406 HARPER— ORGANIZATION, REPRODUCTION 



The data given in Table IV. are based on measurements of seven 

 colonies of P. Boryanum, all of which again have the common ar- 

 rangement of their cells, that is, one cell in the center, five in the 

 second series, and ten in the third series v^ith the long lobes of the 

 cells of series II. and III. directed radially outward. The lettering 

 of the angles, etc., is given as noted in the type diagram. These 

 seven individuals are all relatively regular and symmetrical and the 

 angles of intersection of their cell walls do not fluctuate so widely 

 as is the case in colonies whose cells are more irregularly placed 

 (Figs. 26-28). It seems, however, impossible to include these more 

 irregular colonies with the more symmetrical types in a comparison 

 of the values of the included angles of their cells, since, as I have 

 pointed out already, the typical colonies tend to be bilaterally sym- 

 metrical and a comparison of fluctuation in the included angles of 

 their cells can only be of significance if made between correspond- 

 ingly placed angles (homologous angles of Rhumbler ('02)). In 

 the irregularly arranged colonies it is quite impossible to compare 

 angles as similarly placed with reference to the pressure relations 

 in the colony. In the case of these irregular colonies I have brought 

 together the values of the included angles of all their cells and classi- 

 fied them according to their value in degrees without reference to 

 their specific positions in the colony. The data so obtained will be 

 briefly discussed later. The seven colonies whose angles are here 

 compared are a selected group and the figure which is obtained 

 by averaging their values we may call for convenience the diagram 

 of the average of the common type. I have not drawn this figure 

 as a larger number of measurements is needed to give such a draw- 

 ing fundamental significance. The reentering angles of the cells 

 and our lack of quantitative knowledge of the adhesion and viscosity 

 of the protoplasm make it impossible to compute a theoretical type 

 configuration of sixteen units in such a group which might be made 

 a standard of comparison. The figure derived from averaging the 

 corresponding elements in an exceptionally regular individual as 

 given in my earlier paper we may similarly call the type diagram 

 from a selected individual. The significance of the measurements 

 of such a series of fairly regular colonies may be best discussed in 

 connection with the measurements of the single colony selected for 

 its symmetry. 



