# Page:Popular Science Monthly Volume 79.djvu/462

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THE POPULAR SCIENCE MONTHLY

Each of these combinations is the starting point for a new individual. It will be gray if there is a dominant G in the combination. Hence, among the offspring there will be three gray and one white. The result may be expressed by the formula

${\displaystyle GW.\ GW=1GG+2GW+1WW,}$

which is corroborated by similar experiments of other investigators.

In graphic statics, one of the most valuable branches of structural engineering, may be found the reason for the peculiar distribution of the substance in the upper portion of a thigh-bone along orthogonal trajectories (Fig. 6 a). This is in analogy with the problem of a cranelike structure, as diagrammatically shown in Fig. 6 b. It is well known that the curves of maximum compression and tension in a strained body form an orthogonal system,[1] and it seems natural that in order to insure greatest strength, cell matter should be deposited according to this system.

An orthogonal system formed by the stream lines and lines of greatest tension, which appear as lateral cracks and crevasses, is shown in most glacial movements (Fig. 7). The directions of corresponding stresses and sections upon which they act form an involutoric pencil of rays. The case where the field is exclusively subject to tensions only leads to elliptic involutions around all points. Every involutoric pencil admits of a rectangular pair, corresponding to the maximum and minimum stresses; tensions in this case. The effect of this condition is shown in Fig. 8, representing the cracks of a mud-bed or on a heavily varnished surface which is drying up. In this case only tensile normal stresses act on the rectangular pair. One is a maximum, the other a minimum. After a crack has formed, the maximal stress and strain normal to the crack has been relieved, so that the former minimal normal tension along the crack becomes now the maximum. The next rupture will therefore be orthogonal to the first crack. The reason for this peculiar configuration is thus found by the methods of projective geometry.[2]

A great number of other examples from the realms of natural history might be added which all would give further evidence of the fact, that the whole evolution of the inventive and creative human intellect is reflected by the well-perceived phenomena of nature.

By the laws of the universe the human mind is forced to repeat the same logic conclusions, according to which the rest of the organic world and nature in general manifest themselves.

1. Ritter, "Graphische Statik," Vol. 1, pp. 128-134.
2. Emch, "An Introduction to Projective Geometry and its Applications," pp. 239-241, New York, 1905.