48 



Growth 



from the intersection point with an old one and thus tending to form an 

 angle of 120°, even though the longitudinal walls, which are relatively 

 firm, remain essentially straight and the theoretical angle cannot be 



attained. 



The theory that the position and curvature of dividing cells are what 

 they would be if the walls were liquid films lends itself to some interest- 

 ing geometrical analyses, for which the reader is referred to Thompson's 

 book. Giesenhagen's work (1905, 1909) also has a discussion of the 

 theory and its applications. Various experiments with actual liquid films 

 have been reported by van Iterson and Meeuse (1942), and Matzke 

 (1946) has discussed the role of surface forces in determining cell shape. 

 There is no doubt that the configurations of the cells in an actively grow- 

 ing mass often do resemble a system of bubbles, for there are usually no 

 more than three walls intersecting at a point and the angles between them 

 tend to approximate 120°. The young walls are at least semiliquid, so that 



-f # 



Fig. 3-16. Walls in dividing cells (as shown by position of phragmosome) tend to avoid 

 continuity with adjacent partition walls. ( From Sinnott and Block. ) 



surface forces are doubtless operative to some extent in determining their 

 position. In any morphogenetic analysis the least-surface theory therefore 

 must certainly be taken into account. It greatly oversimplifies the prob- 

 lem, however, and fails to explain some facts with which the student of 

 plant development is confronted. Among the chief objections to it are the 

 following: 



1. The theory in its simplest form is applicable only to weightless 

 liquid films, and young cell walls obviously are not such, though they 

 mav approach this condition. To account for their position the theory 

 would require correction. 



2. Many division walls are formed in positions different from those 

 which the theory demands. Often the new walls are parallel to the longer 

 axis of the cell instead of at right angles to it. The most extreme case of 

 this occurs in dividing fusiform initials at the cambium which are 50 times 

 or more as long as wide but which nevertheless divide lengthwise. 



