MATHEMATICS IN EVOLUTION. 209 



Successive increments of difference in degree may gradually merge 

 and become exalted into a difference in kind. A number of pendu- 

 lums might, if unresisted, vibrate in an arc forever, but, if on one of 

 them the movements of the others are suitably concentrated, its arc 

 will gradually increase in amplitude until it becomes a circle. 



This principle of concentration appears in organic Nature in the 

 physiological division of labor, and in the adaptation of every organ- 

 ism to some particular environment which may be to it its held and 

 kingdom. Analogy would lead us to suppose that the different duties 

 of the brain are performed by special parts. So directly profitable 

 has the division of labor been found in manufacturing industry, that 

 in many cases it has been pushed to an injurious extreme, for a man 

 is stunted in development when all his powers of mind and body but 

 one remain unexercised. Specialists in art and science discover that 

 their highest excellence can only come with a comprehension of wide 

 principles and study in many various fields. 



So far irom concentration being invariably useful, diffusion may 

 be a process incident to progress. A lump is soonest leavened by 

 leaven distributed throughout it, crystallization proceeds more swiftly 

 from separate nuclei than from a concrete mass. Analogously, the 

 best, wisest, and most talented men of a people exert a larger influ- 

 ence when scattered through it than if gathered into an over-central- 

 ized capital, where they radiate chiefly on each other. 



In the laws which have been considered thus briefly, it has ap- 

 peared that their tendencies are continually progressive; that, while 

 the capital of evolution is being increased, so also is the rate of com- 

 pound interest by which it accumulates. It is now fitting that some 

 of the causes should be noticed which reduce these tendencies from 

 their theoretical power to the moderate activity we find them really 

 presenting. 



A minor and unfavorable sort of natural selection is that made by 

 animals not carnivorous when they have a choice of food ; they take 

 the best to be had, and leave the rest to propagate its kind. This 

 residue may be very bad indeed, when the total supply is scanty; in 

 crowded pastures the grazing herds only permit the worst parts of the 

 clover to come to seed, and squirrels always first eat the best nuts 

 stored in their hiding-places, and any surplus that might germinate 

 and grow is commonly of a very poor kind. The acquisition of new 

 powers by an animal is usually accompanied by a gradual and injuri- 

 ous loss of its original ones; neither the omnivorous hos: nor the higher 

 primates can number readiness in swimming among their resources, 

 although their inferior ancestry doubtless could. The introduction of 

 machinery is steadily causing us to lose the deftness and dexterity of 

 the old, unaided handicrafts, yet never so much as now were knack and 

 skill of value, for they are indispensable to the designer and inventor in 

 their work. A highly-cultivated citizen of New York, when he pene- 



VOL. IX. 14 



