Abstract
THE problem of packing the greatest number of equal spheres into a given space, to which Prof. Aldis has drawn attention in your columns, is the simplest case of a more general problem which I have employed in my theory of crystallization (Cam. Phil. Trans., vol. xiv. part 3)—that is, the packing of the greatest number of equal and similar ellipsoids into a given space. The solution is that the ellipsoids should be arranged in a manner similar to that described for spheres by Profs. Aldis and Green-hill, so that every ellipsoid be touched by twelve others, and, further, that all the ellipsoids be similarly situated. The curious result comes out that so long as the ellipsoids are all similarly situated the orientation of the axes makes no difference in the number of them per unit volume. They may be turned about, provided they are all similarly turned, without affecting the ratio between the space filled by them and the unfilled space between them.
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LIVEING, G. Spherical Eggs. Nature 40, 55 (1889). https://doi.org/10.1038/040055c0
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DOI: https://doi.org/10.1038/040055c0
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