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These tables give for the appearance of the permanent teeth the following averages and variabilities:

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For the time of appearance of the wisdom teeth Magitot's tables a are available. He gives the following distribution for the time of appearance of the wisdom teeth:

TABLE XIIa.—Appearance of wisdom teeth.

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We may assume that the number of examined individuals for these ages was nearly equal, and on account of the uncertainty of the distribution we may disregard the cases outside of the limits of 18 and 25 years. If the ages mean those between one birthday and the next birthday, the averages and variabilities will be, for men, 22.2±1.7 years, and for women, 21.8±1.8 years.

Statistics which Dr. G. Meylan had the kindness to collect at our request in the gymnasium of Columbia University give the following numbers:

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Puberty. We have collected the following statistics of the beginning of menstruation:

TABLE XIII.-Beginning of menstruation.

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Psychology of Religion, p. 40.

Journal of Medical Science, Edinburgh, 1850, Vol. XI, pp. 289–296.

Menopause.-Weber a gives the following statistics for St. Petersburg for the percentile frequency of the occurrence of the menopause, the total number of his observations being 578.

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Deaths due to arterial diseases.-Finally, we have tried to calculate the variability of the time of occurrence of deaths due to the phenomena of senility. The most available groups of deaths seemed to be those due to arterial diseases. Doctor Wissler has made an approximate calculation of the distribution of deaths due to arterial diseases in Paris, the method and calculation being contributed by him. He summarizes his results as follows:

The statistics of Paris for 1896 give the number of deaths from arterial affections; but the values must be reduced to the frequencies of deaths for a given number of individuals. For example, the number of males dying of this class of

"See Ploss. Das Weib, 1899, I, p. 578.

Annuaire Statistique de la Ville de Paris, XVIIe Anné, 1896.

diseases at the age from 45 to 49 is 15; the total number of deaths of males from all causes for the same ages, 1,763, and the total number of living males, 80,952. For the succeeding years of life the corresponding numbers will be taken from a different group of individuals and can not be compared to the foregoing until both are reduced to the same base. Hence, a table of the frequencies of death at the successive ages must be based upon the life history of a definite number of individuals. If we begin with 1,000 individuals born at the same time and record the deaths from year to year until all are dead, we obtain a series of numbers expressing the relative age frequencies of death. Statistics of this sort are obviously difficult to obtain, and it is customary to calculate their values from the death rates of successive ages. The French mortality tables used in life insurance give the probable number of deaths during each five years of life. These are calculated from the formula

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in which 7,= the number living; d, the annual death rate for the period; 12, the number of survivors at the end of the period."

According to this method the total mortality table for males in Paris in 1896 was calculated, beginning with 1,000 individuals 10 years of age. In the following table the first column gives the number of survivors for the successive age periods and the second column the number of deaths. Since in the vital statistics of Paris all over 80 years of age are grouped together, it was necessary to make an approximate distribution for these ages based upon the general mortality tables for France. The ratio of the number of deaths due to affections of the arteries to the total number of deaths for each age period enables us to calculate the relative number of deaths from these diseases annually for over 1,000 males. These values are given in the third column of our table:

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In his discussion of the chances of death, Karl Pearson has dissected the general mortality curve into five component elements, giving probabilities of

a E. Dormoy: Théorie Mathématique des Assurances sur la Vie.
The Chances of Death, I, p. 26.

death for infancy, childhood, youth, middle life, and old age. He gives the following variabilities for the time of death:

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The last of these agrees well with the results obtained from Doctor Wissler's discussion of deaths due to arterial diseases.

From the material that has been given the following results for the variabilities of development in various periods of life have been obtained.

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From these data it appears clearly that there is an increase in variability of the time at which certain stages of development are reached. In our series a variety of physiological phenomena have been considered and all give similar results. It must, of course, not be supposed that all the different phenomena must necessarily give the same results, since each of them must be affected by certain peculiar conditions aside from the general variability of development that is characteristic of the whole series. It does not appear clearly from the available material whether there is a difference in this respect between the two sexes. It is interesting to see that a similar increase in variability takes place in the grouping of children according to mental maturity. This may be observed in the arrangement of children of the same age in different grades in school. In Worcester, for instance, the following distribution was observed.

TABLE XVII.-Distribution of girls of various ages in school.

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It is not surprising to find that these variabilities are less than those obtained from physiological data, since the grading in schools involves not only phenomena of acceleration and retardation, but also a selective grouping.

The peculiar distribution of measurements of children of the same age, but in different grades, to which Porter first called attention, are of such a character that the children who are retarded in grade are also retarded in all their physical measurements. They are not simply short or light-weight children of their particular age, but all their measurements correspond to those of younger children, while the measurements of children who are ahead of their age correspond to measurements of older children. The same phenomena are brought out by our Worcester series.

TABLE XVIII.-Statures of girls of the same ages in different grades.

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It will be seen from Table XVII that the correlation between age and grade is very close. Table XVIIf gives the following average ages and average variabilities of stature for each grade:

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In this series the variabilities increase on the whole in the same manner as in the general Table Ib. This correspondence becomes still clearer when we consider each measurement as corresponding to the age to which it would belong according to Table Ib. If we interpolate in Table Ib for 1139 for stature, we find the age of 6.9 years as corresponding to the average stature. Thus we can substitute for Table XVIII the following table of ages:

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