HARPER: CELL TYPES AND RESPONSES IN PEDIASTRUM 211 
two-spined and more or less deeply lobed, three-spined, and four- 
spined forms which are recognized as Monactinia, Diactinia, 
Triactinia, and Tetractinia respectively. It is not obvious on the 
basis of our present knowledge why an ancestral type which had 
developed a unispinous form is more likely to have descendants 
with two- or three- and four-spined cells than with long cylindrical 
cells like Hydrodictyon or spindle-shaped cells like Scenedesmus. 
In most cases again in the subgenera we are confronted with a 
series of continuous variations in the configuration of the colonies, 
which, however, is broken at what appear to be critical points at 
which a further modification of the form of the cell leads to a 
quite characteristic change in the symmetry of the whole colony. 
In some cases, cell forms which have apparently tended to a large 
degree of asymmetry in the colony, when modified to a certain de- 
gree, make the achievement of equal contact and pressure relations 
and a higher degree of symmetry possible, as in the transition from 
Pediastrum simplex to P. triangulum and from P. Ehrenbergii to P. 
Rotula. In other cases a more extreme development of a particular 
cell form may make a new configuration of the colony necessary 
with a symmetry much more difficult to achieve, as in the transi- 
tion from P. asperum to P. clathratum. Throughout, as I have 
already pointed out ('15), we have the conflict of these ortho- 
genetic tendencies in the evolution of the cell form and the law of 
cell reproduction by bipartition, giving the geometrically pro- 
gressing series of cell numbers, 2, 4, 8, 16, 32, etc., with the prin- 
ciple of least surfaces requiring an entirely different series of 
numbers, 1, 7, 19, 37, 61, etc., for its full expression. 
I am presenting elsewhere ('18) the results of a study of the 
organization, reproduction, and heredity of Pediastrum asperum, 
together with further observations on the variations in a series of 
seven colonies of P. Boryanum. The results there described are 
assumed in this paper. These two species represent respectively 
the forms with spines well developed on both peripheral and in- 
terior cells of the colony and rather large intercellular spaces, and 
those with small or no intercellular spaces and the spines little 
developed on the interior cells. In both species, I have pointed 
out, the cells seem in some degree directly adapted to the forma- 
tion of bilaterally symmetrical plate-shaped colonies of sixteen 
