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284 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 unmodified, the chances that man, as at present 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 unchanged, while all the other vertebrate animals around him have, from natural causes, undergone more or less extensive modification, 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 possibility of such an early origin for the human race, it would be unwise to regard it as established except on the clearest evidence.

Embryological Recapitulation.—Prof. A. Milnes Marshall, in his presidential address 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, suggested by Agassiz, had been elaborated by eminent contemporary zoölogists. Natural selection, he showed, explains the preservation of useful variations, but does not account for the formation and preservation of useless organs; but recapitulation solves the problem at once, by showing that those organs, 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 pointed 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. Rudimentary organs are extremely common, especially among the higher groups of animals, and their presence and significance arc now well understood. Man himself affords numerous and excellent examples, not merely 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 elastic-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 embryos of all higher vertebrates. It was the elder Agassiz who first directed attention to the remarkable agreement between the embryonic growth of animals and their palaeontological history.

The Scope of Mathematics.—Mr. J. W. L. Glaisher, President of the Mathematical Section 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 knowledge to branches of inquiry in which only uncorrelated facts have been collected. Considering 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 received in the last fifty years. The mass of the investigations, as measured by the annual additions to the literature of the subject, is so great that it is fast becoming bewildering 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 wonderful are the fields of investigation laid open at each succeeding advance, that we may be sure that, while the love of learning and knowledge continue to exist, there can be no relaxation of our efforts to penetrate still further into the mysterious worlds of abstract truth that lie spread temptingly before the investigator. 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 recondite 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 doubtful whether a satisfactory plea for any further developments can be sustained. Although