388 THE AMERICAN NATURALIST. (VoL. XXXIII. 
in a chemical reaction—the protoplasmic mass reacting rather 
as a substance than as an individual. Some such theory as 
this latter seems to be latent in the minds of many biologists; 
it finds typical expression in the scheme for the reactions of a 
unicellular organism to chemical substances given by Le Dantec 
(La Matière Vivante, pp. 50-54). In this scheme, which is 
illustrated by geometrical constructions and almost takes the 
form of a mathematical demonstration, Le Dantec assumes that 
there is a tension between the chemical in’ solution and the 
surface of the protoplasmic mass, and that this tension acts in 
lines of force directed either away from the center of the proto- 
plasmic mass, or toward that center. The movement of the 
organism is then due to the difference in this tension on the 
two sides of the protoplasmic mass —that directed toward the 
center from which the chemical is diffusing, and that directed 
away from it. As the chemical diffuses from a center, the 
solution is less intense the farther one passes from the center; 
hence the solution is less dense on that side of the protoplasmic 
mass farthest away from that center. Assuming that the ten- 
sion caused by the chemical acts on the protoplasmic mass in 
lines of force directed away from the center of the mass, it is 
mathematically demonstrable that this force will be stronger 
on the side toward the center of diffusion of the chemical, and 
that the resultant of all the lines of force will be a force directed 
exactly toward this center of diffusion. Hence the protoplasmic 
mass will move toward the center of diffusion of the chemical ; 
in this way positive chemotaxis is explained. If, on the other 
hand, the tension acts in lines of force directed toward the 
center of the protoplasm, the same mathematical construction 
Shows that the mass will move away from the center of diffu- 
sion; thus is explained negative chemotaxis. 
The impossibility of reconciling the movements of the three 
Infusoria, whose reactions I have described, with any such theory 
as this is manifest. The theory, though designed expressly to 
explain the movements of the bacteria and flagellates used in 
Pfeffer’s well-known experiments in chemotaxis, neglects en- 
tirely the fact of the differentiation, in those organisms, of 
axes along which movement takes place, as well as the fact that 
