Imagens das páginas
PDF
ePub

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

[ocr errors][ocr errors]
[ocr errors]

in which the number living; d, the annual death rate for the period; l1⁄2, 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: TABLE XV.-Mortality table for arterial diseases.

[blocks in formation]

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

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:

[blocks in formation]

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.

[blocks in formation]

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.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][subsumed][ocr errors][subsumed][merged small][merged small][merged small][merged small][merged small][merged small]

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.

[merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small]

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

[blocks in formation]

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:

[blocks in formation]

If we arrange the variabilities for the grades and ages in accordance with this table of ages corresponding to statures, and smooth the series, which seems necessary on account of the small number of observations, we find:

[merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][subsumed][merged small][merged small][merged small][merged small][subsumed][merged small][merged small][ocr errors][merged small][merged small][subsumed][merged small][merged small][ocr errors][merged small][merged small][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]

See F. Boas,

68

Growth of Toronto children," Rep. Com. of Education, 1896-97, p. 1556.

Thus it appears that the position of a child in the grades conforms in regard to its measurements and variabilities strictly to the values which would result if its age were considered as variable, so that we find in these observations a good confirmation of our general theory. It would be interesting to know whether the physiological data discussed before have a similar relation to the measurement of the body, as we found in the mental variations. Unfortunately no material bearing upon this point is available.

The data collected in Table XVI can be expressed approximately by the formula

6,-0.231-0.06t2, which can be used for
t<20 years.

This formula gives us the following variabilities:

[blocks in formation]

We may also determine a maximum value for this variability from our table of growth. If the variability of stature during the period of growth were due entirely to acceleration and retardation-an assumption which can be

even approximately correct only during the early years of childhood-we may use our formula on page 26.

t

In accordance with the present assumption, 6, would disappear, and we have

66

We have used the tables published in F. Boas's paper on the Growth of Toronto children," a which have been smoothed graphically (figs. 2 and 3, p. 48) and which may be summarized in the following table:

[subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][merged small][graphic][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][ocr errors][subsumed][subsumed][subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][subsumed][merged small][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed][subsumed]

A comparison between Tables XIXa and XIXb shows a fair close correspondence, and suggests that, for stature at least, the variabilites obtained from observations on dentition and puberty give too high results. This may be seen also from a consideration of the physical development of children of 15 years, for instance. If the variability were as high as 2.1, as indicated by the data on dentition, there would be an appreciable number of individuals whose development would correspond to the stages of 10 and 20 years, which is obviously not true. Similar maximum values may be derived from Table III by disregarding for the early years of childhood the value of r6,6, of equation (1) on page 26. Then we have

[ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]
« AnteriorContinuar »