VIII] THE SEGMENTATION OF A DISC 595 



layer surrounds an at first sight irregular agglomeration of "funda- 

 mental tissue". 



In the last paragraph but one, I have spoken of the difficulty of 

 so arranging the meetmg-places of a number of cells that at each 

 junction only three cell- walls shall meet in a point, and all three 

 shall meet at equal angles of 120°. As a matter of fact, the problem 

 is soluble in a number of ways; that is to say, when we have a 

 number of cells enclosed in a common boundary, say eight as in 

 the case considered, there are various ways in which their walls 

 may meet internally, three by three, at equal angles; and these 

 differences will entail differences also in the curvature of the walls, 

 and consequently in the shape of the cells. The question is some- 



a — ^-------^ b 



Fig. 244. Sections of embryo of a moss. After Kienitz-Gerlofif. 



what complex ; it has been dealt with by Plateau, " and treated 

 mathematically by M. Van Rees*. 



If within our boundary we have only three cells all meeting 

 internally, they must meet in a point; furthermore, they tend to 

 do so at equal angles of 120°, and there is an end of the matter. 

 If we have four cells, then, as we have already seen, the conditions 

 are satisfied by interposing a little intermediate wall, the two 

 extremities of which constitute the meeting-points of three cells 

 each, and the upper edge of which marks the "polar furrow." 

 In the case of five cells, we require two httle intermediate walls, 

 and two polar furrows; and we soon arrive at the rule that, for 

 n cells, we require ti — 3 Httle longitudinal partitions (and corre- 

 sponding polar furrows), connecting the triple junctions of the cells f ; 

 and these Httle walls, Hke all the rest within the system, tend to 



* Cit. Plateau, Statique des Liquides, i, p. 358. 



t There is an obvious analogy between this rule for the number of internal 

 partitions within a polygonal system, and Lamarle's rule for the number of "free 

 films " within a polyhedron. Vide supra, ^. b5Q. 



