206 THE POPULAR SCIENCE MONTHLY. 



So that, in the tree of knowledge, as the branches grow in all direc- 

 tions, 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 per- 

 mutatively in the various actions directed to aid maintenance or pro- 

 mote 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 pow- 

 ers 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- 



