122 



NA rURE 



[Di:cKMHEK 8, 1898 



To tlie present writer it has always appeared thnt the 

 suggestion is an extremely interesting anil ingenious one, 

 the chief objection being the immense difficulty in 

 proving that it actually exists or has ever existed as an 

 operative principle. If it exists, then much that is 

 claimed for it would follow. We know that geographical 

 isolation is followed by differentiation, and many evo- 

 lutionists are prepared to admit that some of the minor 

 differences thus prodiued may be independent of natural 

 selection. Most naturalists would probably be inclined 

 thus to explain the differences between the land-shells 

 of adjacent valleys in the Sandwich Islands as described 

 by Gulick. Those who believe in physiological selection 

 consider that what is here brought about through the 

 prevention of interbreeding by geographical barriers, is 

 produced on continuously peopled areas by the physio- 

 logical barrier of infertility. 



This conclusion is capable of being tested to a certain 

 extent by an investigation of the degree of infertility 

 between species which are known to have been produced 

 in the former manner and those (of approximately equal 

 differentiation) which are believed to have been produced 

 in the latter. Apart from its application to the present 

 controversy such an inquiry would be of great interest 

 in itself. 



The results of such an investigation would be far 

 more convincing than the elaborate and ot'tcn very 

 ingenious arguments of the writer, many of which are 

 capable of an immediate and satisfactory answer. For 

 instance on pp. 48, 49, he asks how it is that the repro. 

 ductive system is always affected "'in the same peculiar 

 way," viz. so as to produce mutual sterility, between dif- 

 ferent species of all kinds, animal and vegetable, separated 

 by morphological differences of infinite variety. It is 

 evident that he regards this question as unanswerable 

 except on the view that the infertility is the invariable 

 precursor and condition of the differentiation. But the 

 facts can readily be explained otherwise. Mutual fertility 

 depends upon the exact relotionship of two extraordinarily 

 complex bodies, the germ-cells of male and female : it 

 depends upon a reciprocal adjustment of almost infinite 

 precision. Single individual variations receding from the 

 necessary precision continually arise, but are infallibly 

 exterminated. Such variations are not to be looked upon 

 as due to a single and uniform change in the complex 

 material of the germ-substance. The opposite point of 

 view is the truer : mutual fertility is due to a single and 

 uniform constitution rigidly kept within the narrowest 

 limits, while a minute change of constitution in any 

 direction means infertility. Mutual infertility is, in fact, 

 but the single external indication of numberless changes 

 of constitution. The necessary precision of adjustment 

 of the male to the female germ-substance is only kept 

 up in the sjDecies by unremitting selection, and there is 

 no cause for surprise that it should cease when selection 

 is no longer forthcoming for its support. These consider- 

 ations seem at first sight to indicate that mutual fertility 

 between doinestic breeds is a matter for greater wonder 

 than the infertility between natural species. We cease 

 to wonder, however, when wc reflect upon the length of 

 time which must have elapsed since the separation of 

 natural species such as the horse and ass, which are 

 nevertheless fertile when crossed, although their hybrid 

 NO. 1519, VOL. 59] 



progeny is sterile. Since this is the case the ntutual 

 fertility of our modern domestic races, so far as it has 

 been proved to exist, is only what wc should have been 

 led to expect. In this relationship the present writer has 

 often considered that further experiments upon these 

 latter would be of great value, esi>ecially in the case of 

 races in which the morphological differences have been 

 carried to a very high degree— so much so, indeed, that 

 artificial fertilisation would probably be necessary. 



The argument which has been met in the last para- 

 graph is evidently one on which the greatest stress is 

 laid. Thus we again read on p. 51 of " this one peculiarity 

 of the reproductive system,'' viz. mutual infertility ; and 

 on pp. 52, 53, it is n\ade a chief support for the hypothesis 

 of physiological selection, a good brief account of which 

 will here be found. Throughout the whole work we 

 meet with the same insistence on " this constant primary 

 distinction," " the same peculiar change," iS:c., as one 

 main foundation for the hypothesis. 



If space had permitted, many other interesting points 

 raised in this \ohune n\ight have been discussed. It is 

 of great service to the student of evolution that the 

 hypothesis of physiological selecti on, the arguments for 

 it and evidence which supports it, should have been 

 brought forward in so readable a form. The work is 

 printed m pleasant type, and has been so carefully seen 

 through the press, that there are practically no printer's 

 mistakes. E. B. P. 



THE THEORY OF GROUPS. 

 Theory of Groups of Finite Order. By W. Burnside, 

 M..\., F.R.S. Pp. xvi -f 388. (Cambridge University 

 Press, 1S97.) 



THE theory of groups of finite order is one to which 

 in very recent times the attention of mathemati- 

 cians has again and again been directed. Until a little 

 time ago any one who wished to be<ome acquainted with 

 the elements of the theory would have been referred to 

 J. Serret's ".-Mgebra," to C. Jordan's comprehensive 

 "Traile des substitutions," and to E. Netto's intro- 

 ductory work on the same subject. No one who takes 

 account of the time at which it was written will wish to 

 depreciate the merits of the first of these, but the 

 chapters dealing with groups consist of a series of ex- 

 tracts reproduced from the original memoirs of the 

 masters to whom we owe this branch of mathematics : 

 these e.xtracts are chosen with all the knowledge of an 

 expert as to what should be chosen, but are not worked 

 up. C. Jordan brings together an overpowering wealth 

 of material, which for the most part has its origin in his 

 own researches ; but there can scarcely ever have been 

 any one who would be in a position to work through the 

 treatise from beginning to end ; or who could without 

 guidance from some other source separate the funda- 

 mental portions from the mass of detail. Lastly, 

 Netto's book on substitutions is now fifteen^ years old; 

 it still forms a useful introduction to the subject, but it 

 goes no further than that. 



The most modern treatises on algebra mete out vary- 

 ing treatment to the theory of groups. Nctto leaves it 

 on one side altogether ; Drach makes the interesting ex- 

 periment of attempting to build up the elements of 



