(4) The Registrar-General’s method, the one generally adopted, assumes that the same rate of increase will hold good as in the preceding intercensal period, i.e. that the population increases in geometrical progression, and not in arithmetical progression as under (3).

The application of this method will be best understood by an example. If the census population of a town is 32,000 in 1891, and 36,000 in 1901, what is the mean population in 1905?

(a) Find the rate of increase in 1891-1901.

(b) Apply this to the increase in the next 4¼ years.

By consulting the table of logs, the population corresponding to this number will be found to be 37,848 = population at the middle of 1905.

Estimates made by the last-named “official” method are liable to error, even for the entire country, and still more when applied to special districts. Thus the decennial rate of increase of the population of England and Wales in the 100 years has varied from 15·8 per cent. in 1821-31 to 11·6 per cent. in 1891-1901. The anomalies are even greater when the official method is applied to great towns. In one decennium such a town may, owing to brisk trade, have a rapid increase of working population with many children, and in the next decennium in consequence of emigration or transmigration there may be little or no increase. The declining birth-rate, which is having a greater effect on the number of population than the declining death-rate, is another cause of disturbance which increases the difficulty in forming a correct estimate of the population in intercensal periods. A quinquennial census is highly desirable, in order to avoid the doubts necessarily associated with estimates of population in the later years of a decennium, and with the birth and death-rates which are based on these estimates.

The Registration of Births and Deaths.—Civil registration of births and deaths began in 1837, but was not compulsory till 1870. It will be going beyond the scope of this chapter to give details of the enactments as to registration. It suffices to state that it is the duty of the practitioner to give a certificate stating the cause of death of his patient to the best of his knowledge and belief. There is no registration of still-births in this country. Many deaths are registered of which the cause of death is not medically certified, and the value of our national vital statistics is considerably diminished on this account. Much improvement is desirable in the medical certification of causes of death. Every medical student ought to receive instruction on this subject before the completion of his studies. Names of symptoms as dropsy, hæmorrhage, convulsions; and obscure names, as abdominal disease, should be avoided. If the patient has recently suffered from injury, or recently passed through childbirth, or had a specific febrile disease, this must not be omitted from the certificate.

The Registration and Notification of Sickness forms another valuable source of information. Various attempts have been made to secure a general registration of disabling sickness, but with only partial success. District and workhouse medical officers appointed since February, 1879, are required to furnish the medical officer of health with returns of pauper sickness and deaths. This source of information might with advantage be more fully utilised by medical officers of health. Sec. 29 of the Factory and Workshops Act, 1895, requires that every medical practitioner attending on or called in to visit a patient whom he believes to be suffering from lead, phosphorus, or arsenical poisoning, or anthrax, contracted in any factory or workshop, shall send to the Chief Inspector of Factories at the Home Office, London, a notice stating the name and full postal address of the patient, and the disease from which he is suffering; a fee of 2s. 6d. being payable for each notification, and a fine not exceeding 40s. being incurred for failure to notify.