MOVEMENTS OF GROWTH. 373 



all higher plants, there is a sharp division at the vegetative cone 

 between dermatogen, periblera, and plerome. 



The arrangement of the cells in growing points corresponds, 

 according to Sachs, 1 with his principle of rectangular division. 

 The anticlinals, i.e. the cell-walls which run at right angles to the 

 surface of the growing, point, and the periclinals, i.e. the walls 

 curved in the same sense as the surface, cut one another at right 

 angles. The anticlinal walls form, therefore, a series of orthogonal 

 trajectories with respect to the periclinals. The fact that the 

 cell- walls meet one another at right angles is to be observed very 

 generally in the vegetable kingdom. We may observe rectangular 

 division in its simplest form in filamentous algae (e.g. Spirogyra). 



Errera 2 and Berthold s have recently asserted that there is a 

 still more general principle than that of rectangular division for 

 the arrangement of the membranes. This is the principle of 

 smallest surfaces. Many phenomena, e.g. this, that the cell-walls 

 often meet one another, not at right angles, but at an acute angle 

 (see Berthold, pp. 231 and 253), are only intelligible on the basis 

 of this principle, as the above authors also show in detail. They 

 arrive at the result that the grouping of the membranes is 

 governed by the same laws as regulate the development of fluid 

 sheets. This, as was shown particularly by Plateau, is determined 

 by the principle of smallest surfaces, and it is therefore of interest 

 to make some experiments on the subject. 



We dissolve 375 gr. of powdered medicinal soap (to be obtained 

 from the chemist) in a mixture of 187*5 gr. of distilled watery and 

 75 gr. of concentrated glycerin. The solution is once boiled, and 

 may then be kept for a long time. We now make wire models of 

 different bodies (cube, tetrahedron, cylinder), the wire being bent 

 so as to form the edges of the structures. In the cylinder the 

 upper circle is connected with the lower by three wires. Models 

 about 50 mm. in height are quite sufficient. The soap solution is 

 poured into a beaker, and the models are now dipped into it by 

 means of a wire fixed on at a suitable place. On removing them 

 soap sheets are seen stretching from edge to edge. These are 

 arranged according to the principle of smallest surfaces, as is 

 shown by special examination and mathematical calculation. If 

 we destroy one of the sheets by carefully touching it with a glass 

 rod, then a new state of equilibrium is set up in the system, often 

 with production of very remarkable sheet forms, which however 

 always satisfy the above principle. 



