100 
Miscellanea 
(2) The data dealt with are drawn from the demographic statistics of the City of Buenos- 
Ayres and are published in the Annuaire Statistique de la Ville de Buenos.- Ayre& of which twelve 
volumes ha\'e now appeared. This publication is to some extent a model for municipal statistical 
work, and we have to cordially tliank M. Albert B. Martinez the DIrecteur de la Statistique 
mKnicipale of Buenos- Ayres for our copy of this interesting book. Buenos- Ayres is a town 
which is altering demographically in two very sensible ways ; there is a rapidly increasing 
population, together with improving sanitary and medical conditions, indicated by a falling death- 
rate and a decrease in the percentage of still-born children. The data in our possession started 
from the year 1887, but to allow of extrapolation beyond the start of the range we did not use 
that year. The following thirteen years' returns were then available for investigation at the time 
of the inquiry : 
TABLE I. 
City of Buenos- Ayres. 
Year 
Population on 
Deaths per 
Still-born 
Dec. 31 
1000 
per 1000 
1888 
455,167 
27-17 
2-45 
1889 
523,452 
28-15 
2-49 
1890 
547,144 
30-00 
2-36 
1891 
535,060 
24-32 
2-46 
1892 
554,713 
24-05 
2-29 
1893 
580,371 
22-40 
2-22 
1894 
603,012 
22-72 
2-06 
1895 
677,780 
22-05 
1-73 
1896 
712,095 
19-16 
1-78 
1897 
738,484 
19-25 
1-78 
1898 
765,744 
17-67 
1-70 
1899 
795,323 
17-06 
1-63 
1900 
821,293 
20-09* 
1-68 
The problem was then this: Graduate these results by a sufficiently high parabola, and 
predict by extrapolation the demographic condition of the Umn before and after the period 
covered by the above data. 
The method of solution adopted was as follows : The successive moments of the observations 
about the middle point of the range were calculated by the processes indicated in Biometril-a, 
Vol. II. pp. 15 et seq., and the series of best fitting parabolas was determined. We halted when a 
thoroughly good fit had been found. Thus we stopped at the fifth order parabola in the case of 
population and at the fourth in the case of the death and still-born rates. Judged by any test 
of goodness of fit it will be foimd that unthin the range dealt with our curves give excellent 
graduation. For example, the mean error made in fitting the population with a straight line is 
16-2 thousands, while the mean error made in using a curve of the fifth order is less than half this, 
being 6-5 thousands. This connotes a mean error in the population as estimated by interi^olatiou 
of almost exactly one per cent., which may be considered for all purposes of interpolation in 
vital statistics as very satisfactory. 
If we take the death-rate statistics we do not get anything like the same improvement if we 
pass from a straight line to a jjarabola of the fourth order. In fact the mean error made in the 
death-rate by the latter curve is 1-07, while it is only 1-18 if we use the best fitting straight line, 
or the fourth order parabola makes an error of 4-7 per cent, on an average in the death-rate, the 
straight line an error of 5-7 per cent. This is a sensible but not a considerable improvement, 
and it did not seem that a substantially greater gain would be made by continuing the process 
further. Clearly, when we consider the effect of epidemic sicknesses, we can hardly hope to get 
a closei- result from a graduating curve. 
* Small-pox epidemic. 
