through the white, the first generation should all be grey, which is a case of reversion brought about by re-combination of characters previously existent. This combination of factors gives a ratio 9-1, but we can see that this as well as the 9-3-4 ratio is only a modification of the 9-3-3-1 ratio that we first obtained in dealing with double characters. We have in this way obtained an indication that there may exist a very complicated association of determiners for traits that appear outwardly to be of the most simple character. It is impossible for us to say in fact whether a trait is the expression of a single determiner or of a large number of determiners, and the only way in which this can be settled is extensive experimentation. It appears already

that certain characters never appear in association with other certain characters, while on the other hand some characters appear only in association with each other. This feature has long been familiar to us in the occurrence of hemophilia which is transmitted in a direct relationship to sex, and we have in addition a large number of secondary sexual characters that are ordinarily limited to their respective sexes. In this connection it may be of interest to note that sex itself may be produced by a sex-determiner, although the evidence from the various types of organism is inconclusive as to which sex is the dominant one.

There is still much doubt whether Mendel's law may be applied universally to inheritance. It seems, at least, that many apparent exceptions occur. The majority of these are cases in which the first hybrid generation is apparently a blend of the traits of the

parents, and where this blended condition appears to be continually reproduced in subsequent generations. One of the best known examples of this is the skin-color in man. The mating of a negro with a white man usually produces a mulatto, intermediate between the two colors of the parents. This might, of course, easily occur in the Mendelian method, but if this theory were to be applied to later generations, from the marriage of two mulattoes we should expect one white, two mulattoes, and one negro, which is an uncommon, perhaps unknown, result. It is quite possible, however, that this case is only a somewhat more complicated example of the process which we observed in the color of rabbits. Another more marked example of this blending occurs in the crossing of lop-eared with ordinary rabbits in which case all the descendants have ears of intermediate length. Here again, however, the character of the ear-length may depend on a large number of independent factors, so that no conclusions should be drawn until a very large number of experiments have been made. In these cases we are dealing with characters that have been produced by continuous selection through many, many generations in which the final product is a combination of many factors all having certain effects on the character in question, but independently inheritable. The rebuilding of this combination, once broken down by crossing, must necessarily be a difficult process, unless enormous numbers of individuals are raised in the second hybrid generation. It has also been objected that the pure types in the second hybrid generation are not absolutely pure, that they retain traits of hybrid character, and have a tendency to throw back to it. Here again, however, there may be a question of action of numerous pairs of factors. In the Mendelian crossing all the individuals of the first generation are hybrids, in the second half are hybrids and half are pure in respect to any common character. If all these individuals reproduce at the same rate by self-fertilization the percentage of hybrids is halved in each successive generation and after a time their proportion becomes negligible. A selffertilizing population would therefore be expected to consist of a number of perfectly pure types showing no variations of

hereditary value, and this is exactly what occurs in the results of the pure line experimenters. We cannot by any means yet say that the Mendelian law applies to all characters in all kinds of living organisms. It is certain, however, that it applies to numerous characters in many species of plants and animals, and it seems doubtful whether any real exception has yet been found. While a large group of students of heredity have confined themselves to its Mendelian relations, another but much smaller group has attacked the subject from its statistical side. Sir Francis Galton, who was trained both as physician and mathematician, believing that the phenomena of heredity showed a certain regularity, endeavored to determine the laws under which this acted, and as a result of his investigation promulgated Galton's law to the effect that an individual inherits one-half of its traits from its parents, one-fourth from its grandparents, and so on in diminishing ratio through ascending generations. This law has been modified somewhat by his successors, but it remains approximately true and is distinctly apparent in certain human traits, such as stature. In investigating this character of stature, a secondary principle was indicated, that the offspring of extreme types reproduce the type in an intermediate degree, about half way between the parent and the norm of the race, in other words that in regard to racial traits there is a constant tendency toward a mean between the two extreme variations in regard to each particular trait. The coefficient of heredity for stature in men is .51, which is unusually high, indicating either that stature is very largely a matter of heredity, or that environmental conditions tend to have similar effects on father and son. Within a pure line, the differences being chiefly acquired differences and due entirely to environmental conditions, the coefficient of heredity of these differences is o. We must bear in mind that the statistical method instructs us merely as to effects of heredity in the mass, and that it can scarcely give us an insight into the mechanism by which heredity works. The chief field for the statistical method will include those cases which are too complex for the Mendelian analysis.

Let us consider now briefly some of the practical applications

of our knowledge of heredity, and in this we must be even more cautious, more conservative than we were in accepting laboratory or study-chair conclusions. In plant life, at least, certain valuable suggestions have been obtained from Mendelism, especially in regard to the fixing of new types. If the desired characters are recessive they will breed true and will not require fixing beyond the first selection. With dominants ordinary mass selection will be unsatisfactory because a number of recessives will recur each year, although progressively diminishing. In order to fix a dominant we must grow the seeds of each plant of the second generation separately and among its offspring the groups that show no recessives will contain no hybrids and will therefore breed true. We must bear in mind, however, that in reducing this strain to a pure line, there is at the same time a tendency toward loss of vigor as has been proven both by the scientist and by the practical breeder. The indication from this, then, is that occasional crossings are desirable. The sum of the experience of animal breeders is practically to breed in to fix type, breed out to secure vigor, in general compromise, and theory can offer little in addition.

When we come to apply any rules of heredity to the human race, we shall meet with even still greater difficulty, whether these rules be the few simple ones that we think we have already found, or whether they be the more complete rules that some people expect to find in the future. In relation to the human race, heredity has developed a special school of science,—namely, that of eugenics, which owes its title and its existence to the work of Francis Galton. National eugenics as defined by him "is the study of the agencies under social control which may improve or impair the racial qualities of future generations either physically or mentally." According to Darwin's theory the forces for the betterment of a race consisted of natural selection working by means of a selective death-rate toward the survival of the fitter. This was the mechanism undoubtedly which controlled the evolution of primitive life. We must, however, inform ourselves whether it is effective at present. A selective death-rate means that a certain proportion of a community or

species in any given generation will die as the result of constitutional causes, as the result of weakness or susceptibility inborn in the individual. As long as the environment of the species remains constant, the value of the selective death-rate is unity or 100 per cent. As conditions of environment change, its value is lessened, and at present for civilized communities it is assumed to be between fifty and seventy-five per cent; in fact extensive statistics have placed it at sixty per cent. Our present environment, working largely through the forces of sentimentalism and of democracy, has tended very markedly to diminish this value still further because we do our utmost to protect the weak from death. This procedure would impose its additional burden on each generation but without any marked cumulative effect upon successive generations if it were a fact that all types or classes of human beings were equally fertile, if each group according to its fitness produced an equal number of offspring with every other group; but this does not seem to be the case, because it appears that the fitter stocks are less productive at present, that the less fit or unfit stocks are more fertile, and when we add to this the fact, or what appears to be a fact, that twelve per cent of those born in this generation will produce fifty per cent of the members of the next generation, we can realize that we are facing at least a theoretical degeneration rather than an evolution. One recourse that we have wherewith to correct these harmful influences is to establish a selective birth-rate, because the existing artificial birth-rate appears to disregard numerous characters that make for social welfare. In general there are two courses for us to follow to this end; the first is to eliminate the unfit by segregation as we are already striving to do in some measure, and the second is to stimulate the procreation of the fit.

Such principles as these are easily enunciated but difficult to put into practice, nay even dangerous, because we are dealing here with laboratory material never before used and of the most complicated character. We feel fairly safe in determining certain extremes of badness as harmful to the race, as deserving of elimination, but the cautious scientist will distinctly hesitate before he undertakes breeding experiments in the human race,