HARPER: BINARY FISSION AND SURFACE TENSION 161 



These are the relations of the two groups of four, as described by 

 BiitschU and Overton. As noted, it is with reference to the position of 

 the eight equatorial cells that clear description has been lacking. Text- 

 figure 2 shows an equatorial view of the model and it is obvious at 

 once that a least surface configuration requires the eight equatorial 

 cells to form a zigzag belt, each cell alternating with two cells of the 

 polar groups of four. With this arrangement the colony is made up 

 of eight groups of three cells, the most compact arrangement possible, 

 each of the four cells of each polar group appearing in two of the groups 

 of three. The groups of three are so placed with reference to each 

 other as also to form the groups of four seen in both the polar and 

 equatorial views. The whole colony would consist of eight of these 

 groups of four, since each of the eight equatorial cells is a member of 

 three such groups and each cell of the polar group is a member of 

 two such groups. 



The whole forms as perfect an approximation to a least surface 

 configuration as can be achieved by sixteen cells arranged in as nearly 

 as possible a spherical group. Such a configuration may be regarded, 

 it seems to me, as the type configuration and illustrates the inter- 

 action of surface tension, adhesion and binary fission as morphogenetic 

 factors. In the actual colonies the cells are, of course, flattened upon 

 each other and, as I have pointed out, elongate during division. As the 

 photograph (Fig. 7, PI. II) shows, they are quite variable in both form 

 and size. As is shown clearly by Klein also in all figures of the so- 

 called polar openings, phialopores, the posterior group of four do not 

 form any such definite square group as is maintained by the anterior 

 group of four, yet the tendency to the formation of the groups shown 

 in the model is, it seems to me, obvious. The abundance of pentagons 

 and hexagons in the cell outlines of the adult colonies is good evidence 

 of a tendency to the most compact configuration possible. 



I have not attempted to make the model with any great accuracy. 

 We lack data as to the relative efficiency of adhesion and surface 

 tension in the cells, which would be necessary for the exact determina- 

 tion of their interrelations. The actual relations of fission, adhesion 

 and surface tension in the processes just described are perhaps brought 

 out more clearly in the two diagrams (Text-figs. 3 and 4). 



If the protoplasm of the mother cell were a mass which grows 

 merely by imbibition and swelling, and if the cutting up of the mass 

 into cells were merely a secondary phenomenon following the principle 

 of the rectangular intersection of the cleavage planes and surface 

 tension, as Hofmeister ('67), Sachs ('78), and other critics of the cell 

 theory have assumed, we should expect a configuration of the cells like 

 that shown in text-figure 4. This is the sort of configuration Magnus 



