During the nineteenth century various experimenters demonstrated the possibility of preventing the appearance of animalcules in infusions by a process of sterilization which prevented the entry into the infusions of living germs from the external air. But even as late as 1858 Ponchet asserted before the Paris Academy of Sciences that he had proved that microscopic organisms arise apart from pre-existing germs. However the investigations of Louis Pasteur who showed that all putrefaction and many kinds of fermentation are due to microscopic living organisms and the work of Tyndall who showed that absolute sterilization of infusions could be attained by intermittent applications of heat led to the general acceptance of the law of biogenesis. As at present accepted the law of biogenesis is of a negative character asserting that there is no known evidence that living organisms at present arise from non-living matter. As regards the further question whether we should conceive that under conditions widely differing from those which obtain at present there has been continuity between living and non-living matter the answer must be entirely a matter of speculation because from the nature of the case the only mode of obtaining a decisive answer that of observation and experiment is not available. It is somewhat remarkable that Huxley in stating before the British Association his conviction that the law of biogenesis had been fully established expressed as his opinion that he would have witnessed the origin of protoplasm from non-living matter if he could have been present at the beginning of organic evolution.

There have been various speculations made as to the origin of life on the earth; among these is the suggestion of Lord Kelvin that living organisms reached the earth in meteorites. The persistence of the conception of the continuity of living with inorganic matter is exhibited in the views of prominent men of Science such as Haeckel Ray Lankester the Botanist von Nägeli and the Physiologist Pflüger all of whom accept the idea that this continuity has at some former time been effective in relation to the origin of living matter.

The term “heredity” implies the fact that living organisms can produce their like the resemblance though never absolutely perfect extending to the most minute details of construction and function. The modern theories of heredity have been constructed upon the basis of an enormous amount of work in the collection and sifting of facts. Their aim in accordance with the view developed in these lectures is to represent in one or more conceptual schemes abstract in some greater or less degree the main facts of the general likeness of parent and offspring of the occurrence of variations in the offspring that is of characters not exhibited in the same degree by the parent; of specific similarities in the offspring with characters in one or both parents; of the fact that characteristics may occur in the offspring which are not to be found in either parent but which were exhibited by a grandparent or by a remoter progenitor; and lastly of the fact that characters acquired by a parent in the course of his or her life as the apparent result of interaction with the environment seem in some cases to reappear in the offspring. The last of these facts has given rise to much controversy; and its proper interpretation is one of the most crucial questions which have arisen in connection with theories of heredity and in the more general theories of evolution.

I have pointed out in my earlier lectures the fact that a conceptual theory frequently employs not only concepts to which there are directly corresponding percepts but also concepts which have not or at any given time are not known to have any percepts to which they directly correspond. The modern theories of heredity make use of concepts which belong to both these classes. Not only concepts of the first class but also those of the second class have almost invariably been regarded by those who have originated or developed the theories as denoting really existing entities in the sense attributed to the term by physical realists. But as in the case of the theories of Physics and Chemistry the value of these theories may be estimated quite independently of the acceptance of the views of physical realists; they may be judged exclusively in relation to their coherence conceptual schemes and to their effectiveness in representing the perceptual facts and sequences to which they are applied.

Most of these theories have as their starting point the group of perceptual facts resumed in the cell theory of the construction of the living organism applicable to both animals and plants. There are in the case of most multi-cellular organisms amongst the cells of which they are constituted special kinds of cells known as germ-cells distinct in various respects from the somatic or body-cells which constitute the greater part of the organisms. Prolonged investigation has shown that the embryo of a new individual organism appears to begin in the case of the majority of animals and plants in the union of two minute cells the sperm-cell and the ovum or egg-cell which combine to form a single cell the fertilized ovum. The embryo is then observed to arise by a process of successive formation of new cells obtained by division of the fertilized ovum into two cells followed by a series of successive divisions of cells into two parts each of which is a complete cell. Although this sexual mode of reproduction holds for the great majority of living organisms it is not the only process by which reproduction occurs. In some organisms particularly amongst those which are uni-cellular there is no fertilization of the ovum which divides without previous fertilization into two cells; so that the reproduction is asexual; and in some cases there are no special germ-cells. It will be sufficient for our purpose to leave aside such special modes of reproduction which occur in various lower organisms and to confine our attention to the sexual mode of reproduction which holds good for the higher animals and for many plants.

Since the seventeenth century the ovum and the sperm have been regarded or at least one of them has been regarded as in some sense the physical basis of the new organism. A type of theory called preformationist was held from the seventeenth century until the beginning of the nineteenth. In accordance with preformationism the ovum or the sperm contained a complete preformed miniature organism which only required to be unfolded or evolved and increased in size in order to become the new animal. Moreover either the ovum or the sperm according to the views of two contending parties not only contained the miniature copy of the animal of the next generation but this contained a still more minute copy which would ultimately develop into an individual of the second generation; and this contained a still more minute copy and so on for all future generations. This theory of emboîtement sometimes known as the pill-box theory contained as its essence the principle that nothing new arises that nothing is generated but that everything pre-existed in an invisible form; as it was expressed by Albrecht von Haller “Es gibt kein Werden”; there is no such thing as becoming there is only an unfolding or evolution. The opposite theory of Epigenesis that the evolution of the animal consists of a gradual increase of complexity from what at first appears to be comparatively simple and that thus something essentially new arises was shown by Wolff to be a fact of perception in the case of the embryonic development of the chick and ultimately got the upper hand over preformationism. However arbitrary the preformationists theories may appear to be we must I think recognize when it is remembered that the successive miniature organisms were never supposed to be discernible to the senses that they have some of the essential elements of a genuine scientific theory considered as a purely conceptual representation of what can be observed to happen. The crudity of preformationism as a conceptual scheme exhibits itself in the very restricted range of the perceptual facts to the representation of which it lends itself. It fails for example to distinguish the specific characters which may be inherited from either parent and gives no suggestion as to how the origin of congenital variations is to be represented. That it did not account for the preformation is not a decisive objection to the theory for every scientific theory necessarily suffers at some point or other from a similar defect. Moreover some of the modern theories especially that of Weismann are closely akin to preformationism.

The next type of theory designed to represent facts of inheritance is the pangenetic theory. The general notion of pangenesis was adumbrated by Democritus and Hippocrates and in later ages by Maupertuis and Buffon. The general idea of pangenesis is that the germinal cells contain samples contributed by all parts of the body and that these samples give rise in the embryo to parts similar to those from which the samples came. The modern forms of the pangenetic theory are exhibited in the theory of Physiological units propounded by Herbert Spencer in 1863 and in the well-known theory of Pangenesis suggested as a provisional hypothesis by Charles Darwin in 1868. The essential principle of Darwin's theory is that every cell of the body not too highly differentiated throws off at each stage of its development characteristic gemmules or small particles which can later multiply by fissure and give rise to cells like those from which they originated. These gemmules are continually given off and conveyed in the blood; they become specially concentrated in the germ-cells of both sexes or in buds. In the development of the embryo these gemmules unite with others like themselves and being aggregated in the germ-cells they invest these latter with the power of developing into a new complete organism; but some may remain latent during the development of embryos through several generations before they become active. Each gemmule reproduces the cell from which it was derived and they become active in the same order as that in which the corresponding cells follow each other in the ontogeny of the part to which they belong.

If Darwin's theory be regarded as a purely conceptual theory in which the gemmules are not regarded as representing perceptual objects it possesses the essentials of a genuine scientific theory. The suggestion that the gemmules might be replaced by a theory of transmission of force as in the theory of Herbert Spencer would seem to lead to no improvement on the theory in its original form because it would not increase the capabilities of the theory as a scheme for the representation of observed facts. For force-centres have no advantage over conceptual gemmules in depictive power and the importation of the term “force” in an undefined sense is open to serious objection. As a scientific theory Darwin's seems to be a marked advance in point of effectiveness for its purpose over the preformationist theory; because it lends itself to the representation not only of the simpler facts of heredity with which the latter theory was alone concerned but also to that of the transmission of characters which may remain latent for several generations and further to the transmission of characters special to the male offspring through the female parent without becoming manifest in her. Also as has been pointed out by Sir Ray Lankester the theory can be made to account for the appearance at a particular period of life of characters inherited and remaining latent in the young organism.

It is interesting to quote some remarks made by Weismann in reference to Darwin's theory of Pangenesis. Weismann¹ wrote in his Keimplasma:

This criticism is I think based upon a radical misapprehension of the nature scope and possibilities of a scientific theory. Weismann's own theory of which I shall presently give an account founded as it no doubt is on a much more extensive range of observational knowledge than that of Darwin is open to criticism on similar lines more especially in its latest and most developed form. Neither Weismann's theory nor any other theory does or can “go to the bottom of the matter” or “really explain the phenomena” or find a “real” solution of the problem. Modified theories of pangenesis have been propounded by Francis Galton and by W. K. Brooks; also a general theory of intracellular pangenesis has been developed later by De Vries; but it is not necessary for our purpose to consider these in detail. As in the case of Darwin's theory the scope of the first two of these is limited because they do not come to close quarters with the known detailed facts relating to the inner constitution of germ-cells.

The later theories especially that of Weismann make full use of such knowledge and the scope of their power of representing facts of heredity is correspondingly increased. A most important part of Weismann's views on the mechanism of heredity is contained in his theory of the continuity of germinal protoplasm. This is not the only theory of the kind that has been suggested; the theories of Jäger Galton and Nussbaum are of a somewhat similar character although in some of them the continuity asserted is rather that of germ-cells than of the protoplasmic contents of such cells. As Weismann's system has been worked out in great detail and was gradually developed by him into a form of increased complication designed to increase its scope and to meet objections raised to earlier forms of it; and as it has become not merely a theory of heredity but also of racial evolution I propose here to consider it in some detail as an example of a biological theory developed with consummate skill and with most ambitious aims especially as it has become very prominent in relation to various matters connected with the most crucial questions of Biology in particular the question relating to the inheritance of acquired characters.

Weismann's theory like other theories I have mentioned is based upon the idea that the continuity of characters in heredity is to be depicted by means of a continuity of material between parent and offspring that continuity holding through a complete series of generations. In order to understand the nature of Weismann's theory it is necessary to state a number of observed facts accumulated by many workers in the subject relating to the fertilized ovum its organization and what happens in it on maturation and in the events leading up to the development of the embryo. Every cell in the body of an animal of given species contains a general cell-substance or cytoplasm consisting in part of protoplasm that is of living matter and partly of non-living material of various kinds. Within the cytoplasm is a small body called the nucleus of the cell and within this nucleus there is contained a substance known as chromatin because it can readily be stained and thus distinguished from the rest of the material contained in the nucleus. In many animal cells there are small bodies known as centrosomes which appear to play a very important part in the operation which results in the division of the cell into two cells; in higher plants there appear to be no centrosomes. The chromatin contained in the nucleus in certain conditions of the cell consists of a number of separate masses called chromosomes or idants; these are rod-like looped or granular bodies and in any one species the number of these chromosomes is a definite even number the same in all the cells. In man this number is now said to be 48; but it was for some time thought to be 24; in some other organisms the number is smaller and in some larger. It was shown in 1883 by Van Beneden and has been since confirmed for the cases of many animals and plants that the male sperm-cell and the female ovum when prepared for conjugation each contain only half the number of chromosomes which each somatic cell of the species contains. This process of maturation which results in the halving of the number of chromosomes in a germ-cell either male or female is carried out in a complicated manner; and in the case of higher animals it usually commences two cell-generations earlier than the formation of the gametes that is of the matured sperm-cell and egg-cell which conjugate. When a sperm-cell reaches an ovum it bores its way into it and leaves behind its cytoplasmic substance; the nuclei of the sperm-cell and of the ovum then move towards each other and unite as a single nucleus which contains the chromosomes contributed by the two cells. The number of the chromosomes is thus brought up to the full number characteristic of the cells of the species. The walls of the ovum then become harder and this prevents the entrance of any other sperm-cell. There is no centrosome in the mature ovum but the sperm-cell brings its centrosome with its nucleus. This centrosome then divides into two which appear to play an important part in the subsequent division of the now fertilized ovum into two cells. The ovum is very much larger than the sperm-cell and thus provides the bulk of the material necessary for the initial stage of the development of the embryo. Both parents contribute alike the chromosomes and in Weismann's theory it is these chromosomes upon which rest the foundations of the inherited organization of the offspring; the male parent contributing the centrosome which appears to play the part of directing the process of division of the fertilized ovum. In accordance with the view of Weismann and his school in any given species the nuclei of the two gametes contain the hereditary substance; and more particularly this is contained in the chromosomes; the hereditary substance contains the primary constituents of the whole organism. After the single nucleus of the fertilized ovum has been formed which contains the paternal and maternal chromosomes in equal numbers the process of sub-division of the cell begins. Each chromosome divides longitudinally into two halves and these halves ultimately arrive at the poles of the nucleus one half at each pole where one of the paternal centrosomes is situated. From each centrosome there radiates a system of rays which seem to be associated with the direction by the centrosomes of the movements of the half-chromosomes. Near each pole there comes to be a group of semi-chromosomes half of paternal and half of maternal origin. Each of these groups forms a new nucleus; the cytoplasm of the cell divides into two halves across the equatorial plane and thus two new cells are composed each of which has a nucleus of which the chromatic material is half of paternal and half of maternal origin. In certain cases this process of division of the cell into two each containing a nucleus half of paternal and half of maternal origin has been observed through several successive divisions. The development of the embryo then proceeds by continual cell division starting with the pair of cells into which the fertilized ovum divides. The swarm of new cells which is thus developed consists partly of somatic cells of various constructions which form the various parts and organs of the developing embryo and partly of undifferentiated cells which ultimately become the germ-cells of the new individual. Investigation has shown that in certain cases these young germ-cells contain equal numbers of paternal and maternal chromosomes; in later stages it is thought probable that there is a separation of the paternal and maternal chromosomes such that each cell contains some of each but not necessarily in equal numbers. This is regarded as giving rise to the possibility of various combinations of the paternal and maternal hereditary characters as represented in the final germ-cells of the new individual.

We are now in a position to consider in some detail Weismann's theory of inheritance; a theory which it should be observed takes for granted the essential phenomena of life nutrition assimilation and growth. In the first place the assumption based on evidence of observation to which I have already alluded is made that there is a definite hereditary material located in the chromosomes of the nuclei of the sperm-cell and the egg-cell. Weismann next assumes also on evidence based upon observation that the germ-cell contains not only the primary constituents of a single individual of the species but also those of several often even of many individuals. The whole material of which the chromosomes or idants are composed is called the germ-plasm; as Weismann writes: “I call the idioplasm of the germ-cells germ-plasm or the primary constituent substance of the whole organism and the complex of primary constituents necessary to the production of a complete individual I call ids.” Thus a chromosome or idant is made up of several ids each of which is the bearer of a complete inheritance. The fundamental conception of the theory of the continuity of the germ-plasm as stated by Weismann in 1885 is that in each development of the new embryo a portion of the germ-plasm contained in the fertilized ovum is not used up in the formation of the offspring but is reserved and remains unchanged in the body of the offspring for the formation of the germinal cells of the following generation. Thus what is continuous is usually not germinal cells but the germ-plasm “of definite chemical and special molecular constitution.” This idea of a physical nexus between the successive generations of a race in the handing on from one generation to another of the germ-plasm has sometimes been imaginatively described as the immortality of the germ-plasm. As an embryo is developed by continual bifurcation of cells starting from the fertilized ovum gradual differentiation of these cells sets in and various body-cells with specialized structure and function appear; these form the various parts and organs of the developing embryo. But some cells remain undifferentiated and gradually lead up to the germ-cells of the new organism. Ultimately on the maturity of the new organism these germ-cells become liberated and each of them contains chromosomes both of paternal and of maternal origin. It is then assumed as a generalization of a number of observed facts that each such chromosome contains germ-plasm derived from the ancestors of both parents; and thus there comes to be in the chromosomes an accumulation of material derived from earlier ancestors both on the paternal and maternal sides. It should be observed that up to a certain point namely the existence of ids the concepts employed are of the kind which correspond to perceptual objects. But when as Weismann assumes each id is regarded as containing in itself in some sense all the generic specific and individual characters of a new organism a concept is created to which no perceptual element corresponds; in fact the theory passes beyond the stage in which it is exclusively descriptive of perceptual facts that can be directly observed. But Weismann does not stop at this point; since the dissimilarity of parts of the organism must be represented in the ids he regards each id as consisting of many invisible constituents which he calls determinants. Each determinant is concerned with the formation of some special organ in the embryo. It is not necessary to assume that there are in the germ-plasm as many determinants as there are cells to be determined in the individual at every stage of its development. There must however be as many of these as there are regions in the fully formed organism capable of independent and transmissible variation including all the stages of development. Thus a single determinant can represent a group of cells which can vary en bloc. In order to account for the mode in which the determinants give rise to cells and tissues the special characteristics of which are represented by the different determinants Weismann regards them as composed of groups of biophors which are to be regarded as the minutest vital units. These biophors exhibit the primary vital characteristics assimilation metabolism growth and multiplication by fissure; each such biophor is supposed to have a molecular constitution. Whilst the id represents the complete individual the determinants represent its different parts and groups of cells; the biophors represent characters. A germ-cell contains as many biophors as the individual which this cell is to produce possesses of elementary individual characters; and each biophor may vary independently so as to produce a corresponding modification in the character it represents. The biophors are supposed to be liberated in the cytoplasm of the cells of the embryo. As the fertilized ovum divides and re-divides the blastomeres that is the resulting cells become heterogeneous if not at the very earliest stages of re-division at all events at an early stage; that is they become suited to form certain parts only of the embryo. This fact is represented in Weismann's theory by the conception that the determinants bearing various characters become gradually distributed amongst different cells during the process of successive segmentation of cells. This process of distribution must be regarded as of an orderly character; and thus the various determinants must be looked upon as being definitely localized in accordance with a definite structure of the germ-plasm. In order that this distribution may take place so that each determinant may reach the proper locality in the new individual there must be qualitative differences as regards the distribution of determinants between the first two cells which appear on the first division of the ovum. The blastomere which contains the determinants corresponding to one class of organs will then at the next division split into two cells which again differ from one another in respect of the determinants they contain and so on; the ontogenesis depending at every stage upon cleavage of a cell into dissimilar cells and producing in the end dissimilar structures. As the organs and tissues become differentiated the germ-plasm becomes less complex owing to the release of continually more of its determinants and ultimately transforms itself into the idioplasm to be found in each cell and which only contains determinants of one cell and of parts of it. The biophors then break off from the determinants and these scatter themselves through the cytoplasm and thus impart to the cell its specific character. Some cells may contain determinants which do not break up into biophors but which remain in reserve until a later time when the cell may become more differentiated. The biophors require for the actual production of the characters they represent the co-operation of the cytoplasm which constitutes the body of the cell in which they operate.

Weismann speaks of the determinants as being kept in relation with one another by “vital affinities”; and this can only be taken to mean that it must be accepted as a postulation of his theory that they do keep in relation with one another and that he does not attempt to set up a definite theory as to the modes of such relations. When “vital affinities” and the like make their appearance in a biological theory it is a sure sign that a point has been reached beyond which the descriptive power of the theory cannot pass. The whole secret of the phenomena may be regarded as having been concentrated in these determinants and biophors with their vital affinities and in principle the distance from an “explanation” in any ultimate sense is precisely where it was before the theory was developed. The spatial scale of the phenomena has been reduced and that is all. This does not however imply that such a theory is useless; quite the contrary. The determinants and biophors do not represent perceptual objects although definite properties are assigned to them. They are regarded by Weismann as having a definite chemical constitution and this may differ in different kinds of biophors; or there may be a difference of the arrangement of the atoms in the matter even with one and the same chemical constitution. The biophors may play a similar part in a conceptual scheme to that which atoms or electrons play in physico-chemical schemes and may be equally indispensable. Thus I take it Weismann's scheme when regarded as a conceptual scheme is not open to objection any more than was Darwin's theory of Pangenesis merely on the ground that it employs concepts such as biophors. It should however be remarked that Weismann himself was far from accepting the view that biophors are purely conceptual entities. His physical realism appears clearly in his statement: “The biophors are not I believe by any means mere hypothetical units; they must exist for the phenomena of life must be connected with a material unit of some kind.”

The actual value of Weismann's theory as a descriptive scheme worked out in great detail and with consummate skill is one which only experts can estimate; and the opinions among them seem to be sharply divided. Besides the objection that the primary constituents determinants and biophors are purely ideal the further objection has been raised that these concepts are unnecessary and introduce an undue complication. The weight of this latter objection can perhaps best be estimated by contrasting Weismann's theory with other theories of the germ-plasm such as that advanced by Delage. This does not employ such units as determinants or biophors but relies upon the variety of chemical substances contained in the germ-cells. In Semon's mnemonic hypothesis the basis of heredity is the “unconscious memory” of the organism transmitted in the germ-plasm.

Very serious objections to the correctness or at least to the generality of the assumptions of Weismann's theory have been made upon the basis of experimental observations. Some experiments tend to show that the importance of the chromatic matter of the nucleus as the bearer of heredity is exaggerated in Weismann's theory; that in some cases at least the cytoplasm plays a larger part than that merely of nutrition of the embryo. Experiments carried out by Delage on the eggs of sea-urchins have shown that it is possible to fertilize a fragment of the ovum which contains no nucleus and that some measure of development may occur in this fertilized cytoplasm. Doubt has also been thrown upon the essential character of the effect of the sperm-cell in fertilizing the ovum. It was shown by Loeb that the eggs of the sea-urchin may be fertilized by adding to the water in which they live certain chemical substances This artificial parthenogenesis suggests that in conjugation the essential part played by the sperm-cell is that of introducing some chemical substance which stimulates the ovum to activity. That part of Weismann's theory which has to do with the segregation of the determinants was supported by experiments carried out by Roux. He found that the first division of the fertilized ovum of a frog marked out the right and left halves of the body the one blastomere developing into the right half of the embryo and the other into the left half. Roux succeeded in destroying one of the blastomeres and found that the other one developed into a half-embryo. This seemed to be decisive proof that in the segmentation there was a differentiation of the two blastomeres as bearers of heredity. But a later experiment of Driesch showed that if after one of the blastomeres has been destroyed the egg be turned upside down the uninjured blastomere develops into a whole embryo only smaller than if the whole egg had been allowed to develop. He showed also that if the uninjured egg when in the two-cell stage be turned upside down two whole embryos are developed. This and similar results obtained appear to show that up to the two-cell stage there can be no such segregation of the determinants as is indicated by Weismann's theory. Upon these experiments Driesch has based one of his proofs of the existence of entelechy.

In close connection with Weismann's theory of heredity and with other theories of a more or less similar type is the great controversial question as to the inheritance of acquired characters. Not only on account of its importance in Biological Science especially in connection with theories of Evolution but also on account of the consequences which any answer to it entail in relation to social questions reaching far beyond the narrower sphere of Biology this question has given rise to acute and lasting controversy. By the term “acquired character” or “somatic modification” is to be understood any structural change in the body of a multi-cellular organism of a kind which involves some change from the normal structure of the species to which the individual belongs and which is acquired and remains permanent during the lifetime of the individual and can be shown to be traceable to a change of environment such as climate or to functional use or disuse such as is involved in specialized habits or in mutilations. From the point of view of any theory of germ-plasm the question whether a somatic modification of this kind is heritable or not is equivalent to the question whether such modification is accompanied by a specific change in the germ-cells such that the offspring will inherit in some degree or other the modification which the parent acquired. It is quite clear that this question can only be answered empirically after an abundant amount of observation and experiment specially directed to elucidate the matter. No answer can be accepted as decisive which depends upon a theoretical deduction from a special theory of heredity such as that of Weismann; on the contrary a decisive answer to the question obtained by means of fully sifted observations would be a most crucial test of the value of such a theory as descriptive of the facts of heredity. In the empirical investigation of the matter it must in the first instance be shown that what purports to be an inherited modification is really an acquired character in accordance with a precise definition of the meaning of the term. The mere fact that a bodily peculiarity reappears in several generations is not sufficient proof that it has been inherited as such an acquired somatic modification; it may be a congenital germinal variation which has not been originally produced in the manner described. It must further be shown that the apparent recurrence of an acquired modification in a later generation is not connected with a recurrence of the environmental change or of the specialized habits of life which were the origin of the parental modification. Lastly it must be shown that the somatic modification of the parent is not accompanied by a modification of the germ-cells. If such modification of the germ-cells of the parent can be shown to occur as may happen for instance when the whole body including the reproductive cells is poisoned there will be some effect produced upon the offspring not necessarily owing to the somatic modification of the parent but owing to the accompanying modification of the germ-cells. This last restriction naturally introduces an element of difficulty into the investigation because it cannot be easily possible to ascertain the circumstances in which a somatic modification is accompanied by a change in the germ-cells. The negative answer given by Weismann and others to the question whether acquired somatic modifications are heritable depends upon the assumption that at least in the case of the more ordinary somatic modifications there is no corresponding specific modification in the germ-cells.

In accordance with the theory that the basis of inheritance is the germ-plasm which is separate and remains segregated from the somatic cells everything turns upon the relations between the body-cells and the germ-cells. Weismann's view is that an acquired modification in general affects only the somatic cells and has no influence on the germ-cells at least in the direction of producing in them such specific modification that the acquired somatic modification becomes heritable. It should be observed that Weismann does not assert that the germ-cells remain absolutely unaffected by the modification in the body-cells but only that they are not so specifically affected that the offspring will thereby exhibit the same modification that was acquired by the parent or even a tendency to it. Some of the later developments of the theory of Weismann I shall have occasion to refer to in connection with theories of Evolution.

The theories of heredity to which I have referred all depend upon the procedure of employing facts obtained by observation and experiment to suggest a descriptive scheme or as some would say a mechanism which will enable us to trace out in detail the processes which lead up to the facts that are observed and to use such descriptive scheme as an instrument for predicting occurrences not yet observed which would follow in appropriate circumstances on the assumption that the descriptive scheme is sufficient for this purpose. The verification or lack of verification of the potency of the scheme in such predictions is then to be regarded as a test of the value and scope of the particular theory in question.

There exists however another method of procedure which may be described as the statistical method that has been in recent years applied to matters relating to the study of heredity. The essence of this method consists in the ascertainment by direct observation of the frequency of occurrence of a certain character or group of characters in a large number of individuals of a particular species compared with the occurrence of the same character or group of characters or related characters or of certain conditions in the parents or in the remoter ancestors of those individuals of the species in which they are found. The purely statistical facts obtained are then analysed by the mathematical methods of statistics with a view to the determination of correlations the existence of at least some of which may have been previously unsuspected and in particular of obtaining numerical estimates of the average frequency with which parental or ancestral characters reappear in the offspring. The application of this method does not require the employment of any theory as to the genetic modes in which the correlations between different generations of a race are set up; but the results of statistical theory may be used to assist in the setting up of such theories or in the work of discriminating between alternative theories that have been suggested by workers who proceed by the non-statistical method.

The first person who seems to have fully grasped the possibility of applying the statistical method to problems of heredity and to the general problem of variation in connection with evolutionary conceptions was Francis Galton who applied the method to a variety of questions in this order of ideas. The method has been followed up by a band of researchers of whom the most prominent has been Professor K. Pearson and their work has been incorporated in the department known as Biometrics; this department of research is represented by an important periodical appearing under the name Biometrika. The particular characters amenable to this method are often of a measurable character and are thus capable of being correlated with numbers. In a given race the average measure of a particular character of the kind considered has for a very large number of individuals at any one time an average value known as the mean value of the character for the race. It may happen that the mean value of the character may change from one generation to another but in point of fact many characters preserve their mean value unchanged for many generations. When the mean value changes it cannot be concluded that the character is necessarily heritable; the change may occur without any individual heredity in the particular character. Galton himself conducted a most careful statistical inquiry partly by using the records of about a hundred and fifty families relating to stature colour of the eyes some kinds of disease and artistic faculty. It will be observed that the last two characters are not measurable in the same sense as the others but their occurrence in different members of the families can be counted; moreover Galton applied his method as exhibited in the last case to mental as well as physical characters. He also made observations on characters in sweet-peas and moths as well as various measurements in his anthropometric laboratory. One of the simpler problems which can be treated by this method is that of ascertaining whether a deviation of a particular character such as stature from its mean value in the race is heritable or not. On the basis of a large series of observations it was shown by Galton and more precisely by Pearson that the average stature of a son is reckoned in inches 31⋅1 inches plus nine-twentieths of the number of inches in the stature of his father. This warrants the conclusion that deviation of stature from the mean of the race is heritable. Thus if a father differs in stature from the average of the race the same is on the average true of his son. It also shows that on the average the deviation of stature of the son is in the same direction as that of the father but on the average smaller in amount. This last fact is a particular case of a generalization propounded by Galton after careful statistical inquiry and known as the law of filial regression. This law is most simply illustrated by the case of stature although it has been verified in its general features in the case of other characters. If for example fathers whose height is 72 inches be taken the mean height of their sons is 70⋅8 inches; these are still on the average taller than the average of the general population but differ less from it than the fathers and thus they regress towards the mean of the stock. A similar result holds in the case of fathers who have some height less than that of the average of the stock; their sons are on the average taller than the fathers but less tall than the average of the stock; they have progressed towards the mean. Galton also showed by his statistical studies that the average of human stature is very constant from generation to generation although there is statistical evidence that there is no correlation between the statures of people who marry. These facts Galton attempts to formulate by means of a principle of organic stability of the race in accordance with which there is a stable type or average of the particular character which is preserved unchanged through successive generations. He does not however connect this principle of organic stability with natural selection in virtue of which the stability of the average value of the character and the fact of regression towards it might be accounted for on the principle that the average value was more suited to the environment than a different average value would be. The explanation of this specific stability given by Galton is that each child inherits in part only from the parents and in part from the more remote ancestors and since what he calls the mid-parentage is on the average nearer than the exceptional parents to the mean for the race the children of selected parents are on the average more mediocre than their parents. The fact that the mid-parentage is nearer to the average of the stock than the exceptional parents is supposed to be due to the fact that when the ancestors are counted back for many generations they consist of so many and such varied elements that they become as regards their average characters indistinguishable from the general population. The theory has been criticized by W. K. Brooks on the ground that while the child is descended from a long line of ancestors it inherits from none but the parents and that it can only be said in a figurative sense to inherit from more remote ancestors. To estimate the force of this criticism it should be observed that Galton establishes at most merely the bare fact that there is a correlation between the characters of the child and those of its more remote ancestors and that when this has been done the power of his method at least as regards this particular application is exhausted; the method establishes no intermediate nexus between the remote ancestors and the child. Galton's opinion that the correlation is due to the organic stability of the race is in no sense an explanation of the correlation but consists merely of the introduction of an expression to denote the ascertained fact of constancy of type through many generations. Only such a theory as that of Weismann's theory of the continuity of the germ-plasm is in a position to exhibit by a pictorial representation how the nexus between the child and its more remote ancestors is to be regarded as being through the parents; in that the germ-plasm of the parents contains elements derived from the ancestors. It would thus appear that Galton's ascertainment of the fact of correlation between the characters of the child and those of its more remote ancestors affords some confirmation of the descriptive potency of the theory of the continuity of germ-plasm. The criticism of Galton's theory seems then to be valid only as pointing out a necessary limitation in the scope of the method so long as that method is considered as it should be only as a mode of establishing facts of correlation and not as providing a description of any mechanism of the correlation. Criticism has also been directed against the view that the remote ancestors are so numerous that in the bulk they may be taken to be equivalent for the purposes of discussion to the general population. A man has for example theoretically 4096 twelfth grandparents but it is argued that this number must in practically all cases be markedly diminished since the descendants of the largest part of a more or less isolated population as it exists and intermarries at any one time die out after a few generations; it is thus argued that a tolerably isolated population must actually be descended from a relatively small number of individuals who existed and intermarried at some former period and that this being the case the force of Galton's reasoning is much diminished. But this consideration would seem merely to point out that caution is required in pushing Galton's argument too far rather than to provide a complete refutation. In any case the ascertained facts of correlation stand on a much firmer basis than any attempt to explain them theoretically.

Galton went further than merely to ascertain the fact that there is a correlation between the characters such as the stature of an individual and the corresponding characters in his ancestry. The law of ancestral inheritance which he based upon his observations and statistics includes a numerical estimate of the amount of correlation. The law is that:

It must always be remembered that such a law is purely statistical dealing only with averages in a large population; its correctness cannot be refuted by production of single or a few individual cases in which it can be shown not to represent the facts; the only refutation possible must itself be based upon statistics dealing with a very large number of individual cases.

A very different class of investigations relating to the laws of inheritance in hybrid varieties have been of great prominence in the biological work of the last two decades. These investigations are dependent upon the original discoveries of G. J. Mendel Abbot of Brunn who after many years of experimental investigation chiefly of varieties of peas published them in 1866. The law known as Mendel's law was rediscovered by several botanists in 1900 and the attention of Biologists was drawn to Mendel's results by Mr Bateson who extended them by a series of his own experiments. The theory of the Mendelian school is based upon statistical results relating to the descendants of hybrid varieties obtained by crossing two varieties of a species which differ from one another in respect of some particular character. Mendel found that in investigating the effect of crossing two varieties for example of peas differences in certain specific characters could be separately investigated and this gave rise to the conception that the difference between the two varieties is compounded of differences in respect of separate unit characters. When a variety with one particular character such as tallness is crossed with a variety which differs in respect of the corresponding character such as dwarfness in the offspring one of the two characters in particular tallness is found to occur in all the offspring. That character tallness is said to be dominant and the character which does not appear in the offspring is said to be recessive. The hybrids all of which possess the dominant character were then crossed with one another and it was found that amongst the offspring both characters occurred but the number with the dominant character (tallness) was three times the number of those with the recessive character (dwarfness). When the recessives are crossed with one another they give rise only to recessives and they breed true for any number of generations. But when the dominants fertilized themselves they produced one-third pure dominants and two-thirds cross-bred dominants. The former of these breed true and the latter give rise to a mixture of dominants and recessives in the proportion of three to one.

The law of dominance that is of the fact that one of the two characters is dominant in that all the hybrids possess it is the first part of Mendel's scheme. The second part is the law of segregation which expresses in numerical form the facts in relation to the successive generations as to the segregation of the two characters in sets of individuals which thereafter breed true. Mendel suggested as an explanation of his experimental results a theory of the existence of two kinds of germ-cells which exist in all the hybrids in equal numbers—the theory of gametic segregation; and he made an hypothesis on this basis as to how the segregation of the characters is effected. This theory of gametic segregation and combination has been applied by Mendelians to represent and to predict in accordance with the law of averages the results of crossing varieties and it has been extended to cases in which the characters considered are not distinguishable into dominant and recessive characters.

In certain cases the laws of Mendel have been verified but in the long series of experiments which have been made in this order of investigations various complications have been introduced in the interpretation of the results. Important practical applications of the theory have been made especially in the production of wheat which possesses the quality of immunity to the disease known as rust. Hopes have been entertained that investigations on Mendelian lines might throw light upon the general theory of evolution of species but it appears to be doubtful whether there is at present much prospect that such hope will be fulfilled.