So that, in the tree of knowledge, as the branches grow in all directions, their offshoots come to touch at innumerable points.
The multiplication of effects may be traced not only in physics, chemistry, and cognate sciences, but also in the chapters of natural history and the facts of human life. The organized faculties of an animal which are distinctly different may be considered—of course, with proper qualification—as elements which may be grouped permutatively in the various actions directed to aid maintenance or promote safety; although, in the case of any particular variety of a species, a vast discrepancy must exist between the theoretical results of the mathematical law and the number of different groupings really made, yet, if the discrepancy is tolerably constant in degree in any two successive cases, the relations between two such cases may be stated by the law with an approximation to truth. Thus if a variety of quadrupeds with, say, four distinct and presumedly averaged powers be taken, at first sight it would seem but one-third better off in the struggle for existence than another variety with three several powers; yet the one may have an advantage over the other as great as four to one, for the variety of actions possible to the former may cover a field four times as great as the others. This aids us in understanding why variations in useful rather than those in useless directions tend strongly to persist. They do so because of the immense exaltation of power that comes with the development of any new faculty, any new means of securing a livelihood or escaping danger; and so great is this exaltation that even minor degrees of development have an appreciable value and tend to become permanent and to increase.
The effects of the laws under consideration also help to make clear why transition periods in organic Nature have been brief as revealed in their infrequent traces in such geological records as we possess.
When new circumstances have demanded the acquisition of new powers, or rather the development of dormant ones, the odds have been overwhelming against such individuals of a race as have been inelastic in the required direction, so that in a comparatively short period all that lived knew the new lesson.
A further corollary which harmonizes with observed facts is that, as species progress, an ever-increasing width of gap would separate kind from kind, and the highest individual of a kind from the next below it. The lowest organisms, monera, have no definite shape; polyps, some grades above them, conform very tolerably to a certain outline; and so on in the scale of life an increasing individuality keeps pace with an increasing divergency, until man and the tree mark the two great summits of Nature in her animal and vegetal forms.
Many able students of the theory of evolution stop short at the chasm which divides the human climax from the allied primates, and hesitate to believe that there can be a common origin for apes and the race which has produced a Beethoven and a Raphael; but a con-
