500 THE FORMS OF TISSUES [ch. 



It is obvious, as a simple geometrical fact, that each of these 

 co-equal circles is in contact with six others around. Imagine the 

 whole system under some uniform stress — of pressure caused by- 

 growth or expansion within the cells, or due to some uniformly 

 applied constricting pressure from without. In these cases the six 

 points of contact between the circles in the diagram will be extended 

 into lines, representing surfaces of contact in the actual spheres or 

 cylinders; and the equal circles of our diagram will be converted 

 into regular and co-equal hexagons. The result is just the same 

 so far as form is concerned — so long as we are concerned only with 

 a morphological result and not with a physiological process — what- 

 ever be the force which brings the bodies together. For instance, 

 the cells of a segmenting egg, lying within their vitelhne membrane 

 or within some common film or ectoplasm, are pressed together as 

 they grow, and suffer deformation accordingly; their surface tends 

 towards an area minima, but we need not even enquire, in the first 

 instance, whether it be surface-tension, mechanical pressure, or what 

 not other physical force, which is the cause of the phenomenon*. 



The production by mutual interaction of polygons, which be- 

 come regular hexagons when conditions are perfectly symmetrical, 

 is beautifully illustrated by Benard's tourbillons cellulaires, and also 

 in some of Leduc's diffusion experiments. In these latter, a 

 solution of gelatine is allowed to set on a plate of glass, and little 

 drops of weak potassium ferrocyanide are then let fall at regular 

 intervals upon the gelatine. Immediately each little drop becomes 

 the centre of a system of diffusion currents, and the several systems 

 conflict with and repel one another; so that presently each little 

 area becomes the seat of a to-and-fro current system, outwards and 

 back again, until the concentration of the field becomes equalised 

 and the currents cease. When equihbrium is attained, and when 

 the gelatin-layer is allowed to dry, we have an artificial tissue of 



* The following is one of many curious corollaries to the principle of close- 

 packing here touched upon. A circle surrounded by six similar circles, the whole 

 bounded by a circle of three times the radius of the original one, forms a unit, so 

 to speak, next in order after the circle itself. A round pea or grain of shot will 

 pass through a hole of its own size; but peas or shot will not rtin out of a vessel 

 through a hole less than three times their own diameter. There can be no freedom 

 of motion among the close -packed grains when confronted by a smaller orifice. 

 Cf. K. Takahasi, Sci. Papers Inst. Chem., etc., Tokio, xxvi, p. 19. 1935. 



