300 MEMOIRS OF THE NEW YORK BOTANICAL GARDEN 



only 19 have the nuclei been noted in the form of a rhomb 

 or square; four forms occasionally show pyramids, and in three is 

 found the arrangement in a single row. Of 42 forms which have 

 quadripartition, 37 have the tetrahedral and 11 the rhomboidal 

 or rectangular arrangement; none of these are reported to have 

 the nuclei or spores arranged in a pyramid or row. It will thus 

 be seen that the tetrahedral arrangement is by far the predominant, 

 and the arrangement of the cells in pyramids or rows the most rare. 

 The rhomboidal and rectangular disposition occupy intermediate 

 relations, but the data have not been accurately enough recorded to 

 determine which of these later is the more frequent. Hofmeister, 

 Berthold, and Errera early contributed observations on the adjust- 

 ment of the plasma membrane to Plateau's law of minimal surface; 

 and Thompson (72) has recently called attention to this work, ex- 

 pressing the relation that (p. 424) "in a complex system of films . . . 

 three partition-walls and no more meet at a crest, at equal angles." 

 Harper (28e) in his study of Gonium colonies has laid particular 

 stress upon the tendency of cells to group themselves in threes. 

 He finds a tendency in the four-celled stage to shift from a rect- 

 angular monoplanal arrangement to that of a rhomb, wherein 

 two of the cells opposite each other are closer together than the 

 other pair, but in the older colonies the central four cells usually 

 take the arrangement of a perfect square partly on account of the 

 tension from the peripheral cells of the colony. This tension may 

 be the consequence of the tendency for the peripheral cells to form 

 groups of three with the central cells. The law of least surfaces 

 certainly applies also to these mother-cells in quadripartition. 

 It is evident that in the pyramidal arrangement of four spores in 

 one plane there is one group of three, in the rhomboidal there are two 

 groups of three, and in the tetrahedral there are four groups of 

 three. It is apparent that if a surface be described about four 

 spheres of equal size in such a way that it is tangential to the 

 surface of the included spheres which are in contact with it, the 

 extent of this described surface will vary with the arrangement 

 of those spheres in the following descending order: linear, pyra- 

 midal, rectangular, rhomlioidal, and tetrahedral. If then the 

 mother-cell-wall is exerting a force of compression upon the four 

 spores and the latter adhere closely together, we would expect 

 to find the tetrahedral arrangement of the spores to be the 



