512 
Miscellanea 
Now it is evident that the larger the number of frequency elements for the mortality of the 
first year for which wc can get data, the more accurate will bo the determination of the mean, for 
the reason that the rate of infantile mortality changes rapidly with lapse of time after birth. It 
is fairly easy to get data giving the number of deaths occurring in each month of the first year, 
but a still finer division is desirable. Especially is this true for the first month of life. Roughly 
from 25 to 45 per cent, of all the deaths falling within the first year occur in the first month. Of 
these the larger proportion occur early in the month. Fortunately the German statistics, which are 
in many respects among the best \'ital statistics available, give a rather detailed age grouping of 
the deaths inider one year. I have used in this work the Prussian statistics* for the years 1877 
to 1895, si)lit up into three groups as follows : 1877-81, 1882-90, 1891-95. The data are given in 
the form of death-rates per 1000 horn of the same class, in the given period. Separate returns are 
given for male and female, and legitimate and illegitimate mortality. Up to the fourteenth day 
after birth the mortality for each day is recorded. The mortality of the remainder of the first 
month is grouped together in a single class, and from the beginning of the second month to the 
end of the first year after birth the rates are given by months. Still-births are, of course, 
excluded. A glance at Table I. will make clear the way in which the retvirns are sub-divided. 
It is evident that the grouping here is sufficiently fine to make possible a very accurate 
determination of the mean age at death. The material was dealt with in the following way : the 
rates were treated as frequencies, except in the determination of probable errors where, of course, 
the absolute number of deaths was used. A standard month of 30 daj's was assumed : then with 
a unit of 30 days the first and second moment coefficients about an arbitrary axis were deter- 
mined. From these the position of the mean and the value of the second moment about it were 
easily found. Only the "rough" second moment was calculated, as it was deemed sufficiently 
accurate for present ])urposes, and furthermore it was difficult to determine the proper corrective 
terms to apply in this case. In the calculations each frequency element was for practical 
convenience, centred at the mid-point of its range. The error made by so doing is negligible. 
The results are shown in Table II. 
TABLE II. 
Mean Duration of Life in Days of Individuals Dying in the First Year 
after Birth. 
1877—81 
1882—90 
1891—95 
Mean 
S. D. 
Mean 
S. D. 
Mean 
S. D. 
Legitimate ^ 
? 
111-44 
116-75 
103-92 
106-13 
113-33 
118-65 
101-13 
105-97 
112-54 
117-91 
100-26 
104-50 
Illegitimate ^ 
? 
96-81 
102-86 
91-80 
94-19 
98-64 
104-94 
92-47 
94-89 
98-08 
103-64 
91- 41 
92- 92 
On account of a lack of necessary data it was not possible to determine the probable errors of 
all these constants. The general order of magnitude of the probable errors, however, may be 
seen from a consideration of a single case. For the period 1882-90 data were available from 
* Statistischcs Handhuch fiir den preussischen Staat, Bde. i. ii. and iii. Berlin. 
