Dynamical Ideas in Chemistry, 403 



he triumphantly asks how this is possible, seeing that such mo- 

 dified forms would be crossed by the many which have remained 

 unchanged." 



"Why should not nature take a sudden leap from structure 

 to structure ? On the theory of natural selection we can clearly 

 understand why she should not; for natural selection acts only 

 by taking advantage of slight successive variations; she can 

 never take a sudden leap, but must advance by short and sure 

 though slow steps." 



" On the theory of natural selection we can clearly understand 

 the full uieaning of that old canon in natural history, 'natura 

 non facit saltum.' This canon, if we look only to the present 

 inhabitants of the world, is not strictly correct; but if we in- 

 clude all those of past times, whether known or not yet known, 

 it must by my theory be strictly true." 



Here, then, we have, stated in the clearest language, explicit 

 evidence that the great principle acquired by the naturalist, and 

 now governing the entire extent of his observations, is continuity, 

 a derivative form of the idea of motion. 



I turn to the science of algebra. It, too, has gone through a 

 " new " phase, and now exists under conditions which are most 

 remarkable, though these conditions have been developed in the 

 most gradual and orderly manner from the* time of Newton, as 

 by him from his predecessors. It, too, is morphological; through 

 it every branch of modern mathematics has again become young. 

 The interoperation of algebraic forms corresponds to those con- 

 flicting conditions of nature by which species are produced and 

 maintained. But what sun was it that gave such light to the 

 mathematician ? The same that shone on that other continent 

 of the naturalist. " Time was when all the parts of the subject 

 were dissevered*, when algebra, geometry, and arithmetic either 

 lived apart or kept up cold relations of acquaintance confined to 

 occasional calls upon one another; but that is now at an end; 

 they are drawn together and are constantly becoming more and 

 more intimately related and connected by a thousand fresh ties; 

 and we may confidently look forward to a time when they shall 

 form but one body with one soul. Geometry formerly was the 

 chief borrower from arithmetic and algebra; but it has since 

 repaid its obligations with abundant usury ; and if I were asked 

 to name, in one word, the pole-star round which the mathema- 

 tical firmament revolves, the central idea which pervades as a 

 hidden spirit the whole corpus of mathematical doctrine, I should 

 point to Continuity as contained in our notions of space, and 

 say, it is this, it is this I" 



* Sylvester, British Association's Report (1869), Transactions of Sec- 

 tions, p. 7. 



2E2 



