Pedagogical Anthropology

CHAPTER I
CERTAIN PRINCIPLES OF GENERAL BIOLOGY

In order to understand the practical researches that must be conducted for anthropological purposes, it is necessary to have an adequate preparation in the science of biology. The interpretation of the data that have to be gathered according to technical procedure, demands a training; and this training will form our subject in the theoretic part of the present volume. The limits, however, not only of the book itself, but of pedagogic anthropology as well, preclude anything more than a simple general outline; but this can be supplemented by those other branches of study which are either collateral to it or constitute its necessary basis (i.e., general biology, human anatomy and physiology, hygiene of environment, general anthropology, etc.).

The Material Substratum of Life
The Synthetic Concept of the Individual in Biology

According to the materialistic theories of life, of which Haeckel is the most noted supporter, life was derived from a form of matter, protoplasm, which not only has a special chemical composition, but possesses further the property of a constant molecular movement of scission and redintegration; vital metabolism or interchange of matter, by which the molecules are constantly renewed at the expense of the environment.

It was Huxley who defined protoplasm as the physical basis of life; and, as a matter of fact, life does not exist without protoplasm.

But Schultze and Haeckel carried this doctrine further, to the point of maintaining that a minute particle of protoplasm was all that was needed to constitute life; and that such a particle could be formed naturally, whenever the surrounding conditions were favorable, like any other inorganic chemical substance; and in this way the materialists endeavoured, with great ingenuousness, to maintain the spontaneous origin of life. And when Haeckel thought that he had discovered the moneræ or living cells composed of a single particle of protoplasm, he held that these were the first species to have appeared on earth.

But the further researches of physiologists and the improvements in the technique of the microscope proved that protoplasm does not exist independently in nature; because living cells are always a combination of protoplasm and a nucleus. If the nucleus is extracted from a radiolarium, the latter mortifies, and the protoplasm also dies; if an amœba is severed in such a manner that one part contains nucleus and protoplasm and the other protoplasm alone, it will be found that the latter part mortifies and dies, while the first part continues to live. If an infusorium is divided in such a way that each of the separate sections contains a part of the nucleus and a part of the protoplasm, two living infusoria are developed similar to the original one. Experiments of this kind, to which Verworn has given high authority, serve to prove that life does not exist except in cells divisible into protoplasm and nucleus. Further discoveries confirm this theory, as for instance the presence of a nucleus in hemocytes or red blood corpuscles, which were formerly believed to be instances of anuclear cells; and the discovery of protoplasm in microbes, which had formerly been considered free nuclei.

Now, when we have an independent living cell, it represents an individual, which not only has, as a general feature, this primitive complexity of parts, but also certain special characteristics of form, of reaction to environment, etc., that mark the species to which this particular living creature belongs.

Accordingly, we cannot assert, without committing the error of confining ourselves to a generic detail, that life originates in protoplasm or in a combination divisible into protoplasm and nucleus; we should say that life originates in living individuals; since, aside from abstract speculation, there can be no other material substratum of life.

Such a doctrine is eminently synthetic, and opens the mind to new conceptions regarding the properties that characterise life.

Formerly when life was defined as a form of matter (protoplasm) subject to constant movement (metabolism), only a single general property had been stated; for that matter, even the stars consist of matter and movement; and, according to the modern theory of electrons, atoms are composed of little particles strongly charged with electricity and endowed with perennial motion. Accordingly, these are universal characteristics, and not peculiar to life; and metabolism may be regarded as a variation of such a property, which is provoked by, or at least associated with the phenomenon of life.

The properties which are really characteristic of life have been summed up by Laloy in two essential groups; final causes and limitations of mass, or, to use a term more appropriate to living organisms, limitations of form and size.

The term final causes refers to a series of phenomena that are met with only where there is life, and that tend toward a definite purpose or end. Living organisms take nutriment from their environment, to the end of assimilating it, that is, transforming it from an inert, indifferent substance into a substance that is a living part of themselves.

This phenomenon is undoubtedly one of the most characteristic. But there are still other forms of final cause, such for example as the transformation of the fertilised ovum into the fully developed individual, predetermined in its essential characteristics, such as form, dimensions, colour, activities, etc. There are ova that to all appearances are exactly alike; the human ovum itself is nothing more than a simple cell composed of protoplasm and nucleus, measuring only a tenth of a millimeter (= 1/250 inch); yet all these ovum cells produce living organisms of the utmost diversity; yet so definitely predetermined that, if we know to what species the ovum belongs, we are able to predict how many bones will compose the skeleton of the animal destined to develop from it, and whether this animal will fly or creep upon the ground, or rise to take a place among those who have made themselves the lords of the earth. Furthermore, knowing the phases of development, we may predetermine at what periods the successive transformations that lead step by step to the complete development of the individual will take place.

Another form of final cause is seen in the actions of living creatures, which reveal a self-consciousness; a consciousness that even in its most obscure forms guides them toward a destined end.

Thus, for example, even the infusoria that may be seen through a microscope in a drop of water, chasing hither and thither in great numbers, avoiding collision with one another, or contending over some particle of food, or rushing in a mass toward an unexpected ray of light, give us a keen impression of their possession of consciousness, a dim glimmering of self-will, which is the most elementary form of that phenomenon that manifests itself more and more clearly, from the metazoa upward, through the whole zoologic scale: the final cause of psychic action.

Again, in multicellular organisms there are certain continuous and so-called vital phenomena, which some physiologists attribute to cellular consciousness: for example, the leucocytes in the blood seem to obey a sort of glimmering consciousness when they rush to the encounter of any danger threatening the organism, and ingest microbes or other substances foreign to the blood; and it is also due to a phenomenon that cannot be explained by the physical laws of osmosis, that the erythrocytes or red blood corpuscles and the plasma in the blood never interchange sodium salts for those of potassium; and lastly the cells of each separate gland seem to select from the blood the special substances that are needed for the formation of their specific products: saliva, milk, the pancreatic juice, etc.

Still another manifestation of final cause is the tendency exhibited by each living individual to make a constant struggle for life, a struggle that depends upon a minimum expenditure of force for a maximum realisation of life, thanks to which life multiplies, invades its environment, adapts itself to it, and is transformed.

Another fundamental synthetic characteristic of life is the limitation of form and size that is a fixed and constant factor in the characteristics of each species; the body of the living individual cannot grow indefinitely.

Living creatures do not increase in quantity by the successive accumulation of matter, as is the case with inorganic bodies, but by reproduction, that is, the multiplication of individuals.

Through the phenomenon of reproduction, life has a share in the eternity of matter and of force, that is, in a universal phenomenon. But what distinguishes it is that the individual creatures produced by other living individuals form, each one of them, an indivisible element in which life manifests itself; and this element is morphologically fixed in the limits of its form and size.

The peculiarities which are attributed to the chemical action of protoplasm are of an analytic character, so far as they concern the fundamental characteristics of life. The constant interchange of matter, namely, metabolism, constitutes undoubtedly a phenomenon peculiar to living matter, protoplasm; but protoplasm does not exist apart from living organisms. And what constitutes its chief characteristic is that, when brought into contact with it, inert substances are assimilated, i.e., they become like it, or rather, are transformed into protoplasm; mineral salts such as the nitrates or nitrites of sodium and potassium are transformed in the case of plants into living plasma capable of germinating either into a rose bush or a plane tree or a palm, and inert organic substances such as bread or wine are transformed into human flesh and blood. So that the phenomenon of assimilation outweighs, as a characteristic of life, the molecular chemical action through which it is accomplished. Since metabolism does not occur in nature as a chemical phenomenon, and cannot be produced artificially, but is found only in the matter composing living organisms, it follows that life is the cause of this form of dynamic action, and not that this dynamic action is the cause of life.[4]

Even the latest theory, developed especially by Ludwig in Germany—that protoplasm contains a separate enzyme for each separate function appointed to a particular task—amounts to nothing more than an analysis of the living organism.

The Formation of Multicellular Organisms

We cannot say that the cell is the element of life, because, in an absolute sense, it is not alive; it lives only when it constitutes an individual. Even the brain cells, the muscular fibres, the leucocytes, etc., are cells; but they do not live independently; their life depends upon the living individual that contains them. We may, however, define the cell as the means, the morphological material, out of which all living organisms are formed: because, from the algæ to the orchids, from the cœlenterata up to man, all complex organisms are composed of an accumulation of those microscopic little bodies that we call cells.

The manner of union between the cells in the most primitive living colonies, whether vegetable or animal, is analogous to that followed in the segmentation of the ovum in its ontogenetic (i.e., individual) development.

But the manner of construction differs notably, as between animal and vegetable cells.

Vegetable cells, on the one hand, have a resistant and strongly protective membrane; animal cells, on the contrary, have either a very thin membrane or none at all. Vegetable cells, as though made venturesome by their natural protection, proceed to invade their environment in colonies—in other words, the cells dispose themselves in series of linear ramifications—witness the formation of primitive algæ; and analogously the expansion of the higher types of vegetation into their environment, with branches, leaves, etc. And just as though the vegetable cell acquired self-confidence because it is so well protected, it becomes stationary and strikes its roots into the soil.

To this same fact of cellular protection must be attributed the inferior sensibility and hence the permanent state of obscured consciousness in vegetable life.

This protection against the assaults of environment, and the consequent lack of sensibility, constitute from the outset an inferior stage of evolution.

Animal cells have an entirely different manner of forming themselves into colonies; acting as though they were afraid, they group themselves in the form of a little sphere, enclosing their environment within themselves, instead of reaching out to invade it; and subsequent developments of the animal cell consist in successive and complex invaginations, or formations of layers, one within another—instead of ramifications, after the manner of vegetable cells.

Accordingly, if we advance from that primitive animal type, the volvox, consisting of a simple group of cells arranged spherically, like an elastic rubber ball, to the cœlenterata, we meet with the phenomenon of the first invagination, producing an animal body consisting of two layers of cells and an internal cavity, communicating with the exterior by means of a pore or mouth. The two layers of cells promptly divide their task, the outer layer becoming protective and the inner nutritive; and in consequence of their different functions, the cells themselves alter, the outer layer acquiring a tougher consistency, while the inner remains soft in order to absorb whatever nutriment is brought by the water as it passes through the mouth. In this way, there is a division of labor, such that all the external cells protect not only themselves, but the whole organism; while the internal cells absorb nutriment not only for themselves but for the others. This is the simplest example of a process that becomes more and more complex in the formation of higher organisms; in adapting themselves to their work, the cells become greatly modified (formation of tissues) and perform services that are useful to the entire organism. And at the same time, because of the very fact that they have been differentiated, they become dependent upon the labors of others, for obtaining the means of subsistence. Similar laws seem to persist even at the present day in the formation of social organisms, in human society.

During the development of the embryo, all animals pass through similar phases; and to this man is no exception.

He traces his origin to an ovum-cell formed of protoplasm, nucleus and membrane, measuring only a tenth of a millimetre, yet vastly large in comparison with the spermatic cell destined to fertilise it by passing through one of the innumerable pores that render the dense membrane penetrable.

After the ovum-cell is fertilised, it constitutes the first cell of the new being; that is, it contains potentially a man. But as seen through the microscope, it is really not materially anything more than a microscopic cell, undifferentiated, and in all things similar to other independent cells or to fertilised ovarian cells belonging to other animals. That which it contains, namely, man, often already predetermined not only in species, but in individual characteristics—as, for instance, in degenerative inferiority—is certainly not there in material form.

At an early stage of the embryo's development, it exhibits a form analogous to that of the volvox; namely, a hollow sphere, called the morula; and subsequently, by the process of invagination, two layers of cells, an inner and an outer, are formed, together with the first body cavity, destined to become the digestive cavity, and also a pore corresponding to the mouth.

This formation has received the name of gastrula (Fig. 10, facing page (72)), and the two layers of cells are known as the primary layers, otherwise called the ectoderm and the entoderm. To these a third intermediate layer is soon added, the mesoderm. These three layers consist of cells that are not perceptibly differentiated from one another; but potentially each and every one contains its own special final cause. In each of the three layers, invaginations take place, furrows destined to develop into the nervous system, the lungs, the liver, the various different glands, the generative organs; and during the progress of such modifications, corresponding changes take place in the elementary cells, which become differentiated into tissues. From the ectoderm are developed the nervous system and the skin tissues; from the entoderm, the digestive system with its associate glands (the liver, pancreas, etc.); from the mesoderm, the supporting tissues (bones and cartilage) and the muscles. But all these cells, even the most complex and specialised, as for example those of the cerebral cortex, the fibres of the striped muscles, the hepatic cells, etc., were originally embryonic cells—in other words, simple, undifferentiated, all starting on an equal footing. Yet every one of them had within it a predestined end that led it to occupy, as it multiplied in number, a certain appointed portion of the body, in order to perform the work, to which the profound alterations in its cellular tissues should ultimately adapt it.

Like children in the same school, these embryonic cells, all apparently just alike, contain certain dormant activities and destinies that are profoundly different. This unquestionably constitutes one of the properties of life, namely, the final cause; it is certainly associated intimately with metabolism and nutrition, considered as a means of development and not as a cause. Upon metabolism, however, depends the more or less complete attainment of the final cause of life. In man, for example, strength, health, beauty, on the one hand, degeneration on the other, stand in intimate relations with the nutrition of the embryo.[5]

The Theories of Evolution.—At the present day, there is a general popular understanding of the fundamental principles involved in the mechanical or materialistic theories of evolution which bear the names of Lamarck, Geffroy-Saint-Hilaire, and more especially the glorious name of Charles Darwin.

According to these theories, the environment is regarded as the chief cause of the evolution of organic forms. Charles Darwin, who formulated the best and most detailed theory of evolution, based it on the two principles of the variability of living organisms, and heredity, which transmits their characteristics from generation to generation. And in explanation of the underlying cause of evolution, he expounded the doctrines of the struggle for existence and the natural selection of such organic forms as succeeded to a sufficient degree in adapting themselves to their environment.

Whatever the explanation may be, the substantial fact remains of the variability of species and the successive and gradual transition from lower to higher forms. In this way, the higher animals and plants must have had as antecedents other forms of inferior species, of which they still bear more or less evident traces; and in applying these theories to the interpretation of the personalities of human degenerates, he frequently invoked the so-called principle of atavism, in order to explain the reappearance of atavistic traits that have been outgrown in the normal human being, certain anomalies of form more or less analogous to parallel forms in lower species of animals.

There are other theories of evolution less familiar than that of Darwin. Naegeli, for instance, attributes the variability of species to internal, rather than external causes—namely, to a spontaneous activity, implanted in life itself, and analogous to that which is witnessed in the development of an individual organism, from the primitive cell up to the final complete development; without, however, attributing to the progressive alterations in species that predestined final goal which heredity determines in the development of individual organisms.

The internal factor, namely life, is the primary cause of progress and the perfectionment of living creatures—while environment assumes a secondary importance, such as that of directing evolution, acting at one time as a stimulus toward certain determined directions of development; at another, permanently establishing certain useful characteristics; and still again, effacing such forms as are unfit.

In this way the external causes are associated with evolution, but with very different effects from those attributed to them by Darwin, who endowed them with the creative power to produce new organs and new forms of life.

Naegeli compared the internal forces to invested capital; it will draw a higher or lower rate of interest, according as its environment proves to be more or less favourable to earning a profit.

The most modern theory of evolution is that of De Vries, who, after having witnessed the spontaneous and unforeseen transformations of a certain plant, the Œnohtera Lamarckiana, without the intervention of any external phenomenon, admitted the possibility of the unexpected occurrence of other new forms, from a preexistent parent form—and to such phenomena he gave the name of mutations.

It is these mutations that create new species; the latter, although apparently unheralded, were already latent in the germ before they definitely burst into life. Consequently, new species are formed potentially in the germinating cells, through spontaneous activity.

The characteristics established by mutations are hereditary, and the species which result from them persist, provided their environment affords favourable conditions, better suited to them than to the preexisting parent form.

Accordingly new species are created unexpectedly. De Vries draws a distinction between mutations and variations, holding that the latter are dependent upon environment, and that in any case they constitute simple oscillations of form around the normal type determined in each species by mutation.

Species, therefore, cannot be transformed by external causes or environments, and the mechanism of transformation is not that of a succession of very gradual variations, which have given rise to the familiar saying: natura non facit saltus. On the contrary, what produces stable characteristics is a revolution prepared in a latent state, but unannounced in its final disclosure. A parallel to this is to be found, for example, in the phenomena of puberty in its relation to the evolution of the individual.

Now, when a species has once reached a fixed stability as regards its characteristics, it is immutable, after the analogy of an individual organism that has completed its development; henceforth its further evolution is ended. In such a case, the oscillations of variability are exceedingly limited, and adaptation to new environments is difficult; and while a species may offer the appearance of great strength (e.g., certain species of gigantic extinct animals), it runs the risk of dying out, because of a lower potentiality of adaptability; or, according to the theory of Rosa, it may even become extinct spontaneously.

Accordingly it is not the fixed species that continue the process of evolution. If we compare the tree of life to a plant, we may imagine evolution as soaring upward, sustained by roots far below; the new branches are not put forth by the old branches, but draw their sustenance from the original sources, from which the whole tree draws its life. When a branch matures and flowers, it may survive or it may wither but it cannot extend the growth of the tree.

Furthermore, the new branches are always higher up than the old ones; that which comes last is the highest of all.

Thus, the species which are the latest in acquiring a stable form are the highest up in the biological scale, because the privilege of carrying forward the process of evolution belongs to those species which have not yet become fixed. An apparent weakness, instability, an active capacity for adaptation, are consequently so many signs of superiority, as regards a potential power of evolution—just as the nudity and sensibility of animal cells, for example, are signs of superiority, as compared with vegetable cells—and of man, as compared with the lower animals.

In order to show that the inferiority of a species is in proportion to its precocity in attaining fixed characteristics, Rosa conceived the following striking comparison. Two animals are fleeing, along the same road, before an advancing flood. One of the two climbs to the top of a neighboring tree, the other continues in its flight toward a mountain. As the level of the water rises, it threatens to isolate and engulf the animal now stalled upon the tree; the other animal, still fleeing toward the heights, reaches, on the contrary, a higher and more secure position.

The animal on the tree stands for an inferior species that has earlier attained a fixed form; the other represents a higher species that has continued to evolve; but the animal upon the mountain never was on the tree at all, because, if he had mounted it and become caught there, he would have lost his chance of continuing on his way. In other words, the higher species never was the lower species, since the characteristics of the latter are already fixed.

Some eloquent comparisons might be drawn from the social life of to-day. We are all of us spurred on to choose as early as possible some form of employment that will place us in a secure and definite place at the great banquet of existence. The idea of continuing to follow an indefinite and uncertain path, leading upward toward the heights is far less attractive than the safe and comfortable shelter of the shady tree that rises by the wayside. The same law of inertia applies to every form of life. Biological evolution bears witness to it, in the forms of the different species; social evolution, in the forms of the professions and trades; the evolution of thought, in the forms of the different faiths. And whoever first halts in any path of life, the path of study, for instance, occupies a lower place than he who continues on his road.

The salaried clerk, armed only with his high-school certificate, has an assured income and the pleasures of family life, at a time when the physician, with an independent profession, is still struggling to establish a practice. But the obscure clerk will eventually hold a social position below that of the physician; his income will always be limited, while the physician may acquire a fortune. Now, the clerk, by adapting himself to his bureaucratic environment, has acquired certain well-defined characteristics; we might even say that he has become a representative type of the species, clerk. And the same will be true of the physician in his independent and brilliant life as high priest of humanity, scientist and man of wealth. Both men were high-school students, and now they are two widely different social types; but the physician never represented the type of clerk; or, in other words, he did not have to be a clerk before he could be a physician; on the contrary, if he had been a clerk, he never could have become a physician. It is somewhat after this fashion that we must conceive of the sequence of species in evolution. It follows that man never was an anthropoid ape, nor any other animal now living around us. Nor was the man of the white race ever at any time a negroid or a mongolian. Consequently, the theory is untenable which tries to explain certain morphological or psychic malformations of man, on the principle of atavism—because no one can inherit if he is not a descendant.

So, for example, reverting to our previous comparisons, if the animal on the mountain should climb a tree, or if the physician should become pedantic, this would not prove that the animal from the mountain was once upon a time the animal in the tree, nor that the physician recalled, by his eventual pedantry, certain bygone days when he was a clerk.

The theories of evolution seemed for a time to illumine and definitely indicate the origin of man. But this illusion has so far resulted only in relegating to still deeper darkness the truth that the biologists are seeking. We do not know of whom man is the son.

Even the earlier conceptions regarding the mechanics of evolution are essentially altered. The mystery of the origin of species, like that of the mutability of forms, has withdrawn from the forms that are already developed, and taken refuge in the germinal cells; these cells in which no differentiation is revealed, yet in which the future organism, in all its details, exists in a potential state; in which, we may even say, life exists independent of matter, are the real laboratorium vitæ. The individual, in developing, does nothing more than obey, by fulfilling the potentiality of the germs.

The direction of research has shifted from the individual to its germs. And just as the early Darwinian theories evolved a social ethics, seemingly based upon the facts of life, to serve as a guide in the struggle for existence, so in the same way, to-day, there has arisen from the modern theories a new sexual ethics, founded upon a biologic basis.

The Phenomena of Heredity.—The most interesting biological researches of to-day are in regard to the hereditary transmission of characteristics.

To-day the phenomena of heredity are no longer absolutely obscure, thanks to the studies of Mendel, who discovered some of its laws, which seemed to open up new lines of research prolific in results. Yet even now, although this field has been invaded by the most illustrious biologists of our time, among others, De Vries, Correns, Tschermack, Hurst, Russell, it is still in the state of investigation. Nevertheless, the general trend of researches relative to Mendel's laws is too important to permit of their enlightening first steps being neglected by Anthropology.

The first phenomena observed by Mendel, and the ones which led him to the discovery of the laws of heredity which bear his name, were revealed by a series of experiments conducted with peas.

Exposition of the Phenomena of Hybridism.—If two strains of peas are crossed, one of them having red flowers and the other white flowers, the result in the first generation is, that all the plants will have red flowers, precisely similar to those of one of the parent plants.

Accordingly, in hybridism, the characteristic of one of the parents completely hides that which is antagonistic to it in the other parent. We call this characteristic (in the case cited, the red flowers), dominant; in distinction to the other characteristic which is antagonistic to the first and overcome by it; namely, the recessive characteristic (in the present case, the white flowers). This is the law of prevalence, and constitutes Mendel's first law, which is stated as follows:

Mendel's First Law: "When antagonistic varieties or characteristics are crossed with each other, the products of the first generation are all uniform and equal to one of the two parents."

This result has been repeatedly reached in a host of researches, which have experimentally established this phenomenon as a law.

Thus, for example, if we cross a nettle having leaves with an indented margin, with a nettle having leaves with a smooth margin, the product of the first generation will all have leaves with indented margins, and apparently identical with the parent plant having indented margins, in other words, having the characteristic that has proved itself the dominant one (Russell).

These phenomena discovered by Mendel have been observed in many different species of plants, such as wheat, Indian corn, barley and beans.

They have also been verified in certain animals, such as mice, rats, rabbits, caveys, poultry, snails, silk-worms, etc. One of the most typical experiments was that of Cuénot, who, by crossing ordinary mice with jumping mice, obtained as a result a first generation composed wholly of normal mice; the characteristic of jumping was thus shown to be recessive.

Notwithstanding that the first generation is apparently in every way similar to the parent with the dominant character, there is in reality a difference.

Because, if we cross these hybrids together, we meet, in the second generation, with the following phenomenon: to every three individuals possessing the dominant character, one is born having the recessive character. To go back to Mendel's first example, that of the peas with red flowers (dominant) and with white flowers (recessive), we find, by crossing together the hybrids of the first generation, that for every three plants with red flowers, there is one plant with white flowers.

And similarly, the crossing of hybrid nettles with indented leaves will result in a second generation composed of three plants with indented leaves to every one with smooth-edged leaves (see Fig. 5).

That is, the characteristics which belonged to the first two parents all survive, even though in a latent form, in the descendants; and they continue to differentiate themselves in well established proportions. In one offspring out of four, the characteristics of the grandfather, which have remained dormant in the father, once more reappear. This intermittent heredity of characteristics, that are passed from grandfather to grandson, overleaping the father, is one of the best-known laws of pathological heredity in man; and it is called atavistic heredity, to distinguish it from direct heredity, which denotes the transmission from parent to offspring. But no explanation had ever been found for this sort of phenomenon. Undoubtedly, it must be connected with the phenomena of Mendelism.

Accordingly, in the second generation Mendel's second law has been established, the law of disjunction, which is stated as follows:

Mendel's Second Law: "In the second generation obtained by reciprocal fertilisation of the first hybrids, three quarters of the offspring will exhibit the dominant character, and one quarter the recessive."

Mendel's Hypothesis, Designed to Explain the Phenomena of Heredity.—Mendel's great service is to have conceived a hypothesis that seems to have disclosed the key adapted to unlock all the secrets of heredity.

While the body of an individual is the resultant of forces so mutually exclusive that the appearance of one characteristic means the disappearance of its antagonist; in the development of the sexual cells the two antagonistic characters are distributed in equal proportion. That is to say, one-half of the male cells contain the dominant character, and one-half the recessive; and the same holds true for the female cells. The characters of the two parents, in other words, never merge in the reproductive cells, but are distributed in equal measure, independently of the question whether they are dominant or recessive. Thus for example: in the case already cited of the first hybrid generation of the peas with red flowers, in every one of the plants, without distinction, half the pollen has potentially the red character and half has the white; and in the same way the female cells have, half of them a red potentiality and half of them a white. Such hybrids of the first generation, therefore, although apparently similar to the parent with red flowers, differ in their germinative powers, which are not made apparent in the individual. And the same may be said of hybrid nettles with indented leaves, etc.

Granting Mendel's hypothesis, we have on the one hand pollen and on the other seed ready to come together in every manner included within the range of possible combinations; the individual is, in its characteristics, nothing else than the product of a combination which must necessarily manifest itself in accordance with the well-known mathematical laws of probability.

For instance, let us proceed to diagram the possible disposition of the sexual cells of the hybrids of peas, all of them having red flowers. In terms of percentage, they will give, out of every hundred, fifty red and fifty white.

P = pollen; O = ova; R = red, dominant; w = white, recessive:

The possible number of combinations between the pollen grains and the ova are four; namely, RR, Rw, wR, ww. But where a dominant characteristic encounters a recessive (Rw, wR), the recessive disappears, to make way in the individual for the dominant characteristic alone. The definitive result is three individuals of dominant character, to one of recessive character.

Nevertheless, the hybrids of dominant character are not all equal among themselves. Those belonging to the combination RR, indeed, are permanent in character and in all respects alike, and they reproduce the original red-flower progenitor. The other red-flower hybrids, belonging to the groups Rw and wR are, on the contrary, similar to the hybrids of the first generation and contain reproductive cells differentiated in character; such hybrids, if reciprocally fertilised, will again give three dominant offspring to every one recessive; that is, they will obey the law of disjunction. The hybrids belonging to the fourth group, on the contrary, are constant, like those of the first group, and are permanently of recessive character; and they will reproduce the original progenitor with white flowers.

The same results may be attained with nettles with smooth and indented leaves, and with all other types of plant and animal life that obey the laws of Mendelism.

The figure given actually represents the third generation of nettles; from a combination corresponding to RR, there result only indented leaves, and from another combination corresponding to our ww there result only smooth-edged leaves, and from the two mixed groups there come three offspring with indented leaves to every one with smooth leaves.

It is possible to represent, by means of a general diagram, the mathematical succession of characteristics in hybrids, after the following manner; denoting the dominant character by D, and the recessive by r.

In each successive generation, provided the fertilisation takes place only between uniform individuals, as indicated in the diagram, and as may be effected by actual experiment with plants, groups identical with the original progenitors will continue to be formed, through successive disjunction of the hybrids; the sexual phenomenon operating in obedience to the laws of probability.

An effective experiment, that anyone may repeat for himself, is the one originated by Darbishire. He took two boxes, typifying respectively the male and female organ, and placed in them black and white disks of equal size, so distributed that each box contained fifty disks of each colour. After mixing these disks very carefully, he proceeded to take at random one disk at a time alternately from each box; and he piled up each pair of disks in such a manner that the black ones should be on top and the white underneath. The result was that for every three black disks on top of the piles there was one white disk; but of the black groups one consisted of two black disks, while in the other two the lower disk was white. This is simply one of the many games dependent on the laws of probability.

Now, supposing that instead of one, there are two characteristics that are in antagonism; in that case, we have the occurrence of double hybridism (dihybridism).

Let us take the strains of peas already considered, but let us choose for observation the character of their seed. One of the plants has round seed and yellow cotyledons; and the other angular seed and green cotyledons. These two characteristics, therefore, are both inherent in the seed; condition of surface (rough, smooth), and colour (green, and yellow).

After fertilisation, Mendel's first law, that of the prevalence of the dominant character, will operate, and all the plants of the first generation will have round seed and yellow cotyledons. Hence these are the dominant characteristics, which we will represent by capital letters: R (round), Y (yellow), to distinguish them from the recessive characteristics, which we will designate with small letters: a (angular), and g (green).

According to Mendel's hypothesis, all these hybrids with round seed and yellow cotyledons, contain sexual cells of opposite potentialities, numerically equal and corresponding to the antagonistic characters of the parent plants. That is, they must have in their pollen grains and their ovarian cells all the possible combinations of their different potentialities.

They should produce in equal quantities:

The total number of combinations that may result is sixteen; that is, each one of the four combinations of pollen may unite with any one of the ovarian cells; thus constituting four groups of four. And these groups represent the combinations (of pollen and ova) capable of producing individuals: