290 



NATURE 



January 26, 1893 



We are glad to see the prominence given to the geo- 

 metrical methods of Klein and Poincare ; that of the 

 former is based on the theory of substitutions, reminding 

 the reader much of the " Icosaeder" ; that of the latter 

 s the " Method of Nets," a most ingenious geometrical 

 application throwing light on the theory of " Reduced 

 Forms." 



The "Composition of Forms" given in Chapter VI. 

 is logically and judiciously developed, by means of the 

 bilinear substitution, U3 to the point of showing 

 the method of tabulating the primitive classes 

 of regular and irregular determinants. The chapter 

 on cyclotomy is one of the best written in the 

 book. The discussion of the section of the periods of 

 the roots of unity has engaged the attentions of 

 mathematicians of the first rank since the time of Gauss, 

 so that of necessity much has been written, and while 

 the author states that he has given but an outline of an 

 extensive theory which has not yet been completed, it 

 may be said that the theory as given, with the references 

 to authorities at the end of the chapter, will be quite 

 sufficient to conduct the student bent upon research to 

 the frontiers of the unknown country. 



The determination of the number of properly primitive 

 classes for a given determinant, applications of the 

 theory of quadratic forms, and the distribution of primes 

 complete the volume. Mr. Mathews may be congratu- 

 lated on his resolve to include Sylvester's masterly con- 

 traction of Tchdbicheff's limits with reference to the 

 distribution of primes ; the reader is taken from the 

 "sieve" of Eratosthenes to the work of Legendre, 

 Meissel, Rogel, Riemann, and to the latest researches of 

 Sylvester and Poincare, of which the ink is scarcely dry. 

 English mathematicians will turn with delight to the 

 account given on page 302 of Riemann's great memoir 

 of 1859, which contains the only satisfactory attempt to 

 obtain an analytical formula for the number of primes not 

 exceeding a given numerical quantity. 



In conclusion, though the sequence of the subject 

 matter may be open to criticism, we regard the book as 

 a most valuable contribution to the small library of higher 

 mathematical treatises that, owing chiefly to the energy 

 and enthusiasm of the rising generation of mathematicians, 

 is being brought together. How woefully deficient that 

 library was but a few years since those engaged in 

 research know only too well, and greatly do they rejoice as 

 they see the yawning gaps one by one efficiently filled up. 

 Part II. of the task Mr. Mathews has set himself to 

 accomplish will, we hope, soon appear, and we trust 

 he will be as successful with it as with the present 

 Part I. P. A. M. 



THE DARWINIAN THEORY. 

 Darwin and After Darwin ; an Examination of the 

 Darwinian Theory and a Discussion of Post-Dar- 

 winian Questions. By George John Romanes, M.A., 

 LL.D.,F.R.S. I. The Darwinian Theory. (London: 

 Longmans, 1892.) 



WE had hoped ere now to have received the second 

 instalment of this work, and to have dealt with 

 the two volumes in a single critical notice. Unforeseen 

 causes, one of them deeply to be regretted, have pre- 

 NO. 1213, VOL. 47] 



sumably prevented the appearance of the discussion of 

 Post-Darwinian questions so early as had been anticipated. 

 We therefore propose to give a short expository notice of 

 the present volume, reserving such criticism as we have 

 to offer for a future occasion, when the second volume 

 shall have come to hand. 



Thefirst section consists of an exposition of the scientific 

 evidences of evolution as a fact independent of the Dar- 

 winian theory of the method by which this evolution has 

 been brought about. It may be regarded as an expansion 

 of the author's little volume in the " Nature Series," on 

 " The Scientific Evidences of Organic Evolution," pub- 

 lished ten years ago. Mr. Romanes has spared no pains 

 in the collection and marshalling of his evidence. His 

 object is to convince, by the abundance of facts and by 

 logical inferences based thereon, those who still hold by 

 the tenets of Special Creation. Whether those who still 

 hold by these tenets are likely to be influenced by the 

 facts or the inferences is a question we do not propose to 

 discuss. The author evidently supposes that they are, 

 and has written for them a good many pages in a strain 

 of which we give a couple of examples :— " It would seem 

 most capricious on the part of the Deity to have made 

 the eyes of an innumerable number of fish on exactly the 

 same ideal type, and then to have made the eye of the 

 octopus so exactly like these other eyes, in superficial 

 appearance, as to deceive so accomplished a naturalist as 

 Mr, Mivart, and yet to have taken scrupulous care that 

 in no one ideal particular should the one type resemble 

 the other." Again, " Although in nearly all the numerous 

 species of snakes there are no vestiges of limbs, in the 

 Python we find very tiny rudiments of hind-limbs. Now, 

 is it a worthy conception of Deity that, while neglecting 

 to maintain his unity of ideal in the case of nearly all the 

 numerous species of snakes, he should have added a tiny 

 rudiment in the case of the Python— and even in that 

 case should have maintained his ideal very inefficiently, 

 inasmuch as only two limbs, instead of four, are 

 represented ? " 



The second section of the volume is devoted to the 

 setting forth of the theory of natural selection as it was 

 held by the master. This, as was to be expected, is a 

 well-ordered and lucid exposition. We could wish that 

 Mr. Romanes had been more careful taavoid all appear- 

 ance of personifying natural selection. He says, for 

 example, "it is the business of natural selection to secure 

 the highest available degree of adaptation for the time 

 being.'' Such language is highly metaphorical, if not 

 misleading. If we can talk of business at all we may 

 say that it is the business of various eliminating agen- 

 cies, in the struggle for existence, to weed out and exclude 

 from any share in perpetuating their race all those indi- 

 viduals who are too weakly to stand the stress of the 

 struggle. The survival of the fit is an incidental result 

 of the stern business of elimination. It is here that the 

 naturalistic hypothesis differs most markedly from the 

 teleological interpretation of nature. In conversation 

 a while since a friend observed to us : Since your 

 school of thought admit that the eye of natural selection 

 is ever on the watch for the slightest improvement in 

 adaptation, why should they hesitate to say with us that 

 it is the eye of Beneficence that is thus ever watchful > 

 The misunderstanding of the naturalistic position here 



