568 THE FORMS OF TISSUES [ch. 



and conditions. This latter condition, of asymmetry of field, is 

 frequent in segmenting eggs*, and it then covers or includes the 

 principle upon which Balfour laid stress as leading to "unequal" or 

 to "partial" segmentation of the egg — viz, the unequal or asym- 

 metrical distribution of protoplasm and of food-yolk. 



The second rule, which also has its exceptions, is true in a large 

 number of cases, and owes its vahdity, as we may judge from the 

 illustration of the repeatedly bisected cube, to the guiding principle 

 of minimal areas. It is in short subordinate to a much more 

 important and fundamental rule, due not to Sachs but to Errera; 

 that (3) the incipient partition- wall of a dividing cell tends to be 

 such that its area is the least possible by which the given space-content 

 can be enclosed. 



Let us return to the case of our cube, and suppose that, instead 

 of bisecting it, we desire to shut off some small portion only of its 

 volume. It is found in the course of experiments upon soap-films, 

 that if we try to bring a partition-film too near to one side of a 

 cubical (or rectangular) space it becomes unstable, and is then easily 

 shifted to a new position in which it constitutes a curved cylindrical 

 wall cutting oif one corner of the cube. It still meets the sides of 

 the cube at right angles (for reasons which we have already con- 

 sidered); and, as we may see from the symmetry of the case, it 

 constitutes one-quarter of a cylinder. Our plane transverse parti- 

 tion had always the same area, wherever it was placed, viz. a^\ 

 and it is obvious that a cylindrical wall, if it cut oif a small corner, 

 may be much less than this. We want, accordingly, to determine 

 what volume might be partitioned oif with equal economy of wall- 

 space in one way as the other, that is to say, what area of cyhndrical 



* M. Robert {loc. cit. p. 305) has compiled a long list of cages among the molluscs 

 and the worms, where the initial segmentation of the egg proceeds by equal or 

 unequal division. The two cases are about equally numerous. But like most 

 other writers of his time, he would ascribe this equality or inequality rather to 

 a provision for the future than to a direct effect of immediate physical causation : 

 "II semble assez probable, comme on I'a dit sou vent, que la plus grande taille 

 d'un blastomere est liee a I'importance et au developpement precoce des parties 

 du corps qui doivent en naitre : il y aurait la une sorte de reflet des stades posterieures 

 du developpement sur les premieres phenomenes, ce que M. Ray Lankester appelle 

 precocious segregation. II faut avouer pourtant qu'on est parfois assez embarrasse 

 pour assigner une cause a pareilles differences." 



