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A MANUAL OF PUBLIC HEALTH.

CHAPTER I.

THE CALCULATION AND SIGNIFICANCE OF VITAL STATISTICS.

VITAL STATISTICS have been defined as the science of figures applied to life; the term was first invented by Professor Achenwall, of Göttingen; the science itself by Sir William Petty, who died in 1687.

The materials for the statistics of the health officer are the census returns, any local census which he may make, and returns from the registrars or other persons.

(1) Method of Calculating Populations between the Census Periods.

The ten-year period census is far too long, and in certain rapidly growing or decreasing localities, causes great errors in the calculated rates, whenever such increase or decrease is irregular. If, however, the change is fairly uniform, the population may in any year in the interval between two censuses, be approximately calculated by the following rule.

From the logarithm of the most recent census subtract the logarithm of the previous census, and divide the number so obtained by the number of intervening years; the quotient will be

1 It is difficult and cumbersome to use ordinary arithmetic in the calculation of a variety of data which the sanitarian requires, hence a knowledge of the use of logarithms is essential. Law's Mathematical Tables (Crosby, Lockwood, and Son) are very clear and the directions simple. Woodward's Logarithms and Chambers's Tables may also be recommended.

the logarithm of the ratio of annual increase. By adding this logarithm to the logarithm of the population at any period, the logarithm of the population at the end of the succeeding year will be obtained; and by continually adding the logarithm of the ratio, the logarithm of the population in each successive year will be obtained.1

For example, supposing that in 1886 it is required to calculate the population of a town, for each year from 1881, the census in 1871 giving 156,000, and in 1881 giving 171,000. Then

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1 Let p denote the population at any time; p' the population at any previous time n the number of intervening years; then p = r = 1 the annual rate of p'

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increase. The division of the logarithm of 2 or 3 by the logarithm of r gives the number of years in which at that rate the population will double or triple, &c. (Farr).

2 The census is taken in March, therefore the numbers obtained would be the presumed population in the March of the different years; but if it is required to estimate for the middle of each year, we must begin by adding 4th of the logarithm 0039871 to the 1881 population, which will then represent the logarithm of the population in the middle of 1881; by then adding to the logarithm of each succeeding year the logarithm 0039871, the logarithms of the population in the middle of each year are obtained. Similarly, if the population in the September quarter is required, then we must begin by adding half the logarithm 0039871 to the 1881 population.

Or, if any one year is required, all that is necessary is to multiply the logarithm of the ratio of annual increase by the number of years elapsed from the census, and add it to the logarithm of the population; thus, if the population is required for 1888, 0039871 × 7 and added to 5 232996 gives the logarithm 5.260906, that is 182,350.

On the other hand, supposing the census of 1881 gave a lower figure than that of 1871, the population for the years subsequent to 1881 may then be similarly calculated upon the assumption of a uniform decrease.

(2) Local Censuses.

These may be made in small areas, such as a crowded street, model artisans' dwellings, and villages, by the inspector of nuisances, and will be found of value, the more especially if made at short intervals.

If an accurate enumeration of persons be made in 100 houses of the same size and class, trustworthy averages may be obtained; and such averages may be used for the purpose of calculating the population of small areas. The number of houses can be got from the rate-books, and the number of empty houses from the ratecollectors; the inhabited houses are then multiplied by the average. It is obvious that this method does not give age distribution, and is inferior to personal inquiry, but it is nevertheless useful, for it is not always practicable to make an actual local census.

(3) Death Returns.

It is the duty of every sanitary authority to cause the local registrars to supply the officer of health regularly with copies of the death returns and also the number of births. These returns are usually made weekly, but deaths from zymotic diseases should of course be communicated as soon as the registrar has notice of the fact; this is the more necessary in those places in which the compulsory notification of disease is not in force; where infectious. disease is systematically notified, the health officer will be early acquainted with the nature and locality of the disease.

No. of Entry in

Register.

Cols.

An example of the most useful form of return is the following:

DISTRICT

SUB-DISTRICT.

N.B.-This Return is to be posted in time to secure its delivery by THE FIRST POST ON MONDAY MORNING.

A Return of the number of Births and of Deaths registered in the Sub-District during the Week ending Saturday, the

day of

189 .

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This return gives the following items of information :— Total number of births, male and female, for the week ; total number of deaths, male and female; date of death; address of place of death; sex, age, and occupation of person dying;-added to which the registrar notes when an inquest has been held. All these different facts admit of tabulation and arrangement.

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