THE SHAPE OF COMPRESSED LEAD SHOT AND ITS RELATION TO CELL SHAPE

STUDIES OF the shape of undifferentiated cells as they occur aggregated into tissues have heretofore often emphasized the role of surface tension as a significant physical factor in determining the form of such cells. But, pressure relations between cells, such as parenchyma, aggregated without large intercellular spaces, are also important in shape determination. Experiments were therefore devised for using spheres in a physical system in which surface tension is reduced to a minimum. Small lead shot of uniform diameter were compressed in a cylinder until all the interstices were eliminated, and the shapes of the polyhedra produced by such compression were studied. Early investigators were impressed with the angular and frequently hexagonal appearance of cells in cross section, and Kieser (1815), considering the three-dimensional shape of parenchymal cells, believed them to be fundamentally rhombic dodecahedra. These figures, with twelve quadrilateral faces of equal size, each have six tetrahedral and eight trihedral angles. Rhombic dodecahedra of uniform size will aggregate to fill space without interstices, and this type of polyhedron may be produced by the compression of uniform spheres regularly stacked, twelve in contact with a central one. Later, the work of Berthold (1886) and Errera (1887) emphasized the importance of surface tension in cellular systems. Lord Kelvin (1887), after experimenting with liquid film systems, suggested an ortbic tetrakaidecahedron as an economical surface-volume configuration having trihedral angles and permitting the division of space without interstices. This figure has --eight hexagonal and six square faces; all the edges of the faces are equal; and the surface area of the figure is slightly less than that of a rhombic dodecahedron of equal volume. The orthic tetrakaidecahedron has trihedral, but no tetrahedral angles. The six tetrahedral angles which occur in therhombic dodecahedron are unstable in a liquid film system. The first extensive studies of cell shape in three dimensions are the outstanding contributions of Lewis (1923, 1925, 1928, 1930, 1933). He found that cells in undifferentiated tissues in a number of plants and animals are fundamentally fourteen sided, sometimes approaching in shape the orthic tetrakaidecahedron. METHOD.-In the studies outlined below lead shot of two diameters, 1.27 mm. and 2.54 mm., were used. They were examined under a binocular dissecting microscope, and the asymmetrical ones were discarded. The shot were compressed by means of a 1 Received for publication January 13, 1939. It is a pleasure to acknowledge the stimulating suggestions and advice of Professor E. B. Matzke under whose direction this work was carried out. steel plunger in a steel cylinder with a bore 25 mm. in diameter and 75 mm. long.2 After compression the shot were studied under a binocular dissecting microscope by means of a mechanical manipulator. This instrument consists of two curved steel needles fitted to a pair of mechanical forceps which can be made to open and close. The forceps are in turn attached to a system of geared adjustments in such a manner that the needles, after picking up a lead ball, can be rotated on a horizontal axis or moved up and down or from right to left in the horizontal field of the microscope. With this device it was possible to study all the faces of a polyhedron in sequence. With slight modification, this manipulator can also be used in studying the shape of cells (Marvin and Matzke, 1939). To aid in determining the effect of the position of a shot in the cylinder on its number of faces, an ocular guide was constructed. It consisted of two concentric rings so placed that the cross sectional area of the cylindrical mass of shot was divided into three regions. These regions were of approximately equal radial dimension and were about 4.17 mm. wide. DATA.-In the first experiment, shot 2.54 mm. in diameter were used. These shot were poured into the cylinder and compressed at pressures varying from 1,000 to 35,000 pounds. As the result of several trials, 35,000 pounds pressure on the plunger, when applied at the rate of 0.1 inch per minute, was found sufficient to eliminate all the interstices between the shot, to cause them to aggregate, and to form a cylinder of coherent shot whose individual members were easily separated. The results of these compressions are given in table I, figures 1-7, and figure 9. Figures 1-7 are photographs of the shot as they appear in the cylinder after compression. Figure 1 shows that flattening occurs at the points of contact as the result of 1,000 pounds pressure. A pressure of 2,500 pounds