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three circuits and eight leaves. Strangely enough these fractions express also the ratios between the times of revolution of the planets around the sun measured in days. "The period of Uranus is half that of Neptune, the period of Saturn one-third that of Uranus, the period of Jupiter two-fifths that of Saturn."*

This law of phyllotaxis is certainly a curious and interesting one. It seems to involve a direct and subtile recognition of complicated numerical relations. It has been suggested that this disposition of leaves on a stem would secure the best exposure of each to the light, and, therefore, once occurring, could be laid hold of and perpetuated by natural selection. This is an explanation of the feeblest character. It hardly yields a shimmer of light. It gives no attention to the immense improbability that such an arrangement should occur, not merely in one plant, but generally, in various yet allied ratios, throughout the vegetable kingdom; and it attaches a preposterous value to it in the struggle for life. The leaves on a stem soon fall away, and are not so crowded as to make their precise arrangement a matter of moment in securing light. In most trees, owing to the irregular development of buds, all trace of the law disappears in the tree as a composite whole. In cones, as those of the pine, and in discs, as those of the sun-flower, the arrangement is one simply of interest to the eye, as much so as the corresponding lines of chasing on the back of one's watch. The scales and seeds in each case are set closely, and gain little in light by their peculiar

* Religion and Chemistry, p. 299.