The Cellular Basis of Growth 47 



partition wall between unequal bubbles is thus the difference between 

 the pressure of the smaller bubble and that of the larger one. If R equals 

 the radius of the partition wall, / that of the smaller bubble, and r that 

 of the larger one, then 1/R = 1// — 1/r, or R = rr7(r - r'). In other 

 words, the radius of the partition wall is the product of the two bubble 

 radii divided bv their difference. If two bubbles have radii of 3 and 5, for 

 example, that of the partition wall will be 7.5. In spherical cells of un- 

 equal size which are dividing, the new wall does tend to have this theo- 

 retical radius. 



Where the dividing cell has a relatively firm wall, however, as in micro- 

 spores within which a small prothallial cell is cut off, the situation is 

 different, since only the new dividing wall now acts as a liquid film. It 

 will be curved and will occupy a position such that it intersects the old 

 wall at the stable position of 90°. If the linear distance between the two 



Fig. 3-15. Plate of eight cells (or 

 bubbles) assuming a position of equi- 

 librium where cell surfaces are of mini- 

 mum area. (From D'Arcy Thompson.) 



points of intersection (as seen in section) and the radius of the large 

 cell are known, the radius of curvature of the new wall can readily be 

 calculated. 



There are other cases of division walls, notably in "rib" meristems 

 where the cells are in parallel rows and growth is strongly polar, which 

 may also be interpreted on the liquid-film theory even though the re- 

 semblance to a bubble system is much less close. In such rows of cells 

 it can be observed that the new cross walls, even in the phragmosome 

 stage, always tend to avoid a position that would put them opposite a 

 cross wall in an adjacent row ( Fig. 3-16 ) and would thus bring four walls 

 together, unstably, at a point. The walls are always "staggered," like 

 bricks in a wall. This often prevents a new wall taking its natural posi- 

 tion, which would divide the cell into two equal parts. The angles be- 

 tween the walls are larger than 90° but do not reach the theoretical 120°. 

 It may be that surface forces are operative in pulling the new wall away 



