554 THE FORMS OF TISSUES [ch. 



solidification have vastly complicated the case. We get a curious 

 and an unexpected variant of the same phenomenon in the micro- 

 scopic foam-like structure assumed as molten metal cools. If these 

 foam-cells were again 14-hedra, their facets would all be either 

 squares or hexagons; but pentagonal facets are commoner than 

 either, and the cells often approach closely to the form of a regular 

 pentagonal dodecahedron ! The edges of this figure meet at angles 

 of 108°, not far from the characteristic Maraldi angle of 109° 28'; 

 and the faces meet at an angle not far removed from 120°. A slight 

 curvature of the sides is enough to turn our pentagonal dodecahedron 

 into a possible figure of equihbrium for a foam-cell. We cannot 

 close-pack pentagonal dodecahedra, whether equal or unequal, so 

 as to fill space; but still the figure may be, and seems to be, common, 

 interspersed among the polyhedra of various shapes and sizes which 

 are packed together in a metallic foam*. 



A somewhat similar result, and a curious one, was found by 

 Mr J. W. Marvin, who compressed leaden small-shot in a steel 

 cylinder, as Buffon compressed his peas; but this time the pressure 

 on the plunger ran from 1000 to 35,000 lb. or nearly twenty tons to 

 the square inch. When the shot was introduced carefully, so as 

 to lie in ordinary close packing, the result was an assemblage of 

 regular rhombic dodecahedra, as might be expected and as Buffon 

 had found. But the result was very different when the shot was 

 poured at random into the cyhnder, for the average number of 

 facets on each grain now varied with the pressure, from about 8-5 

 at 1000 lb. to 12-9 at 10,000 lb., and to no less than 14-16 facets or 

 contacts after all interstices were eliminated, which took the full 

 pressure of 35,000 lb. to do. An average of just over fourteen 

 facets might seem to indicate a tendency to the production of 

 tetrakaidekahedra, just as in the froth of soap-bubbles; but this 

 is not so. The squeezed grains are irregular in shape, and pentagonal 

 facets are much the commonest, just as we found them to be in 

 the microscopic structure of a once-molten metal. At first sight 

 it might seem that, though the experiment has something to teach 

 us about random packing in a limited space, it has no biological 

 significance; but it is curious to find that the pith-cells of 



* Cf. Cecil H. Desch, The solidification of metals from the liquid state, Joarn. 

 Inst, of Metals, xxii, p. 247, 1919. 



