596 



THE FORMS OF TISSUES 



[CH. 



incline to one another at angles of 120°. Where we have only one 

 such wall (in the case of four cells), or only two (in the case 

 of five cells), there is no room for ambiguity. But where we have 

 three little connecting- walls, in the case of six cells, we can 

 arrange them in three different ways, as Plateau* found his six 



3 4 5 "* 6 7 8 Cells' 



etc. 

 Fig. 245. Various possible arrangements of intermediate positions, 

 in groups of 3, 4, 5, 6, 7 or 8 cells. 



soap-films to do (Fig. 246). In the system of seven cells, the four 

 partitions can be arranged in four ways; and the five partitions 

 required in the case of eight cells can be arranged in no less than 



Fig. 246.. 



twelve different waysf. It does not follow that these various 

 arrangements are all equally good; some are known to be more 

 stable than others, and some are hard to realise in actual experiment. 

 Examples of these various arrangements meet us at every turn, 

 in all sorts of partitioning, whether there be actual walls or mere 



* Plateau experimented with a wire frame or "cage", in the form of a low 

 hexagonal prism. When this was plunged in soap-solution and withdrawn upright, 

 a vertical film occupied its six quadrangular. sides and nothing more. But when 

 it was drawn out sideways, six films starting from the six vertical edges met some- 

 how in the middle, and divided the hexagon into six cells. Moreover the partition- 

 films automatically solved the problem of meeting one another three-by-three, at 

 co-equal angles of 120°; and did so in more ways than one, which could be controlled 

 more or less, according to the manner and direction of lifting the cage. 



t Plateau, on Van Rees's authority, says thirteen; but this is wrong — unless 

 he meant to include the case where one cell is wholly surrounded by the seven 

 others. 



