H. S., J.Exper. Zool., 11, 1911 (1-134); Ibid., 14, 1913 (270-391). 
8 Erdmann, R., Archiv. Entwicklungsmech. Organ., 46, 1920 (85-148). 
NOTE ON MOVING EQUILIBRA* 
By Alfred J. Lotka 
Brooklyn, N. Y. 
Communicated by R. Pearl, March 12, 1921 
A number of previous publications 1 have been devoted to the study, 
from various angles, of a material system evolving in accordance with a 
system of differential equations 
dX t /dt = F,{X 1 ,X 2 ,...;A 1 ,A 2 ,...;P;Q) (1) 
where the X's denote the masses of the several components of which the 
system is built up; the A's are parameters introduced by any equations 
of constraint to which the X's may be subject; 2 the parameters P include 
geometrical constraints (volume, area, topography) and also other quanti- 
ties serving to define the state of the system (temperature, etc.). The Q's 
define the character of the several components or species. 
The discussion has hitherto been restricted to the case that the param- 
eters A, P, Q remained constant during the transformations taken in 
view. A complete discussion of the evolution of systems of the kind re- 
ferred to must include also the consideration of changes in these param- 
eters. 
Such changes may be grouped under three heads: 
1. Changes of a perfectly general character. A study of these would re- 
solve itself into a discussion, on a general basis, of a system of differential 
equations of the form 
dXi/dt = Fi(X 1} A~ 2 ,...,0 (2) 
