II. i CELL-DIVISION 41 



thus play an important part in the production of the cell pattern. 

 We shall see elsewhere that they, and other protoplasmic move- 

 ments, are also of the very greatest significance in differentiation. 



There remains now to be noticed another principle, which is 

 especially applicable to plant-cells with fixed walls, though it 

 may possibly be used for the phenomena of animal segmentation 

 as well. Berthold has pointed out that when a newly formed 

 cell-wall places itself perpendicular to the previously existing 

 walls it is at least in a good many instances simply obeying 

 the laws of capillarity, it merely conforms to the principle of least 

 surfaces formulated by Plateau. This principle is as follows : 

 ' Homogeneous systems of fluid lamellae so arrange themselves, the 

 individual lamellae adopt a curvature such that the sum of the 

 (external) surfaces of all is under the given conditions a minimum/ 



A fluid lamella, of soap solution, for example, placed across 

 the interior of a hollow, rigid cylinder, or parallelepiped, or 

 cube, is, with the film coating the internal surface of the vessel 

 in which it lies, a special case of such a system of lamellae, and, 

 in obedience to the principle, the lamella places itself at right 

 angles to the walls of the cavity and transverse to the long axis. 



In the case of the plant-cell, the cell-plate, formed by solidifi- 

 cation of the spindle fibres in the equator of the mitotic figure, 

 represents the soap-lamella, and like the latter in its parallele- 

 piped, the cell-plate, or new cell-wall, places itself perpendicular 

 to the old one, and transverse to its length. 



There are very numerous cases in which the law is obeyed, 

 but it is not so in all. Under certain conditions the lamella 

 should be not at right angles, but oblique to the wall of the 

 chamber across which it is stretched. If, to take a concrete 

 case, the lamella be made to move (by abstracting air) towards 

 one end of its receptacle (a cube or parallelepiped), it will reach 

 a critical position in which the principle of least surface can 

 only be satisfied by its occupying an oblique position. The 



point at which this occurs is when the lamella is distant from 



7T 



the end, where a is the length of the side of the cube (short side 

 of the parallelepiped). The lamella now forms the fifth side 



to a wedge-shaped space (quadrant of a cylinder, whose radius 



4 

 is r = -a), but as more air is abstracted, and it moves still 



