130 REPORT— 1870. 



what combination of the physical influences now existing is most potential in 

 bringing about the supposed transition from the not living to living modes of com- 

 bination ; and therefore it is impossible to say how far the apparent very great 

 difi'erence in condition in certain of these experiments ought to have left its im- 

 pression upon the living things met with. If we could only be as sure of starting 

 with materials of precisely the same molecular composition, which, however, was 

 impossible, the author was inclined to believe that we might be able to procure 

 definite kinds of organisms, almost as surely as we could now produce different 

 kinds of crystals. He afterwards fully discussed the various possibilities of error 

 in his own experiments, and gave reasons why he thought that none of these 

 sources of fallacy had existed in four of his ovra. experiments which were made in 

 concert with Dr. Frankland. 



On the TJieory of Natural Selection looked at from a Matliematical Point of 

 View. By Alfred W. Bennett, M.A., B.Se., F.L.S. 



The author gave in his adhesion to that portion of the Darwinian theory which 

 maintains the evolution of species from a common ancestry, but held that that 

 part of the hypothesis which regards natural selection as the prime agent in bring- 

 ing about these changes rests on a much more debateable basis. The title of Mr. 

 Darwin's great work, ' The Origin of Species by means of Natural Selection,' is 

 itself a misnomer, since it only attempts to account for the survival and pei-pe- 

 tuation of certain among a number of " spontaneous " variations. Taking the re- 

 markable facts of mimetism, so largely insisted on by Darwinian writers as a 

 bulwark of their theory, the author luaintained that this explanation really breaks 

 down at the outset. Two points admitted by all advocates of the principle of na- 

 tural selection are, that it always acts with extreme sloAvness, and that every step 

 must be directly of advantage to the species which simulates the outward form of 

 some other species, or of some inanimate object. Proceeding on this basis, and apply- 

 ing mathematical calculation to the solution of the problem, it was attempted to be 

 shown that the earlier steps in the transformation cannot have occurred through 

 the operation of natural selection, because they must be entirely useless to the 

 individual, and that the chances against the accumulation of a sufficient approxi- 

 mation towards the species ultimately mimicked, on which the principle of na- 

 tural selection could operate, is something like ten millions to one, even when 

 every advantage is thrown into the scale of the natural selectionist. The author 

 then proceeds to show that even Mr. Darwin does not claim for the principle of 

 natural selection the origination of the tendency to variation which is the 

 foundation of all differentiation of species on the hypothesis of evolution. Since, 

 therefore, some other principle, at present xuiknown to us, originates these varia- 

 tions, what right have we to say that this principle then ceases to act, instead of 

 being the main agent in all the other subsequent changes ? Of the laws of va- 

 riation, Mr. Dai-wiu says, our ignorance is profoimd. The paper then points out 

 the remarkable analogy that exists between the exhibition of the phenomena of 

 mimetism and the development of instinct. Both faculties are absent in the 

 whole of the vegetable kingdom, very feebly apparent in the Protozoa and Coelen- 

 terata, but slightly in the MoUusca, appear with extraordinary perfection in the 

 Insecta and Arachnida, are comparatively in abeyance among the Pisces and Rep- 

 tilia, and again strongly developed in the Aves. This parallelism would appear 

 to indicate a closer connexion between mimicry and instinct than has been 

 generally supposed. One of the founders of the theory of natural selection, Mr. 

 A. R. Wallace, displays, in his recently published volume of ' Contributions to the 

 Theory of Natural Selection,' a strange want of faith in his own principle, by 

 denying its potency in the case of the evolution of man from the lower animals, 

 and even in producing the different races of mankind. The same luws, the writer 

 thinks, must be supposed to govern the whole organic world ; and if some other 

 principle, connected with man's reasoning powers, must bo looked for to account 

 for his raising himself from the brutes, the same principle, connected with the 

 instinct of animals, must be applied to accoimt for their power of developing new 



