46 



Growth 



application of the liquid film theory is particularly interesting. In the di- 

 vision of an egg into two equal cells, for example, the position of the 

 wall between the two daughter cells, if they behave like soap bubbles, 

 can be determined. This new wall should form an angle of 120° with the 

 tangent to the circumference of each daughter cell at the point where 

 these meet the partition wall, since this is the position where the sur- 

 face forces will be in equilibrium and where the film system thus is stable. 

 It is obvious geometrically that this wall is in such a position that the 

 distance between the centers of the two new cells is equal to their radii 

 (Fig. 3-14). When a single spherical cell, such as an egg or an algal cell, 

 divides thus equally, the position of the two daughter cells relative to 

 each other is approximately what this theory demands. 



Fig. 3-14. Stable partition and walls of minimum surface assumed by two equal 

 bubbles which are in contact. Angles OPQ and OPR are 120°. The distance between 

 the centers equals the radii. ( From D'Arcy Thompson. ) 



Where such a divided bubble divides again but now by a partition at 

 right angles to the plane of the first one, these two walls usually do not 

 meet at an angle of 90° but there is a readjustment in the film system so 

 that they meet at 120°, the stable position. Arrangements like that of 

 Fig. 3-15d may thus result, which resembles a group of actual cells. Any- 

 one familiar with cellular structure and who draws a bit of it comes almost 

 instinctively to make the cell walls intersect at angles of about 120°, 

 much as they would if they were liquid films. 



Where a spherical bubble is divided unequally, the curvature of the 

 partition wall can be calculated. Since the pressure is inversely propor- 

 tional to the radius of curvature, a small bubble pulls itself together, so 

 to speak, more strongly than a larger one. Thus P = 1/R, where P is the 

 pressure and R the radius. The pressure that determines the radius of the 



