practical methods the position of the mode, the median, and the mean will only be approximately the same because such a curve is never perfectly symmetrical.

The quartile is the distance from the median to a perpendicular line extending from the base of the curve at such a distance from the median that it divides the area inclosed by the median, the base, and half the curve into two equal parts. Any given curve will have two quartiles, one on either side of the median. They are shown at Q and Q'. (Fig. 63.)

A variate is one of the separate numerical values from which a curve of variability can be constructed. The accuracy of the statistical method is usually proportionate to the number of variates out of which the curve is built. The biometrician usually deals with some such number as 1,000 variates. The total number of variates is represented by the area inclosed by the curve, and it will be seen that half the total number of variates falls between the two quartiles and half outside of them.

A class may be defined as a group of variates all of which show a particular value or a value falling between certain limits.

The frequency of a class is the number of variates which it contains. The amount of variation shown by a particular group of variates is measured by the degree of slope of the curve. A flat curve indicates greater variability and a steep curve denotes less variability.

The standard deviation of a normal curve is the measure of variability and is more often used than the quartile and is expressed shortly as σ. The value of σ is found by multiplying the square of the deviation of each class from the mean (or mode) by the frequency of the class, adding together the series of products so obtained, dividing this number by the total number of variates, extracting the square root of the result, and multiplying by the number of units in the class arranged. The coefficient of variability is a purely abstract number obtained by dividing the standard deviation by the magnitude of the mean in any particular case and multiplying the result by 100.

The probable error arises from the circumstances that half the total number of variates lies outside the limits of the quartile and half within. The probable error of any statistical determination is obtained by finding a pair of values lying one above and one below the true value required. For further details regarding properties of normal curves the student is directed to Davenport's "Statistical Methods with Special Reference to Biological Variation."

HEREDITY VERSUS ENVIRONMENT

How much of our physical and mental makeup is due to heredity (nature) and how much to environment (nurture) is one of the muchdiscussed problems. It seems evident to students of biology that by far the overwhelming factor in our organization is set and definitely fixed at our birth. Heredity appears to be the overshadowing influence of first and prime importance. Herbert Spencer well said that "inherited constitution must ever be the chief factor in determining character." Environment may influence the individual, but apparently has small and slow power of propagating itself for good; great and rapid power for evil. That is, the hereditary transmission of acquired characters is denied, but the transmission of defects of organization, such as insanity, deaf mutism, the consequences of syphilis, alcoholism, and other vices, are fully recognized. Atavism, reversion, and mutations must not be regarded as instances of the hereditary transmission of acquired characters in the biological sense. The tendency of the artificially bred strains of the civilized human races to revert and deteriorate has already been emphasized.

Despite the teachings of biology we are convinced that life is inexorably conditioned by its environment. Jordan states that "among the factors everywhere and inevitably connected with the course of descent of any species variation, heredity, selection, and isolation must appear; the first two innate, part of the definition of organic life; the last two extrinsic, arising from the necessities of environment, and not one of these can find leverage without the presence of the others." In the present state of our knowledge, while we are convinced that heredity plays the major rôle, we are by no means prepared to deny the influence of environment.

IMMUNITY GAINED THROUGH INHERITANCE

Immunity to disease is either natural or acquired. Natural immunity is inherited through successive generations of a species or a race. Acquired immunity, like other acquired characters, is probably not inherited as a "unit character" in the sense of Mendel. Thus, there has been little variation in our natural power to resist most infections, such as tuberculosis, yellow fever, plague, smallpox, cholera, tetanus, measles, scarlet fever, diphtheria, and so on through a long list, although these diseases have doubtless afflicted the human species through untold ages. The fluctuating virulence of some infections is a matter of common knowledge, and is doubtless due to many factors. In a few well-known instances a certain amount of tolerance or re

sistance has been gained and perhaps transmitted through succeeding generations by a process of the survival of the fittest. Thus, syphilis is much less virulent now than it was during the great pandemic of the sixteenth century. The resistance which the natives enjoy to malaria in badly infected quarters of the globe is largely acquired as a result of early infections, and this increased resistance is perhaps partly transmitted by a weeding out of the very susceptible (see chapter on Immunity).

CHAPTER III

THE HEREDITARY TRANSMISSION OF DISEASE

We are now prepared to discuss more in detail the hereditary transmission of disease. The question whether disease is ever transmitted hereditarily or not rests somewhat upon our conception of disease; that is, whether it is an entity, a process, or a "unit character.” The process itself, of course, cannot be transmitted, but the potentiality of it may be involved in some peculiarity in the organization of the germ plasm. This may be, and often is, transmitted through successive generations. In the limited sense in which the word "heredity" is used in biology and in the limited sense in which the word "disease" is used in pathology, there may be no inherited diseases, but this appears to be a quibble of words or a matter of definitions. While we are not familiar with the intimate processes concerned, we are certain that many abnormal conditions of mind and body are transmitted. Some of them follow the Mendelian principles.

Formerly a large number of diseases were regarded as transmissible, but the list has been revised and restricted as a result of recent studies. The reappearance of a diseased condition in successive generations does not prove that it has been transmitted or even that it is transmissible. This mistake has been made with tuberculosis and other infections.

Lack of completeness vitiates most of the statistics bearing on heredity in relation to human diseases. Even in the case of clearly inherited diseases there are very few pedigrees sufficiently complete for the study of the applicability of Mendelian and other laws of heredity. Sometimes the disease itself is not transmitted, but a tendency to the disease is transmitted. This will be discussed again.

Some unit characters as well as certain diseases are transmitted hereditarily, but limited to one sex; that is, the disease or condition appears in one sex only, although transmitted by the other. The best example of a sex-limited disease is hemophilia, which affects males almost exclusively, but is transmitted through the normal female. Colorblindness is also transmitted hereditarily, but is sex-limited, as it affects males almost exclusively.

This remarkable sort of inheritance, known as sex-limited inheritance,

occurs when the male parent is characterized by the absence of some character of which the determiner is typically lodged in the sex (x) chromosome. A striking feature of this sort of heredity is that the trait appears only in males of the family, but is not transmitted by them; it is transmitted, however, through normal females of the family. Examples of this sort of heredity occur in hemophilia, color-blindness, also in multiple sclerosis, atrophy of the optic nerve, myopia, ichthyosis, and muscular atrophy. The explanation is the same in all cases of sex-limited heredity. The abnormal condition is due to the absence of a determiner from the male sex chromosome.

The diseases, defects, and conditions believed to be transmitted hereditarily are discussed in the following pages. Some of these diseases, malformations, and defects of organization follow Mendel's law. It is probable that other diseases, tendencies, and characters are transmissible, but the subject has only recently been placed upon a scientific basis, and it will require careful and prolonged observation to establish the facts. It is often difficult to determine whether the disease itself or a tendency to the disease has been transmitted in any particular case, and, further, it is often difficult to decide whether an individual has inherited or acquired his affliction.

The transmissible defects which are of principal concern to the human species are the defects of organization of the central nervous system. It is important to remember that the defects of the nervous system do not necessarily propagate just the same defects in the succeeding generations. Thus, an epileptic does not necessarily beget epileptics; epilepsy, insanity, degeneracy, color-blindness, and other stigmata may arise as the result of deficiencies of various kinds in the forebears.

Defects such as harelip, cleft palate, cervical fistula, spina bifida, etc., are not true instances of hereditary transmission of specific characters. They rather represent an inherited deficiency in developmental vigor. These defects for the most part represent the failure of parts to unite during embryological development; in other words, the failure of embryological clefts to close normally. Such deformities, as well as clubfoot, web fingers, and other acquired or congenital deformities or disfigurations, are not, as a rule, transmitted.

Some practical problems of great importance arise from our knowledge of the hereditary transmission of disease and defects. A man or woman who intends marrying is now more than justified in carefully examining the personal and medical histories of the family of his or her intended mate. It is not only possible to foretell the color of the eyes, the nature of the hair, and other Mendelian characters in the future offspring, but it is also possible to foretell, with mathematical precision, the chances of transmitting defects, such as insanity, epi