harper: nature of types in pediastrum 93 



its adhesion to the adjacent cells. The colony as a whole also 

 tends to become as nearly circular in outline as is possible with 

 the number of cells of which it is composed and their individually 

 inherited forms. That is, the cells are arranged as compactly 

 as possible under the given conditions. 



That the organization of the colony is in conformity with the 

 principle of least surfaces is obvious from inspection and can be 

 illustrated statistically as will be shown more fully elsewhere. 

 The common arrangement of the cells in each case approximates 

 that of the most nearly corresponding one of the series of groups 

 of circles consisting of 7, 19, 37, 61, etc., which may be called the 

 least surface groups. In such groups the circles are in concentric 

 series and as compactly placed as possible. The diameters of 

 such groups form the series 3, 5, 7, 9, 11, etc., and each successively 

 larger group differs from the last by one additional peripheral 

 series, the numbers of circles in the successive peripheral series 

 being 6, 12, 18, 24, etc. 



The i6-celled colony, for example, is nearest to the group of 

 nineteen circles which consists of series of six and twelve concen- 

 trically placed about a central circle, while the colony of Pedi- 

 astrum consists of five and ten cells concentrically placed about a 

 central cell. 



In view of the deeply lobed and highly irregular contours of 

 the cells in most species of Pediastrum, it seems perhaps quite 

 contrary to fact to speak of them as illustrating the principle of 

 least surfaces. Still, there can be no doubt that this adult form 

 of the cells, their anomogeneity, as Rhumbler (7) would call it, 

 does not prevent their grouping and the angles of intersection of 

 their walls when in contact from showing a marked tendency to 

 approximate a least surface configuration. 



The lobed form produces in many species intercellular spaces 

 bounded by curves re-entering the cell bodies and is a very char- 

 acteristic structural feature of the cells, but it is not in conflict 

 with the general tendency of the colony to assume a rounded or 

 slightly oval form. I have already noted elsewhere (2) that 

 there can be no question that this lobed form is inherited by the 

 cells as individuals since it is assumed by cells which are practically 

 free from tissue continuity and the ordinary environmental ad- 

 hesions to which they are subjected in the colonies. 



