204 
PHYSIOLOGY: H. SHAPLEY 
Proc. N. a. S. 
in investigating. Finally, groups in which the functions u{x) are dis- 
continuous would seem to be worthy of consideration. 
1 G. Kowalewski, Sitz. her. Math. Akad. Wiss. Wien, 120, Abteilimg Ila^ Ila^, 1911 
(77-109,1435-72). 
2 See writer's doctor's dissertation (Chicago, 1918). 
3 Trans. Amer. Math. Soc, 15, 1914r (139). 
1 In a paper by the writer soon to be published on Linear Partial Differential Equa- 
tions with a Continuous Infinitude of Variables. 
^ This formula has already been obtained by Volterra as the general solution of a 
functional differential equation in his paper, Atte R. Accad. Lincei, Ser. 6, 23, 1914, 
1st semester, (p. 393.) 
6 See paper by writer entitled, Integro-differential Equations with Constant Kernels, 
Bull. Amer. Math. Sac, 26, 1920 (193). 
THERMOKINETICS OF LIOMETOPUM APICULATUM MAYR 
By Harlow Shapl^y 
Mount Wilson Observatory, Pasadena, California 
Communicated by W. M. Wheeler, February 16, 1920 
Variation in the activity of a cold-blooded animal is largely dependent 
on metabolic changes, which in turn probably depend mainly on the ac- 
celleration of oxidation and of other chemical reactions. The physical 
nattue of the environment affects most of these chemical processes, and 
we should expect that the same physical properties would also directly 
influence the kinetic manifestations of animal life. While many observa- 
tions record the qualitative relation of animal activity to such factors as 
humidity and external temperature, only a few give definitive numerical 
results. 
An opportunity for precise quantitative measurement of the variation 
in the rate of expenditure of animal energy under the different natural 
stimuli arising from changing meteorological conditions, is afforded by the 
study of the foraging and patrolling activities of ants of the subfamily 
Dolichoderinae. Although some of my observations have been made 
on other genera of this group {Tapinoma, Dorymyrmex), I find the most 
suitable material to be the "Argentine ant," Iridomyrmex humilis Mayr, 
and two species of Liometopum. In briefly describing the activities of 
these ants and the observations based upon them, a number of reasons are 
proposed in the following paragraphs why members of the subfamily, 
and particularly the California Liometopa, are thought to be better adapted 
than nearly any other organism for the close quantitative investigation 
of kinetic response to changes in field Conditions. 
The trail-running habit, which is common to all genera of Dolichoderinae 
except Leptomyrmex of Australia,^ is fundamental for the observations 
discussed below. It permits permanent observing stations to be set up 
along the trail so that the speed over fixed intervals of distance can be 
