fundamental notions of space, time, and matter, Kirchhoff tries to make his way to the description of the facts of experience and goes beyond his predecessors by delineating by means of pure geometry the supposed logically fundamental notions of force and mass. Force is to him the acceleration (change of velocity) experienced by a material particle in a unit of time; the knowledge of all these accelerating forces in a given moment of time would suffice to describe the world; experience has shown however that the description gains in simplicity, if we multiply the acceleration by a certain positive constant, called mass of the moving particle. I have mentioned this abstract train of thought be cause it is very characteristic of Kirchhoff. The necessity of looking at natural forces as something really existing, or the mass as something really constant, remaining equal to itself, he does not recognize. It is only a fact of experience that the movements in nature hitherto observed have taken place in such a way that they seem to be represented in the simplest manner by making those suppositions. We can build up mechanical systems on quite different bases, but it would not help us to describe simply the real movements. The problem of mathematical physics will be solved when the observed phenomena will be described by means of the simplest possible supposition as to the nature of forces and distribution of matter. There is nothing impossible in it; it can be proved in fact that all that men can observe in finite time must be sus. ceptible of being described mathematically. Even an outsider will not fail to notice, I think, that something is not included in Kirchhoff's programme. The simplest description can not produce the conviction that the phenomena, even in future time, shall run in accordance with the description; its equations are, so to say, not laws. There exists a stand-point differing somewhat from that of Kirchhoff; it looks for what is in accordance with a law in the change of phenomena. Experience teaches us that nature acts according to laws; because without laws experience would be impossible. Experience is the collecting of what is similar in different particular perceptions. That the laws exist is accordingly an observed fact and not a hypothesis. We feel them acting at every moment independently of our will. We must ascribe to them the same reality as to our will; these two things are opposite to one another, power against power. We designate them accordingly by the names of forces, and forces as causes of motion; they have the same reality as the motion itself. Up to this point nature may be said to be intelligible. What a force is we know not; we can only say that it manifests itself in the acceleration it imparts to the mass, and de facto accordingly, we do not go beyond Kirchhoff's description of nature. As to results, the search after a law and the endeavor after the simplest description of nature is one and the same thing; the difference lies only in the formulation of the problem and sometimes possibly in the way towards its solution. It follows for instance from Kirchhoff's definition, that it must be permitted (not only upon pedagogical but even upon philosophical grounds) to use hypothe ses, even when they are recognized not to be sufficient in all cases, provided they are still the simplest. In fine, only that will appear to us simple which is logically true. From what precedes one sees how near sometimes mathematical physics approaches to metaphysics. Kirchhoff gave to empiricism in the theory of cognition, its most precise and most consequent expression, and placed himself accordingly at the acme of the whole of modern mathematical physics. Kirchhoff's endeavor after clearness and truth appears also in his philosophical stand-point, and makes him prefer to give the definition of his own problem in the study of nature from a narrow view, rather than to suffer in it even a semblance of a proposition accepted on faith, as nature's conformity to law possibly is. And still he analyzed nature not merely as a critical thinker. His greatest discovery shows that he possessed also the alert introspection, the sympathetic investigation, and the intuitive insight into the working of natural forces, without which no true student of nature can make investigations. We repeat, Kirchhoff was one of the greatest students of nature, because he was a mathematical physicist in the sense explained above. ON HEREDITY.* By Sir WILLIAM TURNER. The subject of heredity (if I may say so) is in the air at the present time. The prominence which it has assumed of late years is in connection with its bearing on the Darwinian theory of natural selection, and consequently biologists generally have had their attention directed to it. But in its relations to man, his structure, functions, and diseases, it has long occupied a prominent position in the minds of anatomists, physiologists, and physicians. That certain diseases, for example, are hereditary was recognized by Hippocrates, who stated generally that hereditary diseases are difficult to remove, and the influence which the hereditary transmission of disease exercises upon the duration of life is the subject of a chapter in numerous works on practical medicine, and forms an important element in the valuation of lives for life insur ance. The first aspect of the question which has to be determined is whether any physical basis can be found for heredity. The careful study, espe cially during the last few years, of the development of a number of species of animals, mostly but not exclusively amongst the invertebrata, by various observers, has established the important fact that the young animal arises by the fusion within the egg or germ cell of an extremely minute particle derived from the male parent, with an almost equally minute particle, derived from the germ cell produced by the female parent. These particles are technically termed in the former case the male pronucleus, in the latter the female pronucleus, and the body formed by their fusion is called the segmentation nucleus. These nuclei are so small that it seems almost a contradiction in terms to speak of their maguitude, rather one might say their minitude; for it requires the higher powers of the best microscopes to see them and follow out the process of conjugation. But notwithstanding their extreme minuteness, the pronuclei and the segmentation nucleus are complex, both in chemical and molecular structure. From the segmentation nucleus produced by the fusion of the pronuclei with each other, and from corre *Presidential address before the Anthropological Section of the British Association, A. S., at Newcastle, September, 1889. (Report of the British Association, vol. LIX, pp. 756-771.) sponding changes which occur in the protoplasm of the egg which surrounds it, other cells arise by a process of division, and these in their turn also multiply by division. These cells arrange themselves in course of time into layers, which are termed the germinal or embryonic layers. From these layers arise all the tissues and organs of the body, both in its embryonic and adult stages of life. The starting-point of each individual organism-i. e., of each new generation is therefore the segmentation nucleus. Every cell in the adult body is derived by descent from that nucleus through repeated division. As the segmentation nucleus is formed by the fusion of material derived from both parents, a physical continuity is established between parents and offspring. But this physical continuity carries with it certain properties which cause the offspring to reproduce, not only the bodily configuration of the parent, but other characters. In the case of man we find along with the family likeness in form and features, a correspondence in temperament and disposition, in the habits and mode of life, and sometimes in the tendency to particular diseases. This transmission of characters from parent to offspring is summarized in the well-known expression that "like begets like," and it rests upon a physical basis. The size of the particles which are derived from the parents (called the male and female pronuclei), the potentiality of which is so utterly out of proportion to their bulk, is almost inconceivably small when compared with the magnitude of the adult body. And yet these particles are sufficient to stamp the characters of the parents, of the grandparents, and of still more remote ancestors on the offspring, and to preserve them throughout life, notwithstanding the constant changes to which the cells forming the tissues and organs of the body are subjected in connection with their use and nutrition. In considering the question of how new individuals are produced, one must keep in mind that it is not every cell in the body which can act as a center of reproduction for a new generation, but that certain cells, which we name germ-cells and sperm-cells, are set aside for that purpose. These cells, destined for the production of the next generation, form but a small proportion of the body of the animal in which they are situated. They are as a rule marked off from the rest of the cells or of its body at an early period of development. The exact stage at which they become specially differentiated for reproductive purposes varies however in different organisms. In some organisms (as is said by Balbiani to be the case in Chironomus) they apparently become isolated before the formation of the germinal layers is completed; but as a rule their appearance is later; and in the higher organisms, not until the development of the body is relatively much more advanced. The germ-cells after their isolation take no part in the growth of the organism in which they arise; and their chief association with the other cells of its body is that certain of the latter are of service in their nutrition. The problem therefore for consideration is the mode in which these germ or reproductive cells become influenced, so that after having been isolated from the cells which make up the bulk of the body of the parent they can transmit to the offspring the characters of the parent organism. Various speculations and theories have been advanced by the way of explanation. The well-known theory of Pangenesis, which Charles Darwin with characteristic moderation put forward as merely a provisional hypothesis, assumes that gemmules are thrown off from each different cell or unit throughout the body which retain the characters of the cells from which they spring; that the gemmules aggregate themselves either to form or to become included within the reproductive cells; and that in this manner they and the characters which they convey are capable of being transmitted in a dormant state to successive generations, and to reproduce in them the likeness of their parents, grandparents, and still older ancestors. In 1872, and four years afterwards, in 1876, Mr. Francis Galton pub lished most suggestive papers on kinship and heredity.* In the latter of these papers he developed the idea that "the sum total of the germs, gemmules, or whatever they may be called," which are to be found in the newly fertilized ovum, constitute a stirp, or root. That the germs which make up the stirp consist of two groups; the one which develops into the bodily structure of the individual, and which constitutes therefore the personal structure; the other, which remains latent in the individual, and forms, as it were, an undeveloped residuum That it is from these latent or residual germs that the sexual elements intended for producing the next generation are derived, and that these germs exercise a predominance in matters of heredity. Further, that the cells which make up the personal structure of the body of the individual, exercise only in a very faint degree any influence on the reproductive cells, so that any modifications acquired by the individuals are barely, if at all, inherited by the offspring. Subsequent to the publication of Mr. Galton's essays, valuable contributions to the subject of heredity have been made by Professors Brooks, Naegeli, Nussbaum, Weismanu, and others. Professor Weismann's theory of heredity embodies the same fundamental idea as that propounded by Mr. Galton; but as he has employed in its elucidation a phraseology which is more in harmony with that generally used by biologists, it has had more immediate attention given to it. As Weismann's essays have during the present year been translated for, and published by the Clarendon Press, under the editorial superintendence of Messrs. Poulton, Schönland, and Shipley, they are now readily ac cessible to all English readers. Weismanu asks the fundamental question, "How is it that a single cell of the body can contain within itself all the hereditary tendencies of the whole organism?" He at once discards the theory of pangenesis, * Proceedings Roy. Soc. Lond., 1872, and Journ. Anthrop. Inst., 1876, vol v. |