Chapter II: Part 2

In much the same way the germ acts, and its action is similarly a reaction between the structure of the germ and its environing conditions. The germ reacts by producing certain parts, differentiating certain structures, in short, by developing. The normal activities or reactions of the adult organism we call in general its "behavior." The normal activities or reactions of the germ and embryo we call "development"; the normal behavior of the germ is development. And in the latter, as well as in the former, changes in either set of factors lead to changes in the nature of the result of their interaction, i. e., to changes in the characteristics actually appearing as the result of development.

In their fully developed state some of the traits or characteristics of organisms are single, simple, fundamental characters, not analyzable into more elementary factors. Such are the number of fingers, or of joints in the fingers, absence of pigments of several kinds from the eyes or hair, presence of cataract, _et cetera_. These so-called "unit characters" are roughly analogous to the chemical elements which may, as units, be combined and recombined in diverse ways, but which always maintain their integrity as elements although different combinations produce wholes that are unlike. Each unit character in the adult is the result of a series of reactions between the environing conditions of development and a germinal structural unit, as yet hypothetical and provisionally called the "determiner," which in some way not yet understood represents this adult trait.

On the other hand, there are many of these things which we call characteristics which seem to be composite, capable of being analyzed or factored into a group of simpler components or unit characters. Such apparently are stature, span, resistance to fatigue, and probably most psychic traits. Each of these complexes results apparently from a series of reactions between the conditions of development and a group of hypothetical germinal determiners that tend to be associated within the germ.

The presence or absence of a determiner in a germ is thus the primary cause of the corresponding presence or absence of a certain characteristic in the adult organism.

But whatever the essential nature of the characteristic in this respect, whether simple or complex, we know further that every organismal characteristic is subject to variation. In any group of human individuals, for example, we can find persons of different stature, different weight, with fingers of different length and form, with heads of different size and shape, hair and eyes of different shades, different blood pressures, pulse rates, digestive possibilities, different degrees of determination, cheerfulness, alertness, and so forth. This fact of variation is not limited to the comparison of the individuals of a given group or generation among themselves, but successive generations considered as the units of comparison show the same sort of thing. And further successive broods from the same parents exhibit this same phenomenon of variation when compared with one another. Variation is a universal fact--not only among organic things but in the inorganic world as well. The variation which any company of persons shows in stature is paralleled by the variation in the diameter of the grains in a handful of sand, or of the drops in a rainstorm.

When we examine the phenomena of variation carefully we find that they are of two quite distinct categories. The first kind of variation, that which we most frequently think of as "variation," should properly be termed _variability_. Differences of this type are small _fluctuations_ in any and every character, centering about an average or mean, which is itself fairly definite and fixed--less subject to variation in different groups or through successive generations. For example, if we measure by inches the stature of a thousand or more persons chosen at random we find that they may vary from fifty-four to seventy-six inches; the most frequent heights might be about sixty-nine and sixty-four inches among the men and women respectively. The results of such a measurement may be expressed graphically as in Figure 3, which is an expression of the measurement of 1,052 mothers. The measurement of almost any characteristic in a large group of any organisms usually gives a result of the kind figured. The most significant fact here is that this normal variability exhibited by the traits of living organisms follows closely the laws of chance or probability. That is to say, the number of individuals occurring in any class which has a certain deviation above or below the average, is directly related to, or dependent upon (in mathematical terms, "is a function of"), the extent of the deviation of the value of that class from the average of the whole group. The significance of this is that the precise fluctuation which we find in any individual is the result of the operation of a large number of causes or factors, each contributing slightly and variably to the total result.

Many of the most important facts about variability can be illustrated by a simple model such as that suggested by Galton. This is a modification of the familiar bagatelle board, covered with glass and arranged as shown in Fig. 4. A funnel-shaped container at the top of the board is filled with peas or similar objects (Fig. 4, _A_). Below this is a regular series of obstacles symmetrically arranged, and below these, at the bottom of the board, is a row of vertical compartments also arranged symmetrically with reference to the chief axis of the whole system. If we allow the peas to escape from the bottom of the container and to fall among the obstacles into the compartments below we find that their distribution there follows certain laws capable of precise mathematical description, so that it might be predicted with fair accuracy (Fig. 4, _B_). The middle compartment will receive the most; the compartments next the middle somewhat fewer; those farther from the middle still fewer; and the end compartments fewest. If we connect the top of each column of peas by a curved line we get just such a curve as that given by the stature measurements above (Fig. 3), i. e., the normal frequency curve. A curve of the same essential character would result from plotting the dimensions of a thousand cobblestones, the deviations from the bull's-eye in a target-shooting contest, or by plotting the variability of any organismal character--whether it be the stature or strength of men, the spread of sparrows' wings, the number of rays on scallop shells, or of ray-flowers of daisies.

With this model we may illustrate many other essential facts about variability which must be borne in mind when approaching the problems of Eugenics. Before we allow the peas to fall we know quite definitely what the general distribution of them all will be, but we do not know at all the future position of any single pea. Of this we can speak only in terms of probability; the chances are very high that it will fall in one of the three middle compartments, very low that it will be in one of the extreme compartments. But the chances are equal, whatever they are, that it will fall above or below the average or middle position. We see then that in any group there are many more individuals near the average, i. e., mediocre, than there are in the classes removed from the average and the farther the remove of a class from the average the smaller the number of individuals in that class. Yet all the individuals belong to the same whole group. This leads to the very important fact that _an individual may belong to a group without representing it fairly_. The average individuals are the most representative. But in order to get a correct idea of the whole group we must know, first, to what _extent_ deviations occur in each direction, above and below the group average, and, second, the average _amount_ by which each individual of the group deviates from this group average. That is, we must know the amount of variability as well as the extent of the greatest divergence from the average. The best measure of the amount of variability exhibited by any group of objects or organisms is not the simple average or mean of all the individual deviations from the average of the group; it is the square root of the mean squared deviations from the group average. This is called the _index_ of variability or "standard deviation." In order to make possible the comparison of the variabilities of characteristics measured in unlike units, such as weight and stature, this index must be converted into an equivalent abstract quantity. This is done by reducing the index of variability to per cents of the group average, giving what is called the _coefficient_ of variability. Thus, for example, in stature the index of variability (standard deviation) of certain classes of men is approximately 2.7 inches; that is, in a large group of men the amount of individual variation from the average height of 69 inches amounts to 2.7 inches. This gives an abstract _coefficient_ of about 4.0 per cent, for 2.7 equals 3.9 per cent of 69. Similarly the index of variability of the weight of a group of university students has been found to be about 16.5 pounds; the average weight is about 153 pounds, and the coefficient of variability is therefore about 10.8 per cent (16.5 equals 10.78 per cent of 153). Although pounds and inches may not be compared, these two abstract coefficients may be, and we may say that men are more than twice as variable in weight as in stature.

Turning now to variation of the second type we find what are ordinarily called _mutations_, or differences quite properly termed _variations_, in a strict sense, as distinguished from the preceding fluctuations or variability phenomena. Mutations or variations are abrupt changes of the average or type condition to a new condition or value which then becomes a new center of fluctuating variability. The difference between variability and variation may be illustrated through an analogy suggested by Galton (Fig. 5). A polygonal plinth, or better a polyhedron, resting upon one face is easily tipped slightly back and forth, but after slight disturbance it always returns to its first position of stable equilibrium. Each face of the plinth or polyhedron represents an organismal characteristic; these slight backward and forward movements represent fluctuations, always centering about the average condition. An unusually hard push sends the plinth over upon another face in which it has a new position of stability; this represents true variation or mutation. In this new position it is again stable, may again be rocked back and forth showing fluctuations about its new average position.

The essential difference between true variation and fluctuation or variability of an extreme nature, is with reference to the inheritance of such divergence. In the second generation the offspring of extreme variates or fluctuations have not the same average as their own parents but an average much nearer that of the whole group to which their parents belonged; the average stature of the children of unusually short or tall parents is respectively greater or less than that of their own parents--that is, is nearer the average of the whole group of parents, provided the shortness or tallness of the parents is a fluctuation. When the shortness or tallness is a true variation or mutational character, offspring have approximately the same average stature as their immediate parents, although the children of course show fluctuation in height so that some are slightly above and others slightly below the parental height.

Mutations may occur through the addition or the subtraction of single characters of the simple or unit type. Such are the variations from brown or blue eyes to albino, five fingers to six, and the like. These are the familiar "sports" of the horticulturalist and breeder. They are of the greatest value in evolution, for it seems quite likely that it is only through the permanent racial fixation of these mutations that permanent changes in the characters of a breed may be effected, i. e., evolution occurs primarily through mutation.

In connection with the general subject of variation we should mention briefly certain aspects of the recent work of Johannsen and Jennings, showing that many organic specific groups or "species," whose characters, when measured accurately give what is called a normal variability curve similar to that of stature illustrated in Fig. 3, are not really homogeneous groups of fluctuating individuals as the curves would indicate superficially, but that each gross group or species is actually composed of a blend of a number of smaller groups, each with its own average and fluctuating variability. It is only when these are taken all together as a lump that they fuse into a single and apparently simple curve.

For example, the curve shown in Fig. 6, A, which is approximately that of a normal distribution, in some cases might be shown by experimentation to consist in reality of several truly distinct elements, say three for purposes of illustration, as shown in Fig. 6, B. Each of these sub-groups has its own average and its own amount and extent of variability (fluctuation) and it is only by adding them together that we get the larger group. Each of these elementary groups is called a "pure line," which is defined as a group of organisms, all of which are the progeny of a single individual. The characteristics of each pure line remain stable through successive generations, each about its own average; and it is chiefly this fact that enables us to identify the different lines. Transition from the condition of one pure line to another occurs only as a mutation. At present the theory of the pure line is strictly applicable only to organisms reproducing asexually or to self-fertilizing forms where the group observed is actually composed of the progeny of a single organism. It is hardly possible to say as yet whether or not this extremely important theory is essentially applicable to the human species or any species where two organisms are involved in the establishment of a race or line, but there are some indications of a circumstantial nature that it is thus applicable in its essentials and so modified as to include this fact of biparental inheritance.

With this bare skeleton of the subject of variation before us let us see how facts of this kind may have any significance for the subject of Eugenics, any bearing upon the possibility of racial improvement. When any of the varying human traits, and they all vary, is measured carefully and the results tabulated we find that they give us a curve approximating the normal frequency curve, such as we have described above and illustrated in Fig. 3. The coefficients of variability of a great many human traits are known and a few representative coefficients are given in Table I. This type of variability is given then, by measurements of physical characteristics of all kinds, and, what is of greater importance, physiological traits, including mental and moral characteristics, so far as they can be measured by present methods, vary in just the same way. Annual individual earnings give us a curve closely similar to that of a normal frequency curve with an approximate minimum limiting value. Even the tabulation of citizens according to their social standing or "civic worth" gives the same sort of thing. This has been brought out nicely in Galton's discussion of Booth's classification of the population of London.

TABLE I

_Coefficients of Variability of Certain Human Traits_

Adult Stature 3.6 to 4.0
Length at Birth 5.8 to 6.5
Length of Limb Bones 4.5 to 5.5
Cephalic Index 3.7 to 4.8
Skull Capacity 7.0 to 8.0
Weight (University Students) 10.0 to 11.0
Weight at Birth 14.2 to 15.7
Weight of Brain 7.0 to 10.6
Weight of Heart 17.4 to 20.7
Weight of Liver 14.3 to 22.2
Weight of Kidney 16.8 to 22.5
Lung Capacity 16.6 to 20.4
Squeeze of Hand 13.4 to 21.4
Strength of Pull 15.0 to 22.6
Swiftness of Blow 17.1 to 19.4
Dermal Sensitivity 35.7 to 45.7
Keenness of Eyesight 28.7 to 34.7

It is not so easy to answer the question whether mutations or true variations are occurring frequently in the human species. Usually it is impossible to distinguish between an extreme fluctuation and a true variation without experimental test and the observation of the behavior of the varying trait through several generations. In most instances this has been impossible with human beings. From collateral evidence it seems quite probable that man is mutating with considerable frequency, especially with respect to psychic traits.

The evolution of the race could be directed more easily and permanent results attained more rapidly through taking advantage of valuable mutations than in any other way. A race truly desiring to progress would foster carefully anything resembling mutation in a favorable direction. As a matter of fact, however, our social custom leads us to look with disfavor upon most youthful traits that seem unusual or out of the ordinary. It would be difficult to devise a system of "education" which could more effectively repress than does our own the development of unusual mental traits. In this connection "abnormal" or "eccentric" may often mean a mutation in a profitable direction, a getting away from the average of mediocrity in the direction of improvement.

It is clear that we have the raw materials for race improvement. There are some individuals with more and some with less than the average in any respect--physical, mental, moral. The average of a whole social group can be shifted by subtraction at one end or addition at the other, or more easily and more effectively by both together. In order to raise the general average of the value of any of these traits it is not necessary to strive to exceed the known maximum value in any respect. The study of the "pure line," as mentioned above, shows that this may for a long time remain impossible, or at any rate difficult, pending the appearance of a mutation in a favorable direction. We can, however, raise the general average of physical strength or of mental or moral ability by increasing the relative number of individuals in the upper groups or by diminishing the number in the lower groups, most easily of course and most effectively by doing both of these things. By increasing the numbers composing the lines which form the upper elements of a social group we not only add immensely to the total value of the group but we do actually change somewhat the general average. On the other hand numerical increase in the lines in the lower part of the group will actually lower the average of the whole, though it does not actually affect the number of individuals in the more able and valuable classes.

Another consideration is of great importance here. The average is affected only slightly by the change of individuals from class to class near the average. But the shifting of even one or two per cent of the individuals into or out of extreme positions has a very marked effect upon the character of the total group and upon the average. In the life of the State the character of the general average of the citizens is of the greatest importance, and comparatively small deviations in the average of civic worth may mean much as regards the history of a democracy. Of course the average individuals in a social group may not be those of greatest influence; even when taken all together they may not determine the trend of the life of the society; but that does not alter the essential fact that the condition of the average of the population is of very great moment to a democratic state.

Many of our social endeavors to-day serve in effect to raise individuals from one of the lower groups up to or toward the average. Millions of dollars and an incalculable amount of time and energy are spent annually in striving to accomplish this kind of result. How immeasurably greater would be the benefit to society if the same amount of energy and money were spent in moving individuals from the middle classes on up toward the higher. In the development of our societies we need to use every possible means to carry individuals from positions near the average to positions above the average, and the farther this remove is above the average both in its starting point and its stopping point, the better for the social group. Elevation from mediocrity to superiority has far greater effect upon the social constitution than has elevation from inferiority to mediocrity.

As the Whethams have written recently: "Of late years, the duty of the State to support the falling and fallen has been so much emphasized that its still more important duty to the able and competent has been obscured. Yet it is they who are the real national asset of worth, and it is essential to secure that their action should not be hampered, and their value sterilized, by the jealousy and obstruction of the social failures, and of others whom pity for the failures has blinded. Mankind has been shrewdly divided into those who do things and those who must get out of the way while things are being done, and if the latter class do not recognize their true function in life, they themselves will suffer the most. The incompetent have to be supported partially or wholly by the competent, and, even for their own good, it would be worth while for the incompetent to encourage the freedom of action and the preponderant reproduction of the abler and more successful stocks. It is only where such stocks abound that the nation is able to support and carry along the heavy load of incompetence kept alive by modern civilization."

In discussing the general subject of variation and variability in this connection, we must take always into account the biological distinction between variation and functional modification, between innate and acquired traits. Only the former are of real and primary value in evolution. The distinction is familiar and we cannot dwell upon it here; but it is of particular importance in dealing with social improvement and we shall return to it in the next chapter. Many "social variations" are in reality not variations at all, but modifications; although these may be of the greatest value to the individual modified, they are artificial things without permanent value to the race. So many of the distinguishing personal traits are the results of nurture rather than of nature. They represent the result of the incidence of special factors in the environment. It is extremely difficult and at times impossible to distinguish between variations and modifications in adult characters, but in general the distinction is usually clear upon careful analysis.

The changing of the innate characters of the human race is a slow process, depending chiefly upon the advantage taken of the appearance of real mutational variations. On the other hand, it is comparatively easy to improve the condition of the individual by improving his environing conditions--cleaning him, educating him, leading him to higher ideals in his physical and mental and moral life. But as this is easy, so it is impermanent. All this is modificational and has no influence upon the stock. This is not opposed by the Eugenist; it simply is no part of his province, for its effect is not racial. By releasing a deforming pressure it may permit the individual to come back to his real structurally determined condition, but the structural condition itself is not thus affected. It is temporary and must be done over with each generation, or on account of the unfortunate habit of "backsliding," even at intervals shorter than that of a generation.

* * * * *

Let us now turn to another phase of our subject and consider the biological methods of the description and measurement of heredity, as a preliminary to our next chapter in which we shall discuss the bearings of the facts of human heredity upon the possibility of the formation of a permanently improved human breed.

The fact of heredity is one of the most familiar and patent things about organisms. "Do men gather grapes of thorns or figs of thistles?" For we may define heredity as the fact of general resemblance between parent and offspring. This simple definition is disappointing to many persons. "Heredity" is so often supposed popularly to refer only to some occasional, striking, and unusual similarity within a family respecting certain traits or peculiarities. Very often the idea of heredity seems shrouded in mystery: it is some uncanny relation which explains peculiarities and helps the novelist out of difficulties, but is itself inexplicable. In truth, however, the fact that a boy, like his father, has a head and a heart and hands and feet, physical traits characteristic of the human species, that he begins to walk and talk and shave at about the same age as his father did--all this is the fact of heredity. The fact that guinea pigs produce guinea pigs and not rabbits is the fact of heredity. Often it is true that this resemblance is strikingly particular. All know of family traits; we may have our father's eyes or nose, our mother's hair or disposition, a grandfather's determination or a grandmother's patience. But these particular individual resemblances are no more and no less illustrations of heredity than the fact that on the whole children are more like their parents than like other human beings.

The subject of heredity is of supreme importance in the practice of Eugenics. The facts of no other department of biological inquiry are of equal value, and at the same time there is probably no biological subject regarding which there is so much misunderstanding. Of the many phases of this extremely fascinating subject there are chiefly two with which we are particularly concerned as Eugenists. These are the questions: first, how completely are all the distinguishing traits of either or both parents represented in the offspring; and, second, how completely is each trait inherited that is inherited at all? In other words, what we are chiefly interested to know, as bearing upon the subject in hand, is whether all or only some of the characteristics of our parents are heritable, and whether the offspring show each inherited trait with the same intensity shown in the parent, or more, or less.

One of the leading British students of heredity has said that no one should undertake the study of this subject unless he can instantly detect and explain the fallacy involved in the familiar conundrum, "Why do white sheep eat more than black ones?" It is perhaps the elasticity of our language that makes possible the mental confusion involved in this question, but yet it is certainly true that we do tend to confuse individual and statistical statements. We must remember, in connection with this subject particularly, that an individual may belong to a group without representing it, and that within a group there are many more individuals with average than with exceptional characteristics. The mediocre is common, the extremes are rare. And yet an unusual individual may really be an outlying member of a normal group.

In describing the facts of hereditary resemblance between successive generations two formulas are available. One deals ostensibly with the individual--the Mendelian formula: the other deals with the group--the statistical formula. It seems entirely probable that these are not formulas for describing two essentially different processes or forms of heredity, but that in reality these are two ways of describing the same facts seen from two different points of view. The Mendelian formula regards each individual separately and describes its heredity thus. The statistical formula regards the whole group as the unit and considers the individual not as such, but as one of the crowd, concerning which statements can be made only in terms of averages and probabilities; black sheep and white. Of these two formulas the Mendelian is obviously of much the greater importance on account of its more exact, more particular character; its greater definiteness gives it a value in the treatment of eugenic problems that statistical statements must inherently lack. While much has been written of late regarding the Mendelian formula of heredity, we shall find it profitable to repeat here its general outlines and to recall a few of the essential features of this important law that we shall make much use of later.

Let us have a concrete illustration. One of the simplest cases is that of the heredity of color in the Andalusian fowl which has been so clearly described by Bateson. There are two established color varieties of this fowl, one with a great deal of black and one that is white with some black markings or "splashes"; for convenience we may refer to these as the black and white varieties respectively. Each of these breeds true by itself. Black mated with black produce none but black offspring, white mated with white produce none but white offspring. Crossing black and white, however, results in the production of fowls with a sort of grayish color, called "blue" by the fancier, though in reality it is a fine mixture of black and white. At first sight we seem to have a gray hybrid race through the mixture of the black and the white races. Not so: for if we continue to breed successive generations from these blue hybrid fowls we get three differently colored forms. Some will be blue like the parents, some black like one grandparent, some white like the other grandparent. Not only this but we get certain definite proportions among these three classes of descendants. Of the total number of the immediate offspring of the hybrid blues, approximately one half will be blue like the parents, approximately one fourth black, and one fourth white like each of the grandparents. Now comes the most important fact of all. These blacks, bred together produce only blacks, the whites similarly produce only whites; the blues, on the other hand, when bred together produce progeny sorting into the same original classes and in the same proportions as were produced by the blues of the original hybrid generation. Their blacks and whites each breed true, their blues repeat the history of the preceding blues. No race of the hybrid character can be established: blues always produce blacks and whites, as well as blues. A summary of this history in graphic and diagrammatic form is given in Fig. 7.

This law of heredity was first discovered about forty-five years ago by Gregor Mendel, working with peas in the garden of the Augustinian monastery in Bruenn, Austria. His work curiously failed to arouse the interest of contemporary scientists and his results were soon completely lost sight of. The independent rediscovery of Mendel's formulas of heredity, about ten years ago, was probably the most important event in the history of biology and evolution since the publication of "The Origin of Species."

In most cases of Mendelian heredity the progeny are less easily classified than in the case above, because the hybrid individuals resemble one or the other of the parents, quite or very closely. For instance the crossing of the black and white varieties of guinea pigs gives hybrids that are all black like one parent. That is, when the black and white characters are brought together these do not appear to blend into a gray or "blue," as in the case of the Andalusian fowl, but one character alone appears; the black seems to cover up or wipe out the white. This illustrates the frequent phenomenon of _dominance_; one of the two contrasting characters, in this case the black color is said to dominate over the other and the two traits are described as _dominant_ and _recessive_ respectively. Fig. 8 gives a graphic representation of the history of such a cross. When the black looking hybrids are crossed together the progeny fall into but two groups, one resembling each of the grandparental forms. Three fourths of the progeny now resemble superficially the hybrid form and at the same time one of the grandparents--the dominating black form, while the remaining fourth resembles the other white grandparent. However, we know that the black three fourths do not in reality constitute a homogeneous class but that this includes two distinct groups; one group of one fourth of the whole number of progeny (i. e., one third of all the blacks) are truly black like their black grandparents and in successive generations will, if bred together, produce none but blacks of the same character, i. e., pure blacks: the remaining two fourths of the whole number of progeny (two thirds of all the blacks) in this generation are actually hybrids and in the next generation, if bred together, will give the same proportions of the two colors as were found in the whole of the present generation, i. e., three fourths black, one fourth white. Of these the whites always produce whites, the blacks always produce blacks and whites in the approximate proportions of 3:1; a certain proportion of these--one third (one fourth of the whole generation) always remain blacks, the other two thirds (one half of the whole generation) again produce blacks and whites. In such cases as this where the phenomenon of dominance appears, and this is the usual course of events, it is impossible to say which individuals _are_ the hybrids. Only after their progeny are studied can we say which _were_ the hybrids.

In the crossing of the black and white Andalusian fowls described above the phenomenon of dominance does not appear; when the two color characters are brought into a single individual neither appears alone, neither overcomes nor is overcome by the other. In the crossing of the black and white guinea pigs dominance is complete; when the two color characters are brought into a single individual only one color appears, the second becomes recessive, that is, it remains present as we know from the later history of such hybrids, but it is not visibly indicated. Besides the Andalusian fowls there are known several other instances of the absence of dominance and there are many cases where dominance is incomplete, i. e., where one character merely tends to dominate the other. And in a few instances dominance is irregular, i. e., sometimes one character dominates, at other times or under other circumstances it does not, as with certain forms of the comb or the feathering of the legs in the common fowl, or with the presence of an extra toe in the domestic cat, the rabbit, and guinea pig. And even in those cases where dominance is said to be complete the trained eye of the breeder can frequently distinguish between the hybrid and the pure bred dominant individuals. The phenomenon of dominance, therefore, is not an essential of the Mendelian theory although it is a frequent, we may say usual, relation.

It does not come within our province to attempt an explanation of this formula of heredity by describing some of the more fundamental conditions upon which it depends. In fact, no complete explanation is yet possible, although several explanatory hypotheses have been suggested. We may outline briefly that which seems the most satisfactory in that it serves to account for most of the facts in Mendelian heredity in a comparatively simple manner. The germ of an organism, we have seen, somehow contains dispositions of materials which primarily determine the characteristics of the organism developed from that germ. To these dispositions or configurations the term of "determiners" has been applied. In a pure variety like the black Andalusians, all the germ cells of each fowl are alike in having this determiner for black color. When two such fowls are mated together their descendants will result from the fusion of two germ cells, _each_ containing the determiner for black color; that is, the germ of the new individual comes to have a double determiner, one from each parent, for this trait. In the white variety all the germ cells are alike in _lacking_ this determiner; blackness is entirely absent and all their descendants are formed from germ cells entirely without black determiners. When the single germ cell of a black fowl with its single black determiner is fertilized by a germ cell from a white fowl without any determiner for black the resulting hybrid has a color produced by only a single determiner, that from the black parent, and in this case the blackness is not as fully expressed because produced by only this single determiner and the fowl appears gray or "blue"; that is, the black produced by a single determiner is in this case not as black as that produced by the double determiner. Now of course this hybrid fowl forms germ cells containing determiners for color, but these cells, instead of being all alike and with semi-black determiners corresponding with the semi-black characteristics of the individual, are of two different kinds--some are like those of each of the grandparents which fused to give origin to the parent forms, and these are formed in approximately equal numbers--one half with the black determiner, one half without it. When two such fowls are bred together the chances are equal for certain combinations of germ cells; the chances are equal that the "black" or "white" germ cell of the one individual shall meet and conjugate with the "black" or "white" germ cell of the other individual. The result may be expressed algebraically as follows, using the letters _B_ and _W_ to indicate respectively germ cells with and without the black color determiner.

Germ cells of first parent _B_ + _W_
Germ cells of second parent _B_ + _W_
-------------
_BB_ + _BW_
_BW_ + _WW_
-----------------
Combinations in the germ of the offspring _1BB_ + _2BW_ + _1WW_

That is, one fourth are pure black (_BB_), one fourth pure white (_WW_), and the remaining half are hybrids, black and white (_BW_). The pure blacks again form germ cells, all possessing the determiner for blackness; the pure whites form germ cells all lacking the determiner for blackness; the hybrid blues produce again equal numbers of germ cells possessing and lacking the determiner for blackness. The relation of the germ cells and the organisms forming them and developing from them is shown in the diagram in Fig. 9.

In the more common cases where the phenomenon of dominance appears, as in the guinea pig, this is explained by saying that here a single determiner for blackness is somehow sufficient to produce the color. In such cases the black color observed may result either from a single (_BW_) or from a double (_BB_) black determiner in the germ which forms the organism. Only when the black determiner is entirely absent (_WW_) does the white color appear in the developed organism and the individual is then said to exhibit the recessive characteristic.

Another possible type of mating is that between a member of a pure race, either dominant or recessive, and a hybrid individual. This form of mating is very common in some of the pedigrees that we shall examine later. The results of such a mating, first between a hybrid and a recessive individual can be most easily described by considering a cross between black and white forms and expressing the result algebraically.

Germ cells of first parent (white or recessive) _W_ + _W_
Germ cells of second parent (hybrid) _B_ + _W_
-------------
_BW_ + _BW_
_WW_ + _WW_
---------------------
_2BW_ + _2WW_

That is, returning to the example of the Andalusian fowls, the progeny will be one half hybrid blues and one half whites--no black at all. If the cross had been between black hybrid guinea pigs and white recessive specimens the result would have been half hybrid blacks and half pure whites.

Or supposing the mating to have occurred between the pure dominant (black) and the hybrid the result would have been, in the fowls half pure black and half hybrid blue; in the guinea pig all the progeny would have been black, half pure blacks and half hybrid blacks.

Germ cells of first parent (black or dominant) _B_ + _B_
Germ cells of second parent (hybrid) _B_ + _W_
-------------
_BB_ + _BB_
_BW_ + _BW_
----------------------
_2BB_ + _2BW_

In the case of the guinea pigs, although the progeny all look alike (black) their history would show that they were fundamentally unlike, for if crossed with white again the result would be the production of all black looking guinea pigs from the cross with the _BB_ forms, and half black and half white from the _BW_ cross.

On account of the fact of variation every individual is in a certain sense a hybrid. One's two parents have the species characters in common but there are certain distinctive traits that hybridize and follow Mendel's law of heredity. By no means is it to be understood that all individual distinctive traits follow this rule in heredity. Many individual characteristics are what we have learned to call fluctuations--small deviations above or below an average condition of a group. Such differences play no part in Mendelian heredity. Other characteristics may be bodily modifications resulting from the direct reaction between the body tissues and the environing conditions; such traits would not be represented in the organization of the germ cells and consequently would not be inherited at all. At present it seems that the only characteristics that "Mendelize" are those known as "unit characters." Such characters seem to have their origin in real variations or mutations and though each may show fluctuations, these fluctuations in themselves are not hereditary.

This conception of the unit character is an extremely important element in the whole Mendelian theory and it has extended beyond the field of heredity and led to a radical change in our notions of what an organism really is. It is, of course, true in a sense that an organism is a unit, an organism is one thing; but at the same time it is true that an organism is fundamentally a collection of units, of structural and functional characteristics which are really separable things. A few of these units were mentioned in the first pages of this chapter and others are mentioned on a later page. They serve as the building blocks of organisms: individuals of the same species may be made up of similar combinations or of different combinations. One unit or a group of units may be taken out and replaced by others.

From the standpoint of heredity, and particularly from our eugenic point of view, the most important results of the unit composition of the organism lie in the fact that these units remain units throughout successive generations and throughout successive and varying combinations, whatever their associations may be from generation to generation. It is a fact of the greatest eugenic significance that a pure bred individual may be produced by a hybrid mated either with a pure bred or with another hybrid; and that the pure bred resulting will be just as pure bred as any. "Pure bred" now means pure bred with respect to certain traits only. An individual may be pure bred in certain of its characteristics, hybrid in others. Practically there is no such thing as an individual which is either pure bred or hybrid in _all_ its traits. One of the chief contributions, then, of Mendelism to the subjects of Heredity and Eugenics is this--that a pure bred may be derived from a hybrid in one generation: the pure bred produced by a long series of hybrid individuals is just as pure as the pure bred which has never had a hybrid in its ancestry. Another important consequent is, that among the offspring of the same parents some individuals may be pure bred and others hybrid. Community of parentage does not necessarily denote community of characteristics among the offspring. Yet by knowing the ancestry for one or two generations we can know the qualities of the individual. Guesswork is eliminated and the importance of the qualities of the individual is enormously emphasized. It is necessary only to suggest the social and eugenic significance of such facts relating to characteristics that are of social or racial importance.

We shall have occasion in the next chapter to enumerate some of the human unit characters whose heredity has been traced and which have been found to Mendelize, but we may mention here a few Mendelizing units in other organisms in order to give some idea of the kind of character which behaves as a unit and of the range of the forms which have been found to show Mendelian phenomena in their heredity. Among the higher animals one might mention the absence of horns in cattle and sheep; the "waltzing" habit of mice and the pacing gait of the horse; length of hair and smoothness of coat in the rabbit and guinea pig; presence of an extra toe in the cat, guinea pig, rabbit, fowl; length of tail in the cat; and in the common fowl such characters as the shape and size of the comb, presence of a crest or a "muff," a high nostril, rumplessness, feathering of the legs, "frizzling" of the feathers, certain characters of the voice, and a tendency to brood. Among plants may be mentioned such characters as dwarfness in garden peas, sweet peas, and some kinds of beans; smoothness or prickliness of stem in the jimson weed and crowfoot; leaf characters in a great variety of plants; in the cotton plant a half dozen characters have been found to Mendelize; seed characters such as form and amount of starch, sugar, or gluten; flat or hooded standard in the sweet pea; annual or biennial habit in the henbane; susceptibility to a rust disease in wheat. We should not fail to mention that scores of color characters are known to Mendelize, such as hair or coat color and eye color in animals and the colors of flowers, stems, seeds, seed-coats, etc., in plants. The list of Mendelizing traits in different organisms now extends into the hundreds and is increasing almost weekly.

Before leaving the subject of Mendelism we should say that the phenomena, as described above in the Andalusian fowl and guinea pig, are among the simplest known. And while such simple formulas serve to describe the phenomena of heredity in a large number of instances, yet in a great many other cases the descriptive formulas are more complicated. We cannot in this place describe any of these complications. For a full discussion of these and of the whole subject of Mendelism the interested reader is referred to Professor Bateson's work on "Mendel's Principles of Heredity" (1909). It must suffice to say here that in color heredity, for example, such ratios as 9:3:4 or 12:3:1 in the second filial generation instead of the more frequent 1:2:1 or 3:1 are explainable upon essentially the same relations as these simpler and more typical ratios. And further, many less usual Mendelian phenomena, which we cannot undertake to describe here, are associated with what the specialist technically terms "sex limitation," "gametic coupling," and the like.

It is often said that the Mendelian formula has a very limited applicability to human heredity. This is probably true if we consider carefully the grammatical tense in which this statement is made. And yet it is almost certainly true that heredity in man is to be described by this law. This apparent paradox is easily explained. The only characters whose history in heredity follows this formula are the unit characters. A complex trait is not heritable, as a whole, but its components behave in heredity as the separate units. It is perfectly well known that we are deeply ignorant regarding this phase of human structure. Our ignorance here is not the necessary kind, however, it is merely due to the newness of the subject--we have not had time to find out. How can we say that a complex trait is or is not inherited according to some form of Mendel's law when we do not know the nature of the units of which it is composed? We can make no statements about the Mendelian inheritance of such a trait until it is factored into its units. A considerable number of human characteristics are really known to be heritable according to this formula, enough so that several general rules of human heredity have been formulated. But it is also quite within the range of possibility that some traits really do not follow this law, although it cannot yet be said definitely that this is or is not the case. On the whole, then, we cannot, for the next few years, expect too much from the application of Mendel's laws to human heredity, however much this is to be regretted.

Shall we then decline to say anything about the heredity of the great bulk of human characteristics? By no means: we have seen that in our bagatelle board we talk very definitely about the distribution of all the peas, though only about the probable history of one pea. Mendel's law deals with individual inheritance. When we cannot apply this formula we have left still the possibility of talking about human heredity in the group as a whole. That is to say, we have left the opportunity of describing heredity by the statistical methods, with the crowd, not the individual, as the unit. Since we are forced into extensive use of this formula by our present and temporary ignorance of the applicability of Mendel's rule we must get a clear notion of how the statistical method is applied in this matter.

The method is the same as that employed by the statistician in measuring the relatedness of any two series of varying phenomena. If two quantities or characteristics are so related that fluctuations in the one are accompanied in a regular manner by fluctuations in the other, the two quantities or characters are said to be correlated. For instance, the temperature and the rate of growth of sprouting beans are related in such a way that increase in the former is accompanied in a regular way by increase in the latter; or the width and height of the head, or the total stature and the length of the femur similarly vary regularly together so that they are said to be correlated to a certain extent which can be measured. This correlation may result from the fact that one condition is a cause, either direct or indirect, of the other; or there may be no such causal relation between the two phenomena, both resulting more or less independently from a common antecedent condition or cause.

This phenomenon of correlation is not limited among organisms to the comparison of two or more different characters in a single series of individuals; it is applicable also to the comparison of two series of individuals with respect to the same characteristic. Thus we may compare the stature of a series of fathers with the same measurement in their sons. It is this form of correlation with which we are particularly to deal here. While it is not necessary to understand just how this subject is dealt with by the statistician we should know one or two of the elementary principles involved, in order to appreciate the statistical form of many statements about heredity.

The stature of men may be said to vary usually between limits of 62 and 76 inches, the average height being about 69 inches. In the complete absence of heredity in stature we should find that fathers of any given height, say 62 or 63 or 76 inches would have sons of no particular height but of all heights with an average of 69 inches, the same as in the whole group. Or if stature were completely heritable from one generation to the next the _total generations being the units compared_, then 62 or 63 or 76 inch fathers would have respectively sons all 62, 63, and 76 inches tall. When we examine the actual details of the resemblance we find, as a matter of fact, that neither of these possibilities is actually realized. What we do find is that fathers below or above the average height have sons whose average height is also below or above the general average but not so far below or above the general average as were the fathers. If we measured a large number of pairs of fathers and sons with respect to stature we should find each generation with a variability such as that illustrated in Fig. 3 of the stature of mothers, the limits here, however, being about 62 and 76 inches. But if we measured all the sons of 62-inch fathers they would be found to vary say from 62 to only 69 inches, averaging about 66 inches. Similarly 63-inch fathers would have sons from 62 to 70 inches tall, averaging about 66.5 inches, or 76-inch fathers might have sons from 69 to 76 inches in height, averaging about 72 inches, and so on for fathers of all heights. In general, then, we may say that fathers with a characteristic of a certain plus or minus deviation from the average of the whole group have sons who on the whole deviate in the same direction but less widely than the fathers, although the fact of variability comes in so that some few of the sons deviate as widely as, or even more widely than, the fathers, others deviate less widely than the fathers from the average of the whole group. This is the general and very important statistical fact of _regression_.