JENNIXGS: DEVELOPMENT OF ASPLAXCHNA HERKICKII. 59 



by Berthold's principle, so that all the cases cited later as opposed to 

 Hert wig's law cau be utilized equally well against the principle of least 

 surfaces as a determining force. 



It should be noted that Berthold did not in any sense maintain that 

 this principle is the decisive factor in cell division, or the arrangement of 

 cells in tissues. He recognized that the conditions in a living cellular 

 body are widely different from those in a simple vesiculated fluid, and 

 that the conditions actually found in plant tissues are often inexplicable 

 by the principle of least surfaces, — in many cases, indeed, directly 

 opposed to it. " Aber nothwendig ist das in der Zelle nicht, wie bei den 

 Fltissigkeitslamellen. Denn wir sahen schon frtiher, dass die Symmetrie- 

 verhaltnisse der Zellen von der ausseren Form oft vollstandig unab- 

 hangig werden, und auch unter Mitwirkung der ausseren Formverhaltnisse 

 konnen bei dem iueinandergreifen der verschiedeuen Factoren sich Thei- 

 lungsrichtungen ergeben, die mit den Forderungen des Princips der 

 kleiusten Flachen nicht in Uebereinstimmuiig stehen." (Berthold, '86, 

 p. 230.) Berthold (^'^jQ, p. 230, Taf. 4) describes and figures many cases 

 in which the aiTangement and division of cells is not iu accordance with 

 the principle of least surfaces. 



The foct that a single cell may at one time take such a form as that 

 ■which d^-^ shows in the surface view iu Figure 37 (Plate 5), and in 

 section in Figure 38, and at another time have the form exhibited by the 

 same cell in Plate?, Figui-e 54 (surfece), and Plate 6, Figure 48 (section), 

 while the shape of the egg remains unchanged, demonstrates that we are 

 not here dealing with a problem of the statics of a vesiculated fluid ; 

 a single simple principle can no more account for the forms taken than 

 it can for the protean changes of shape of an Amoeba. 



By this I of course do not mean to imply that it is not possible, and 

 perhaps probable, that the laws of surface tension do, within certain 

 limits, modify the form and arrangement of cells, as maintained and 

 discussed at length by Berthold. Wherever the arrangement demanded 

 by the principle of least surfaces is not in conflict with other purposes of 

 the organism, or, to put it upon a less teleological basis, where it is not 

 in conflict with stronger influences than the force of surfiice tension, the 

 cells probably accommodate themselves to the demands of that principle. 

 The point of importance, however, is that this is not a decisive factor, 

 but may at once be overcome when other influences in the oi'ganism 

 antagonize it. 



Zimmerman ('93) holds that the general arrangement of cells in 

 accordance with the principle of least surfaces in plant tissues is not 



