. Contributions from the Botanical Laboratory, vol. 7. Botany; Botany. A B Fi^. 11. A Pentagonal, 5 Rhombic dodecahedra Tlu' alveolar structure of protoplasm 195 Four bodies—we can for the moment think of squares or cubes— meeting in a point in the manner of a plus sign (-f-), present an opportunity for lateral slippage, but when three bodies meet, as in the case of hexagons, no such slippage can take place. Consequently, systems such as emulsions and foams, with tetrahedral angles at nodal points, are less stable than those with trihedral angles. In this respect the dodeca- and the tetrakaide
. Contributions from the Botanical Laboratory, vol. 7. Botany; Botany. A B Fi^. 11. A Pentagonal, 5 Rhombic dodecahedra Tlu' alveolar structure of protoplasm 195 Four bodies—we can for the moment think of squares or cubes— meeting in a point in the manner of a plus sign (-f-), present an opportunity for lateral slippage, but when three bodies meet, as in the case of hexagons, no such slippage can take place. Consequently, systems such as emulsions and foams, with tetrahedral angles at nodal points, are less stable than those with trihedral angles. In this respect the dodeca- and the tetrakaidecahedron have a decided advantage over cubes, and the 12-sided figure has an advantage over the 14-sided one because the trihedral angles of the former are equal (I20^i, while those of the latter are not. Plateau (36), in his exten- sive experiments on the figures of equilibrium of liciuid masses with- drawn from the action of gravity, ascertained that four films meeting in a point and forming a tetra- hedral angle give a configuration which is unstable. Lord Kelvin (22) then demonstrated that a more stable figure, which yet fills space with minimal partitional area, is the orthic tetrakaidecahedron. The three faces of an orthic tetrakaidecahedron form one angle of 109^28'16" and two of 125M5'52". If the condition of maximum stabilitv is to be attained the three angles must be equal and of 120^ Kelvin, therefore, described a form the hexagonal faces of which are slightly curved. This modification is not applicable to liciuid droplets, and there- fore not to protoplasmic alveoli. We must, conse(iuently, chose between the less stable tetrakaidecahedron and the less economical dodecahedron. The original arrangement of the spherical bodies is our fifth condition. It is an important factor in determining cell forms but it does not often come into play. F. T. Lewis (27) has diagrammatically shown the effect of the initial arrangement of spheres on their final shape when
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