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THE POPULAR SCIENCE MONTHLY. 



bear in mind that of the vertebrate land 

 animals of the Eocene no one has survived 

 to the present time, while of the Pliocene 

 but one the hippopotamus remains un- 

 modified, the chances that man, as at pres- 

 ent conditioned, should also be a survivor 

 from that period seem remote, and against 

 the species Homo sapiens having existed in 

 Miocene times almost incalculable. The 

 a priori improbability of finding man un- 

 changed, while all the other vertebrate ani- 

 mals around him have, from natural causes, 

 undergone more or less extensive modifica- 

 tion, will induce all careful investigators to 

 look closely at any evidence that would carry 

 him back beyond Quaternary times ; and 

 though it would be unsafe to deny the possi- 

 bility of such an early origin for the human 

 race, it would be unwise to regard it as estab- 

 lished except on the clearest evidence. 



Enibryological Recapitulation. Prof. 



A. Milnes Marshall, in his presidential ad- 

 dress before the Biological Section of the 

 British Association, after remarking on the 

 general subject of the study of embryology, 

 spoke more particularly of its relation to 

 the doctrine of recapitulation, which, sug- 

 gested by Agassiz, had been elaborated by 

 eminent contemporary zoologists. Natural 

 selection, he showed, explains the preserva- 

 tion of useful variations, but does not ac- 

 count for the formation and preservation of 

 useless organs ; but recapitulation solves the 

 problem at once, by showing that those or- 

 gans, though now useless, must have been 

 of functional value to the ancestors of their 

 present possessors, and that their appearance 

 in the ontogeny of existing forms is due to 

 the repetition of ancestral characters. Such 

 rudimentary organs are, as Darwin has point- 

 ed out, of larger relative or even absolute size 

 in the embryo than in the adult, because the 

 embryo represents the stage in the pedigree 

 in which they were functionally active. Ru- 

 dimentary organs are extremely common, es- 

 pecially among the higher groups of ani- 

 mals, and their presence and significance arc 

 now well understood. Man himself affords 

 numerous and excellent examples, not mere- 

 ly in his bodily structure, but by his speech, 

 dress, and customs. For the silent letter b 

 in the word doubt, or the w of answer, or the 

 buttons on his clastic-side boots are as true 



examples of rudiments unintelligible but for 

 their past history, as are the ear muscles he 

 possesses but can not use, or the gill-clefts 

 which are functional in fishes and tadpoles, 

 and are present, though useless, in the em- 

 bryos of all higher vertebrates. It was the 

 elder Agassiz who first directed attention to 

 the remarkable agreement between the em- 

 bryonic growth of animals and their palaeon- 

 tological history. 



The Scope of Mathematics. Mr. J. W. L. 



Glaisher, President of the Mathematical Sec- 

 tion in the British Association, in his address 

 spoke of the range of subjects comprehended 

 within the scope of mathematics. Its field 

 extends from the most exact of all knowl- 

 edge to brauches of inquiry in which only un- 

 correlated facts have been collected. Con- 

 sidering pure mathematics, or that of the 

 abstract sciences which could be conquered 

 and explored only by mathematical methods, 

 it is difficult not to feel somewhat appalled 

 by the enormous developments it has re- 

 ceived in the last fifty years. The mass of 

 the investigations, as measured by the an- 

 nual additions to the literature of the sub- 

 ject, is so great that it is fast becoming be- 

 wildering from its mere magnitude and the 

 extraordinary extent to which many special 

 lines of study have been carried. There can 

 be no end to this. So wide and various are 

 the subjects of research, so interesting and 

 fascinating are the results, so wouderful are 

 the fields of investigation laid open at each 

 succeeding advance, that we may be sure 

 that, while the love of learning and knowl- 

 edge continue to exist, there can be no relax- 

 ation of our efforts to penetrate still further 

 into the mysterious worlds of abstract truth 

 that lie spread temptingly before the inves- 

 tigator. The speaker did not believe that 

 the bearing of the modern developments 

 of mathematics on the physical sciences is 

 likely to be very direct or immediate, but it 

 would be rash to assert that there is any 

 branch of mathematics so abstract or so re- 

 condite that it may not at any moment find 

 an application in some concrete subject. 

 Still, it appears that if the extension of the 

 pure sciences can only be justified by the 

 value of their applications, it is very doubt- 

 ful whether a satisfactory plea for any further 

 developments can be sustained. Although 



