harper: nature of types in pediastrum ioi 



with their corresponding sides in the same order. If the colony 

 is divided along the line fg, which is in the surface of contact of 

 the central cells, and one half is rotated through i8o° on a median 

 line at right angles to the line fg, the two central cells form a 

 bilaterally symmetrical figure but two of the outer cells are divided 

 unequally. 



The area of each of the central cells i and 2, as seen in the 

 figure, appears smaller than that of those in the peripheral series. 

 It is quite possible, however, that the central cells are propor- 

 tionally thicker than the peripheral cells. It is not easy to get 

 exact evidence by measurement as to the thickness of the colonies 

 at different levels as seen in ecfge view. The cell bodies appear, 

 however, to thin out toward the margin of the colony. 



These two examples may suffice to illustrate the possibility of 

 recognizing what may perhaps be regarded as biological form 

 types of a group of related but fluctuatingly variable individuals. 

 The configurations shown in the diagrams (figs, ib and 2b) repre- 

 sent only the eight- and sixteen-celled colonies. The species has 

 8, 16, 32, 64, and even 128-celled colonies and for each different 

 number of cells the configuration presents new problems of equi- 

 librium and surface tension relations. 



The configurations shown in these diagrams are, so far as my 

 observation goes, strictly ideal and while the form relations in- 

 volved are relatively simple as compared with the complexity 

 found in the higher plants it is certainly doubtful whether such 

 perfect regularity and equality of corresponding spatial elements 

 (lines and angles) could ever be a common occurrence in nature. 



Such a figure does not, of course, represent the average indi- 

 vidual of a population, judged by degree of deviation from perfect 

 regularity. All these form elements, lines and angles, fluctuate 

 rather symmetrically about their modes and these modes are 

 approximately the line and angular dimensions of the perfectly 

 regular colony. It is the exceptional rather than the average 

 individual that approximates simultaneously in all elements this 

 standard of perfect symmetry. The average individual will nat- 

 urally fall below the specially favored one in its approach to an 

 ideal standard, determined in terms of the surface tension rela- 

 tions here involved. 



While these figures, so far as form relations and cell arrange- 

 ment are concerned, may be considered as form types of sixteen- 



