CHAPTER XLVIII.

VITAL STATISTICS.

Vital Statistics is the science of numbers applied to the life-history of communities. Its significance is similar to that of the more recently coined word—Demography—though the latter does not necessarily confine itself strictly to study of life by statistical means. Another term has been frequently used in recent years—“Vital and Mortal Statistics.” The continued use of the word “mortal” in this connection is undesirable and objectionable. The term “Vital Statistics” is comprehensive and complete, as death is but the last act of life.

Of the problems of life with which the science of Vital Statistics is concerned, population, births, marriages, sickness, and deaths, possess the chief importance; and in the following sketch of the subject I shall concern myself chiefly with these. The subject naturally divides itself into two sections: the sources of information, and the information derived from these sources, and both of these will require consideration.

The importance of numerical standards of comparison in science increases with every increase of knowledge. The value of _experience_, founded on an accumulation of individual facts, varies greatly according to the character of the observer. As Dr. Guy has put it: “The _sometimes_ of the cautious is the _often_ of the sanguine, the _always_ of the empiric, and the _never_ of the sceptic; while the numbers 1, 10, 100, and 100,000 have but one meaning for all mankind.” Hence the importance of an exact numerical statement of facts. The sneering statement that statistics cannot be made to prove anything can only be made by one ignorant of science. In fact, nothing can be proved without their aid, though they may be so ignorantly or unscrupulously manipulated as to appear to prove what is untrue. Instances of fallacious use of figures will be given as we proceed.

An accurate statement of =population= forms the natural basis of all vital statistics. Thus the comparison of the number of deaths in one with the number of deaths in a second community has no significance unless we know also the number living out of which these deaths occurred. Even then our knowledge would be defective, without further particulars as to the proportion in each population living at different ages, and the number dying at the corresponding ages. For other purposes we should require to know the number married and unmarried, the number engaged in different industries, and so on; in order that the influence of marital conditions, of occupation, etc., on the prospects of life may be calculated. The first desideratum of accurate vital statistics is a =census enumeration= of the population at such intervals as will not cause the intervening estimates of population to be very wide of the mark. In this country a decennial census is taken, the last occurring in 1901. In the intervals the population of the entire country, and of each town or district is estimated. Various methods of =estimating the population= have been adopted. (1) If a strict record of emigration and immigration is kept, then in a country in which a complete registration of births and deaths is enforced, the population can be easily ascertained by balancing the natural increase by excess of births over deaths, and the increase or decrease due to migration. This is done in New Zealand, but is impracticable in England, as no complete account of migration can be kept.

(2) The increase of inhabited houses in a district being known year by year, the increase of population may be estimated on the assumption that the number of persons per house is the same as at the last census. This may not be strictly accurate. In 1901 it was found that in England and Wales the average number of persons per house was fractionally less than in 1891.

(3) It may be assumed that the annual increase during the present decennium will be 1∕10 of the increase during the last decennium 1891-1901. If so, the population, _e.g._ in 1905, is the enumerated population in 1901 _plus_ 4¼ times the annual increase occurring during 1881-91. (The _fourth_ is required because the census is taken early in April, and the population is estimated to the middle of the year). This method is fallacious, because it makes no allowances for the steadily increasing numbers who year by year attain marriageable age and become parents. It assumes, in other words, simple interest, when compound interest is in operation.

(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._

If P = population at census 1891, and if P^{1} = „ „ 1901, and if R = rate of increase of population, then P^{1} = P - R^{_n_} in the _n_th year. log P^{1} = log P + 10 log R. 1∕10(log P^{1} - log P) = log R. (4·556303 - 4·505150)∕10 = ·0051153 = log R.

(_b_) _Apply this to the increase in the next 4¼ years._

Here P_1905 = P_1901 R^(17∕4)

log P_1905 = 4·556303 + (17∕4) (·0051153)

= 4·578043.

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.

=The Compulsory Notification of Infectious Diseases= is enforced by the Act of 1889, which now applies to the whole country. The list of diseases to be notified is as follows:

“Small-pox, cholera, diphtheria, membranous croup, erysipelas, the disease known as scarlatina or scarlet fever, and the fevers known by any of the following names: typhus, typhoid, enteric, relapsing, continued, or puerperal, and also any infectious disease to which the Act has been applied by the Local Authority in manner provided by the Act.”

It is the duty of the medical practitioner to ascertain whether in his own district, such diseases as whooping cough and measles have been added to the schedule of notifiable diseases. It is the duty of (_a_) the head of the family to which the patient belongs; in his default, of (_b_), the nearest relatives in the house; in their default, of (_c_), every person in attendance upon the patient; and in default of any such person, of (_d_) the occupier of the building, as soon as they become aware that the patient is suffering from an infectious disease to which this Act applies, to send notice thereof to the Medical Officer of the District. (_e_) The more formal duty of sending to the Medical Officer of Health a certificate stating the name of the patient, the situation of the building, and the infectious disease from which in his opinion the patient is suffering, is imposed on every medical practitioner attending on, or called in, to visit the patient, on becoming aware that the patient is suffering from an infectious disease to which this Act applies. He is entitled to a fee of 2s. 6d. if the case occurs in his private practice, and of 1s. if the case occurs in his practice as medical officer of any public body or institution. He is subject to a fine not exceeding 40s. if convicted of failure to notify. The value of returns of infectious diseases as enabling preventive measures to be taken is increased by interchange of notification returns of different districts. This is now undertaken weekly for a large number of districts by the Local Government Board, and the Registrar-General publishes quarterly summaries of such returns, as well as weekly returns of infectious diseases for the metropolis.

=Marriages= are usually stated in proportion to the total population, or the number per thousand of population; but a more accurate method would be to base the marriage-rate for comparative purposes on the number of unmarried persons living at marriageable ages. In England the marriage-rate is always higher in large towns than in rural districts. Thus in 1900 the marriage-rate in London was 17·6 as compared with an average marriage-rate in 1891-95 of 15·2 per thousand of the estimated population in England and Wales. The higher marriage-rate in towns is chiefly owing to the fact that higher wages and greater scope for remunerative work attract young country people of marriageable ages to towns.

=Births= are usually reckoned as a rate per thousand of population. Clearly, however, if one population had a larger proportion than another of women of child-bearing years this method of comparison would not be free from possible error. Even were the proportion of women of child-bearing ages equal, the comparison might be fallacious if in one population the proportion of single women was much higher than in the other. Illegitimate births do not materially vitiate this conclusion, as such births do not constitute more than 4 per cent. of the total births, and this number is not excessive in the districts in which there is the greatest excess of single women, viz. in districts in which a large number of domestic servants are employed. The only strictly accurate method is to subdivide the births into legitimate and illegitimate, stating the former per 1,000 married women of child-bearing years, and the latter per 1,000 unmarried women of child-bearing years. I append an example of the relative accuracy of the three methods above indicated[12]:—

┌─────────────────────┬────────────────────────────────────────┐ │ │ BIRTH-RATE │ │ ├──────────────┬────────────┬────────────┤ │ │ │ │ PER 1,000 │ │ │ PER 1,000 │ PER 1,000 │ MARRIED │ │ │ INHABITANTS. │ WOMEN │ WOMEN AGED │ │ │ │ AGED 15-45.│15-45 YEARS.│ ├─────────────────────┼──────────────┼────────────┼────────────┤ │ _Kensington_ │ 21.8 │ 61.6 │ 215.4 │ │ _Whitechapel_ │ 39.9 │ 172.1 │ 328.3 │ ├─────────────────────┼──────────────┼────────────┼────────────┤ │_Percentage excess │ 83% │ 179% │ 53% │ │ of birth-rate in │ │ │ │ │ Whitechapel over │ A │ B │ C │ │ that in Kensington_│ │ │ │ └─────────────────────┴──────────────┴────────────┴────────────┘

Thus, according to the ordinary method (A) of stating the legitimate birth-rate, it is 83% higher in Whitechapel than in Kensington, whereas it is really only 53% higher. Similarly a statement of the illegitimate birth-rate in the two districts “per 1,000 inhabitants,” shows an excess of only 6% in Whitechapel, while a statement “per 1,000 unmarried women aged 15-45 years” shows the real excess of 144%. Both in this and other civilised countries there has been in the last 25 years a steady decline in the birth-rate. In England the maximum birth-rate was 36·3 per 1,000 of population in 1876, and the minimum 29·3 in 1899. This diminution is only caused to a minor degree by postponement of marriage to more mature years, and by a larger proportion of celibacy. Nor is there any reasonable ground for the view that a diminished power of either sex to produce children has been produced by alcohol, syphilis, tobacco, or other causes. The main cause of the diminution of the birth-rate is “the deliberate and voluntary avoidance of child-bearing on, the part of a steadily increasing number of married persons.”

=Deaths= are calculated in proportion to every 1,000 of the population, the unit of time being a year. This unit is preserved even when death-rates for shorter periods, _e.g._ a week, are stated. Thus the death-rates for the 33 great towns published weekly in the chief newspapers are _annual death-rates_; they represent the number who would die per 1,000 of the population, supposing the same proportion of deaths to population held good throughout the year. The best plan to obtain the weekly annual death-rate is as follows: the correct number of weeks in a year being 52·17747, if the population of a town be 143,956, and the number of deaths in a given week are 35, then the death-rate is 12·687. Thus:—

143,956∕52·17747 = 2758. 1,000∕2,758 = 0·3625. This is the factor by which the weekly number of deaths must be multiplied.

35 × 0·3625 = 12·6875 or 12·7.

The above is the _crude death-rate_. Various corrections are required, which must now be considered. The most important of these are for public institutions, for visitors, and for age and sex. A public institution, _e.g._ a workhouse, infirmary, or asylum, in a given district may consist almost entirely of persons belonging to another district. The rule is to relegate to the district to which they belong all deaths of inmates of an institution, _i.e._ subtract all deaths of outsiders occurring in inside institutions, and add all deaths of inhabitants occurring in outside institutions. The population as well as the deaths of these institutions should be excluded, in so far as they are derived from the outside district, in order to make the net death-rate approximately correct.

Theoretically the correction ought to be extended so as to apply to visitors who do not die in public institutions. In practice, however, this cannot be effected, until a central “clearing house” is established. The exclusion of deaths of visitors from the district in which they occur is easy; their inclusion in the returns of the district from which they come is more difficult to secure. For the present, they should be included in the death-rate of the district in which they occur.

=Death-rate according to Age and Sex.=—To obtain a true conception of the death-rate in a community, it is necessary to state the number of deaths in each sex in proportion to the number living at different ages. The importance of this is shown by the following extract from the Registrar-General’s report for 1899.

England and Wales.—_Deaths to 1,000 living at each of 12 groups of ages._

┌─────────┬───────┬──────┬─────┬─────┬─────┬─────┬─────┬──────┐ │ │ ALL │ AGED │ │ │ │ │ │ │ │ │ AGES. │ 0─ │ 5─ │ 10─ │ 15─ │ 20─ │ 25─ │ 35─ │ ├─────────┼───────┼──────┼─────┼─────┼─────┼─────┼─────┼──────┤ │_Males_ │ 19·5 │ 60·4 │ 3·8 │ 2·2 │ 3·6 │ 5·3 │ 7·1 │ 12·3 │ │ │ │ │ │ │ │ │ │ │ │_Females_│ 17·3 │ 50·7 │ 3·9 │ 2·3 │ 3·3 │ 4·3 │ 6·1 │ 10·0 │ └─────────┴───────┴──────┴─────┴─────┴─────┴─────┴─────┴──────┘ ┌──────┬──────┬──────┬───────┬──────────┐ │ │ │ │ │ 85 AND │ │ 45- │ 55- │ 65- │ 75- │ UPWARDS. │ ├──────┼──────┼──────┼───────┼──────────┤ │ 20·0 │ 37·2 │ 69·8 │ 152·6 │ 300·3 │ │ │ │ │ │ │ │ 15·4 │ 29·8 │ 61·5 │ 142·6 │ 272·0 │ └──────┴──────┴──────┴───────┴──────────┘

Thus at ages over 5 and under 45 for males, and under 55 for females, the death-rate is lower than is the total death-rate for all ages. For females at all ages except from 5 to 15, the death-rate is lower than for males. From the above statement it will be clear that a considerable excess of women (as in a residential district with a large number of domestic servants) or a considerable excess of either sex at the ages of 15 to 45 (as in most large towns) in proportion to the number living at other ages, would produce a lower total or crude death-rate, which does not imply any truly more healthy condition than that of another district, which is less favourably constituted so far as the proportion of the sexes and the numbers living at different ages are concerned. By a means of correction now to be described this source of error can be eliminated. The method of obtaining the _factor for correction_ can be best understood by an example. The annual death-rate of England and Wales in 1881-90 was 19.15, and the death-rate at each age-group is given in the following table:

┌─────────────────┬────────────────────────────┐ │ AGES. │ MEAN ANNUAL DEATH─RATE │ │ │ IN ENGLAND AND WALES │ │ │1881─90, PER 1,000 LIVING AT│ │ │ EACH GROUP OF AGES. │ ├─────────────────┼────────────┬───────────────┤ │ │ _Males._ │ _Females._ │ │ _Under_ 5 │ 61.59 │ 51.95 │ │ 5 │ 5·35 │ 5·27 │ │ 10 │ 2·96 │ 3·11 │ │ 15 │ 4·33 │ 4·42 │ │ 20 │ 5·73 │ 5·54 │ │ 25 │ 7·78 │ 7·41 │ │ 35 │ 12·41 │ 10·61 │ │ 45 │ 19·36 │ 15·09 │ │ 55 │ 34·69 │ 28·45 │ │ 65 │ 70·39 │ 60·36 │ │ 75 _and upwards_│ 162.62 │ 147.98 │ └─────────────────┴────────────┴───────────────┘

┌──────────────────────┬───────────────────────┐ │ POPULATION │ CALCULATED │ │ OF HUDDERSFIELD IN │ NUMBER OF DEATHS │ │ 1891. │ IN HUDDERSFIELD. │ ├─────────┬────────────┼──────────┬────────────┤ │_Males._ │ _Females._ │ _Males._ │ _Females._ │ │ 4,551 │ 4,785 │ 280 │ 249 │ │ 4,691 │ 5,081 │ 25 │ 27 │ │ 5,113 │ 5,165 │ 15 │ 16 │ ├ 4,905 │ 5,549 │ 21 │ 25 │ │ 4,541 │ 5,461 │ 26 │ 30 │ │ 7,466 │ 8,834 │ 58 │ 65 │ │ 5,576 │ 6,265 │ 69 │ 66 │ │ 3,944 │ 4,649 │ 76 │ 70 │ │ 2,393 │ 3,017 │ 83 │ 86 │ │ 1,128 │ 1,590 │ 79 │ 96 │ │ 250 │ 466 │ 41 │ 69 │ ├─────────┴────────────┼──────────┴────────────┤ Totals │44,558 50,862 │ 773 799 │ │ \──────/ │ \───────/ │ │ 95,420 │ 1,572 │ └──────────────────────┴───────────────────────┘

The population of Huddersfield at each of the corresponding periods as given by the census of 1891, is also shown in this table, and in the last column the number of male and female deaths that would occur by applying the death-rates for England and Wales to the population of Huddersfield are shewn. The total number of deaths thus calculated is 1572 in a population of 95,420, and the total death-rate = 16·47 per 1000. This is the _standard death-rate_, _i.e._, the death-rate at all ages calculated on the hypothesis that the rates at each of 12 age-periods in Huddersfield were the same as in England and Wales during the ten years of the last intercensal period, viz. 19·15 in 1881-90.[13] But the standard death-rate of Huddersfield would have been 19·15 instead of 16·47, were it not for the fact that the distribution of age and sex in the Huddersfield population is more favourable than in the country as a whole. Hence it must be increased in the ratio of 19·15: 16·47, _i.e._, multiplied by the factor 19·15∕16·47 = 1·1627. When the crude or recorded death-rate for 1900 of 16·78 is multiplied by this factor we obtain the _corrected death-rate_ of 16·78 × 1·1627 = 19·51 per 1000, which is the correct figure to compare with the death-rate of 18.31 for England and Wales in that year. If the death-rate of England and Wales be stated as 1000, then 1000 × 1951∕1831 = 1066, is the _comparative mortality figure_ for Huddersfield. Similarly in the year 1900 the comparative mortality figure of London was 1093, of Croydon 831, of Norwich 919, while that of Liverpool was 1539, of Salford 1541. In all the towns except Plymouth and Norwich the corrected death-rate is higher than the crude or recorded death-rate. This implies that, in all except these two towns, the factor of correction is greater than unity.

This is a convenient point for briefly discussing the =relationship between the birth-rate and death-rate=. The opinion is commonly held that a high birth-rate is a direct cause of a high death-rate, owing to the great mortality amongst infants. The table on page 340 shows that the death-rate at ages under five is three times as high as at all ages together, and it is therefore natural to suppose that a high birth-rate by producing an excessive proportion of persons of tender years will cause a high general death-rate. This might be so, if the birth-rate were to remain high for only five years. But if the high birth-rate continued longer, the proportion of the total population at ages of low mortality would be increased, and the general death-rate would be lowered. We have already seen that in nearly all the great towns, in which the birth-rate is higher than in rural districts, the age distribution of the population is more favourable to a low death-rate than in rural districts; and their higher crude death-rate is made still higher than that of rural districts when the necessary factor of correction is applied.

The =Infantile Mortality= should be stated in terms of the infantile population. This is more accurately assumed to be equal to the number of births in the given year, than estimated from the number stated to be under one year of age at the last census. The number of deaths under one year of age per 1000 births was 163 for England and Wales in 1899, being lowest in the agricultural counties and highest in manufacturing counties. In the 33 great towns it averaged 172 in the year 1900, ranging from 132 in Croydon, Huddersfield and Halifax to 236 per 1000 births in Preston. Of 1000 male children born in England and Wales in 1881-90, the number surviving at the age of three months was 921, at the age of six months 889, twelve months 839, while the number of female children surviving one year of 1000 born was 869. In towns a smaller number survive. Of the conditions causing this high infantile mortality, ignorance and inexperience on the part of parents bear a considerable part, especially as influencing the food and mode of feeding. The death-rates at other age-groups beyond infancy are given in the table on page 340. =Season= influences the death-rate. The third quarter of the year has the lowest death-rate, unless the amount of Epidemic Diarrhœa has been excessive. In the first quarter of the year, the highest death-rate usually occurs. Mild winters and cool summers both lower the mortality. The seasonal incidence of infectious diseases need only be mentioned in passing.

=Density of Population= has important bearings on the death-rate. Thus the urban districts in 1899 had a death-rate of 19·2 and the rural of 16·3 per 1000 of population. Farr found that the death-rate increased with the density of populations, not in direct proportion, but in proportion to the 6th roots of the contrasted populations. This rule does not now hold generally good. It is only after the density has reached a certain degree of intensity that it begins to exert an appreciable effect. Even then it is what is implied in aggregation rather than the aggregation itself that is pernicious. In particular, poverty is usually greater in densely populated districts than elsewhere, with its accompaniments of deficient food and clothing and bad housing. Hence the excess of phthisis in tenemented houses, especially in houses with only three rooms. I have shown that the true density that should be considered is the number of persons to each room, not the number of persons on a given area (“The Vital Statistics of the Peabody Buildings,” _Roy. Statist. Soc., Feb., 1891_).

=Occupation and Mortality.=—To obtain correct statistics showing the influence of occupation on vitality, one must know the number and age of those engaged in each industry, and the corresponding number of deaths. A statement of the mean age at death of those engaged in different occupations would be most fallacious (page 344). The best plan is to restrict the statistics to men aged 25-65, and calculate for these _death-rates in a standard population_, after the fashion already described (page 340). By this means a “comparative mortality figure” can be obtained. For all males it is 1000, for farmers 563, teachers 603, lawyers 821, doctors 966, butchers 1096, plumbers 1120, brewers 1427, innkeepers 1659, potters 1706, file-makers 1810. Speaking generally, the occupations are most unhealthy in which there is most exposure to dust, to the breathing of foul air, and to excessive indulgence in alcoholic drinks (for further details see the author’s _Elements of Vital Statistics_, page 169 _et seq._).

=Deaths from Various Causes.=—These may be stated in proportion to total deaths from all causes, or in terms of the population. The first plan must be adopted only when it is desired to ascertain the proportional share of a given cause of death in the total mortality. In 1899, in England and Wales the diseases named in the first column of the table (page 344), were the most prolific causes of deaths.

ENGLAND AND WALES, 1899.

DEATHS FROM VARIOUS CAUSES TO 10,000 DEATHS FROM ALL CAUSES.

_Bronchitis_ 880 _Phthisis_ 729 _Pneumonia_ 685 _Old age_ 541 _Diarrhœa_, _Dysentery_ 511 _Cancer_ 452 _Apoplexy_ 327 _Influenza_ 213 _Whooping cough_ 174 _Measles_ 172 _Diphtheria_ 160 _Enteric fever_ 108 _Scarlet fever_ 64 _Small-pox_ 3

The diseases in the second column are given in order to indicate their proportional share of the total number of deaths.

The proper plan of stating the death-rate from a given disease is in terms of the population, or better still subdivided into death-rates from the disease for different age-groups as in the table on page 340, if the number of deaths is not too small to admit of this. The importance of stating the death-rate for different age-groups is greatest for such diseases as diarrhœa, whooping cough, and measles, in which most of the deaths occur at ages under five. In the following table are given the death-rates from the causes of death which are most important, either from their magnitude, or because of their preventible character:—

ENGLAND AND WALES, 1899.—DEATH-RATE PER 1,000 PERSONS LIVING.

_Small-pox_ ·005 _Measles_ ·32 _Scarlet fever_ ·12 _Influenza_ ·39 _Whooping cough_ ·32 _Diphtheria_ ·29 _Enteric fever_ ·20 _Typhus fever_ ·001 _Cholera_ ·04 _Diarrhœa_, _Dysentery_ ·94 _Intemperance_ ·09[14] _Cancer_ ·83 _Phthisis_ 1·34 _Other tubercular diseases_ ·58 _Premature birth_ ·58 _Old age_ ·99 _Apoplexy_ ·60 _Convulsions_ ·57 _Valvular disease of heart_ ·38 _Bronchitis_ 1·61 _Pneumonia_ 1·26 _Gastro-enteritis_ ·61 _Bright’s disease_ ·29 _Accidents_ ·59 _Ill defined and not specified causes_ ·73 —— _All causes_ +18·33+

=Determination of Longevity.= We have hitherto considered only death-rates, _i.e._ the number dying each year out of each 1,000 of population. The mean duration of life involves another aspect of the same problem. Although nothing is more uncertain than the duration of individual life, the duration of life for the entire community is subject to so little variation that annuities and life assurance can be made the subject of exact calculations. Of the tests employed to measure the duration of human life the most commonly employed is the =mean age at death=.[15]

sum of ages at death. Mean age at death = ——————————-——————————-. number of deaths.

This is a fair method of stating the average longevity of a particular group of persons, if the group is sufficiently large to avoid the possible error caused by paucity of data (page 349). But it would be entirely unsafe to assume that by this means a safe standard of comparison between two groups can be formed. Thus in 1890 it was stated that the mean age at death of workmen was 29-30 years, of the well-to-do classes 55-60 years. This statement throws no light on the relative vitality of the two classes under comparison. The well-to-do classes consist largely of those whose working days are past; and it is as untrustworthy to compare their mean age at death with that of workmen, as it would be to base any conclusion on the fact that mean age at death of bishops is much higher than that of curates. The mean age at death is lowest in countries with a high birth-rate. Hence it would be very fallacious to compare the mean age at death in England and France.

The =probable duration of life= (_vie probable_) is a term sometimes employed to denote the age at which any number of children born into the world will be reduced to one half. In practice it can only be ascertained from a life-table.

The true mean duration of life or expectation of life can only be ascertained from a =Life Table=, and this must therefore be briefly described. This is the true _biometer_, of equal importance in all inquiries connected with human life with the barometer or thermometer and similar instruments employed in physical research. The Life Table represents “a generation of individuals passing through time.” The data required for its construction are the number and ages of the living, and the number and ages of the dying, _i.e._ the data required for ascertaining the death-rate for each year of life. Theoretically the best plan for forming a Life Table would be to observe a million children, all born on the same day, through life, entering in a column (headed _l_{x}_) the number who remain alive at the end of each successive year until all have died; and in a second column (headed _d_{x}_) the number dying before the completion of each year of life. This method is impracticable, and were it otherwise, the experience would be obsolete before it could be utilised. The method employed in constructing the national Life Tables for England is, without tracing the history of individuals through life, to assume that the population being given by the census returns and the death-rate for each age for a given decennium being known, that the same death-rate will continue during the remainder of the lives of the population included in the census returns.

The total mean number living and the total number dying for a given age-period are known. The mean chance (_p_{x}_) of living one year during this age-period is found by the fraction

Population - ½ Deaths ———————————-———————————- = _p_{x}_ Population + ½ Deaths

It is usual to start with a million or 100,000 children at birth, and to make a separate table for the proportionate number of males and females at birth. Thus in Brighton in 1881-90 these were in the proportion of 51,195 and 48,805. Starting with 51,195 male infants at birth, and multiplying this number by ·84608, the probability of surviving for one year, we obtain 51,195 × ·84608 = 43,315. For the second year of life, the probability of surviving was ·93398; hence the number of survivors is

43,315 × ·93398 = 40,452, and so on.

The general arrangement is shewn in the following example of a Life Table, which only gives the data at or near the two extremes of life, the intermediate figures having been omitted from considerations of space.

BRIGHTON LIFE TABLE.—MALES.

(Based on the mortality of the 10 years 1881-90.)

┌────┬───────────┬───────────┬────────────────────┬────────────────┐ │AGE.│ DYING IN │ BORN AND │SUM OF THE NUMBER │ MEAN AFTER │ │ │ EACH YEAR │ SURVIVING │LIVING, OR YEARS OF │ LIFE-TIME │ │ │ OF LIFE. │ AT EACH │LIFE LIVED AT EACH │(EXPECTATION OF │ │ │ │ AGE. │AGE, _x_ + 1, AND │ LIFE) AT EACH │ │ │ │ │UPWARDS, TO THE LAST│ AGE. │ │ │ │ │AGE IN THE TABLE. │ │ │ │ │ │ │ │ │ x │ d{x} │ l{x} │ Σl{x}+1 │ e{x}º │ ├────┼───────────┼───────────┼────────────────────┼────────────────┤ │ 0 │ 7,880 │ 51,195 │ 2,206,174 │ 43·59 │ │ │ │ │ │ │ │ 1 │ 2,863 │ 43,315 │ 2,162,859 │ 50·43 │ │ │ │ │ │ │ │ 2 │ 996 │ 40,452 │ 2,122,407 │ 52·96 │ │ │ │ │ │ │ │ 3 │ 733 │ 39,456 │ 2,082,951 │ 53·29 │ │ │ │ │ │ │ │ 4 │ 440 │ 38,723 │ 2,044,228 │ 53·29 │ │ │ │ │ │ │ │ ── │ ── │ ── │ ── │ ── │ │ │ │ │ │ │ │ ── │ ── │ ── │ ── │ ── │ │ │ │ │ │ │ │ 97 │ 12 │ 29 │ 43 │ 1·60 │ │ │ │ │ │ │ │ 98 │ 7 │ 17 │ 26 │ 1·53 │ │ │ │ │ │ │ │ 99 │ 4 │ 10 │ 16 │ 1·48 │ └────┴───────────┴───────────┴────────────────────┴────────────────┘

The 43,315 males surviving to the end of the first year of life out of 51,195 born will each have lived a complete year in the first year, or among them 43,315 years. Similarly the 40,452 males will live among them 40,452 further complete years, and so on, until all the males started with become extinct at the age of 105. Evidently, therefore, the total number of complete years lived by the 51,195 males started with at birth will be

43,315 + 40,452 + 39,456 + 38,723 + ... + 10 + 6 + 4 + 3 + 2 + 1 = 2,206,174 years, this sum being obtained by adding together the numbers living at each age beyond (_i.e._ below on this table) the age in question right down to its last item. This number of years is lived by 51,195 males. Hence the number of complete years lived by, _i.e._ the expectation of life of, each male

2,206,174 = ————-————- = 43·09 years. 51,195

This is the _curtate expectation of life_. It deals only with the complete years of life, not taking into account that portion of life-time lived by each person in the year of his death, which may be assumed to be on an average half a year. Hence the _complete expectation of life_ according to the above table is 43·59 years.

In the following table the expectation of life (complete) for various towns and for England is given:—

LIFE TABLE.—EXPECTATION OF LIFE AT BIRTH.

_Male._ _Female._ English Life Table, 1838-54 (_Farr_) 39·91 41·85 „ „ 1871-80 (_Ogle_) 41·35 44·62 „ „ 1881-90 (_Tatham_) 43·66 47·18 London, 1881-90 (_Murphy_) 40·66 44·91 Brighton, 1881-90 (_Newsholme_) 43·59 49·25 Manchester City, 1881-90 (_Tatham_) 34·71 38·44 Glasgow, 1881-90 (_Chambers_) 35·18 37·70

Formulæ of varying degrees of accuracy have been devised for giving in the absence of a Life Table an approximation to the expectation of life.

=Willich’s Formula= is as follows:—If _x_ = expectation of life, and _a_ = present age, then _x_ = 2∕3 (80-_a_). Thus, at the age of 50 years the expectation of life, according to this formula, is 20 years. By the English life-table for 1881-90 it was 18.82 for males, and 20·56 for females. =Farr’s formula= is based on the birth and death-rates. If b = birth-rate and d = death-rate per unit of population, then

Expectation of life = (2∕3 × 1∕d) + (1∕3 × 1∕b).

Thus b for England and Wales, 1889-98 = 30·3∕1,000 = ·0303.

and d „ „ „ = 18·4∕1,000 = ·0184.

(2∕3 × 1∕·0303) + (1∕3 × 1∕·0184) = 47.2 years, as compared with the expectation of life for 1881-90 shown in the above table.

In a life-table the number out of which one dies annually} are the mean age at death} identical and the expectation of life} in value

when the whole duration of life from birth to death is included in the calculation. This is only true for a stationary or life-table population, in which the number dying is assumed to be regularly replaced by a corresponding number of persons of the same age.

=Life Capital.=—The life-tables now in use are those based on the experience of 1881-90. The gain in any subsequent year, as in 1900, may be ascertained as follows: the mean population and the death-rate for each age-group as 0-5, 5-10, etc., are calculated. Then the mean death-rate of the same community for 1881-90 is applied to this population. By this means the “calculated number” of deaths in 1900 is obtained. The difference between these numbers and the “actual number” obtained from the death-registers, gives the gain or loss during the year. Next multiply these differences by the mean expectation of life for the corresponding groups of years. By adding the gains thus ascertained and subtracting any losses, we obtain the net gain in “life-capital” (Tatham) during the year 1900.

=Tests of the Health of a Community.= 1. The _general death-rate_ is the test most commonly applied, and generally trusted. It has its limitations in this respect. It may usually be trusted in comparing a town or district for a single year with preceding years, as the age and sex distribution of a given population only changes slowly. But when comparison with other towns or districts is made, the possibility that erroneous conclusions may be drawn becomes considerable. (_a_) Before the death-rates of two districts can be compared, either this comparison must be made by means of death-rates for age-groups (0-5, 5-10, ... 65-75, etc.) or the factors of correction, the method of obtaining which is described on page 341, must be applied. (_b_) It must be ensured that in the two compared districts, an equal amount of correction has been made for deaths occurring in public institutions and among visitors (page 340). (_c_) Even when the above precautions are taken, it is conceivable that a town with a death-rate of 15 per 1,000 may really be as healthy as another with a death-rate of 12 per 1,000, though a statistical justification of this statement is a difficult task.

Social conditions quite irrespective of the sanitary condition or the natural salubrity of a district have an important influence on the death-rate. Poverty and all that it connotes, necessarily involves a higher death-rate than occurs among the well-to-do. Furthermore, the domestic servants employed by the latter frequently die in districts other than those in which they are employed, without any possibility of the requisite correction being made.

2. _The zymotic death-rate_ is frequently quoted as a test of sanitary condition. This is a death-rate based on the deaths from the “seven chief zymotic diseases,” small-pox, measles, whooping-cough, diphtheria, scarlet fever, fever (chiefly enteric), and diarrhœa. This death-rate should be entirely discarded, the death-rate from each infectious disease being separately stated. A high death-rate from enteric fever would be a much more serious reflection on the health of a town than a high death-rate for whooping-cough.

The death-rate from each of these diseases in London and in England in 1899 was as follows:—

DEATH-RATE IN 1899 PER 1,000 LIVING.

_England and Wales._ _London._

_Small-pox_ ·005 _nil_ _Measles_ ·32 ·47 _Scarlet fever_ ·12 ·08 _Diphtheria_ ·29 ·43 _Typhus_ ·001 _nil_ _Enteric fever_ ·20 ·18 _Whooping cough_ ·32 ·38 _Diarrhœa_ ·94 ·92

A statement of the death-rate from each of these diseases for a series of years is a much more trustworthy test than a similar statement for a single year, in which accidental causes may have caused a temporary increase, or than a statement of the average result for a series of years, which tends to conceal the epidemic variations of the disease in question. The danger of such averages has been well exposed by Chadwick in the remark that “a mean between the condition of Dives and Lazarus tends to make it appear that after all Lazarus has not so much to complain of.”

3. _The infantile mortality_ (page 342) is a delicate test of mixed sanitary and social conditions, and stress may always be laid on it from these standpoints. The importance of comparing death-rates at other age-groups has already been explained.

4. The most delicate and exact method, if all the data are accurate and complete, is to construct a _Life Table_, and ascertain the expectation of life in comparison with that of other communities.

The preceding statistical tests of the salubrity of a community, and any others that may be available, should all, when practicable, be utilised; and it should always be remembered that these tests, especially the general death-rate, are most trustworthy when contrasting the experience of a community with its past experience, and least trustworthy when contrasting its experience with that of others; owing to the difficulty in the latter case of ensuring the avoidance of error arising from _non ceteris paribus_.

=Statistical Fallacies.=—If “fallacies” be regarded as synonymous with “errors,” clearly they may occur at every step. They may be classified as errors of data, and errors of methods. The most important _errors of data_ are erroneous estimates of population, and erroneous returns of deaths, especially in the direction of exclusion of certain deaths (page 340). Death-rates for short periods are relatively untrustworthy. The erroneous use of the mean age at death as a test of longevity has been mentioned (page 344). These are in part also _errors of methods_, and numerous mixed examples are given below.

=Errors from Paucity of Data= frequently arise, the “fallacy of small numbers,” a too hasty generalization, being the most common fault in medical writings, especially in therapeutics. The degree of approximation to the truth of a varying number of observations is estimated by means of =Poisson’s formula=.

μ = total number of cases recorded in two groups. m = number in one group. n = number in the other group, so that μ = m + n.

The extent of variation in the proportion of each group to the whole will vary within the proportions represented by—

m∕μ + 2√(2mn∕μ^3), and n∕μ - 2√(2mn∕μ^3)

The larger the number of the total observations (μ), the less will be the value of 2√(2mn∕μ^3), and the less will be the limits of error in the simple proportion m∕μ.

Thus, of 147 cases of enteric fever, 17 died, a fatality of 11·4 per cent. The possible error is determined by the second half of the above formula—

= 2√(2 × 17 × 130∕147^3) = 2√(4,420∕3,176,523) = ·0746.

_i.e._ the possibility of error = ·0746 to unity or 7·46 per cent. In other words, in a second series of cases of enteric fever under the same conditions as the above, the fatality may vary from 3·94 to 18·86 per cent., a vague result which indicates that the first series cannot be regarded as establishing more than a _primá facie_ case in favour of any special method of treatment that may have been adopted.

=Non ceteris paribus.=—The necessity that data to be compared shall be collected on a uniform plan, and be of a strictly comparable nature, is very frequently ignored. The conclusion that the administration of a given antiseptic is a valuable means of treating enteric fever is not demonstrated by the fact that the fatality in the series of cases thus treated is 7 per cent., while in another series treated without antiseptics it is 14 per cent., unless it is shown that the age and other previous conditions of the patients in the two cases were not widely different, and unless the series are sufficiently long to avoid the fallacy due to paucity of data.

=Errors from the Composition of Rates.=—If the death-rate of A having a population of 10,000 is 10 per 1000, and of B having a population of 20,000 is 15 per 1000, the combined death-rate is not (10 + 15)∕2 = 12·5. To obtain the correct combined death-rate, the number of deaths in A (=100) and in B (=300) must first be ascertained, and the death-rate on a population of 30,000 in which 400 deaths occurred will then be found to be _13·3 per 1000_.

=Errors from Stating Deaths in proportion to Total Deaths.=—There is nothing erroneous _per se_ in stating the proportion of deaths at one age as a ratio of the total deaths at all ages, or the deaths from one cause as a ratio of the total deaths from all causes. It is a useful and in fact the only method practicable when it is required to give the proportion of one of these to the other. But beyond this, such a ratio cannot be trusted. For instance, the proportion of fatal accidents among male infants is 12·2, and among female infants 25·1 per cent. of the total fatal accidents in the male and female sex respectively. But it would be erroneous, if it were concluded from these figures that female are more subject to fatal accidents than male infants. The only conclusion that they justify is that at higher ages females are much less subject to fatal accidents than males. In actual facts, for every 1000 infants born, only 2·9 female as against 3·1 males die under one year of age as the result of accident.

Again, suppose the case of two towns, A and B. A with a population of 10,000 has 150 annual deaths, of which 20 are caused by cancer; the general death-rate therefore being 15, and the death-rate from cancer 2·0 per 1000, while the deaths from cancer form 2∕15 of the total deaths. B, with the same population as A, has 300 deaths, its death-rate being 30 per 1000, and 40 deaths from cancer, its cancer death-rate being 4·0 per 1000; while the proportion of the deaths from cancer to the total deaths is 2∕15 as before. It is useful to know in regard to each of these individual communities that cancer causes 2∕15 of its total mortality, but no comparison between the two is practicable on this basis. The only proper comparison is between the death-rate from cancer per 1000 of population in A and B, which shows that it is twice as high in B as in A. A still more accurate method is to ascertain the number of deaths from cancer, and the number living at different age-groups, thus avoiding any errors due to variations in age and sex distribution of population.

=Errors as to Averages.=—The most common of these results from paucity of data (page 349). Note that the results obtained from an average cannot be applied to a particular case. The mean duration or expectation of life, obtained from a life-table, expresses with almost mathematical certainty, the number of years of life of the members of a community _taken one with another_, but is often not accurate when applied to a single individual.

In _Army statistics_ errors have arisen by failure to comprehend what is meant by the _average strength_ of a force. The statistics must comprise the lives of a given number of persons as well as the deaths occurring among them _for an entire year_, or allowance must be made in this respect when required.

_Hospital statistics_ for similar reasons are frequently fallacious. Thus death-rates have been frequently given per 100 occupied beds, which are most misleading, as the frequency of succession of patients as well as the nature of the patients’ complaints will vary greatly in different hospitals. The only proper method of stating hospital-returns is on the basis of the aggregate annual number of cases treated to a termination. The cases should be further subdivided according to age and sex and disease. _Average death-rates for epidemic diseases_ when used to compare one community with another may give rise to erroneous conclusions. This is inseparable from the nature of such diseases. During the period under comparison, one town may happen to have, say, three epidemics, and the other four; possibly if two or three additional years had been added to the series, the place of the two towns would have been reversed as regards their average death-rate from the disease in question. The proper plan is to give the death-rates from the epidemic disease for every year recorded, to draw a curve of these death-rates for the two towns on the same scale, and to compare the height, the variations of height, and the trend of the curve in each instance.

INDEX.

A

Acarus Scabiei, 276

Achorion Schönleinii, 276

Acne, 161

Aerated Waters, 46

Ague (see Malaria)

Air—Bacteria in, 109, 121 Composition, Properties of, 100 Contagia and, 109, 114 Degree of Moisture of, 119, 128 Gaseous and Other Impurities of, 111 Examination of, 126 Moisture of, 234 In Soil, 221 Suspended Impurities of, 105 Temperature of, 119, 128 of Mountains, 228 Purification of, 129

Air-space, amount required, 142

Alcohol, 55

Amines process, 191

Ammonia—in Air, 101 in Water, 86

Amyloids, 7

Amylaceous Foods, 19

Anopheles (see Mosquito)

Anthrax, 274, 306

Anti-cyclones, 233

Antidiphtheritic Serum, 268, 299

Anti-syphonage, 174

Antill Trap, 180

Apjohn’s Formula, 242

Arnott’s Valve, 149

Arrowroot, 19

Arsenic—in Beer, 62 in Wall Papers, 214 in Clothing, 272

Artesian Wells, 71

Artificial Ventilation, 152 Relative Value, 154

Ascaris, 278

Ash-pits, 199

Aspect, 201

Atavism, 246

B

Bacteria, 273

Bacterial Methods, Sewage Treatment, 192

Ballard’s Researches, 303

Barley, 18

Barometers, 237

Barometric Pressure, 231

Baths, 262

Beaufort’s Scale, 243

Beef, 10

Beer, 61

Bell-trap, 180

Benham’s Gas Burners, 157

Berkefeld Filter, 98

Beverages, 46

Bilharzia Hæmatobia, 277

Birds, Flesh of, 11

Birth-rate, 339

Black Death, 1

Bonds, English, Flemish, 205

Borax and Boric Acid, 44

Boyle’s Mica Valve, 149

Bowels, Attention to, 248

Brandy, 63

Bread, brown and white, 17, 41

Bricks, 205

Broad Irrigation, 192

Burnett’s Solution, 327

Butter, 14

Buys Ballot’s Law, 232

C

Caffeine, 48

Calorigen Stove, 157

Carbohydrates, 6

Carbolic Acid as Disinfectant, 327

Carbon Filters, 97

Carbonic Acid—in Air, 102, 111 estimation of, 126

Carbonic Oxide, 112

Calorie, 32

Carpets, 218

Cement, 213

Cereal Foods, 15

Cesspools, 183

Cheese, 13

Chicory, 50

Chigoe, 277

Chlorides in Water, 81

Chlorine as Disinfectant, 324

Cholera, 92, 225, 302

Cisterns, 76

Clarke’s Process, 94 Soap Test, 79

Climate, 227

Closets, 168

Clothing, 265

Coal Gas, 115

Cocoa, 51

Cod Liver Oil, 14

Coffee, 50

Cols, 233

Comparative Mortality Figures, 342

Concrete, 207

Condiments, 45

Condy’s Fluid, 325

Conservancy Methods, 194

Constipation, 248

Constitution, 245

Consumption (see Tuberculosis)

Container, 169

Cooking, 339

Cooper’s Ventilators, 149

Corrosive Sublimate as Disinfectant, 327

Cotton, 270

Cream, 15

Cyclones, 232

Cysticercus Cellulosæ, 23, 279

D

D-Trap, 169

Damp, Cause of, 211

Damp-proof Course, 210

Death-rate, 2 Crude, 340 Corrected, 342 Zymotic, 297, 348

Decomposed Meat, 24

Demography, 335

Density of Population, 343

Destructors, 200

Dew Point, 241

Diarrhœa, Epidemic, 302

Diet, 29

Dietaries, 33

Diffusion, 129

Diphtheria, 225, 298

Diseased Animals, Meat of, 23

Disinfection, 324

Distillation, 94

Drainage, 166 of Soil, 226

Drains, 177 Examination of, 180

Drugs, 54

Dust in Air, 105

Dust-bins, 199

Dyspepsia, 28, 248

E

Earth-closets, 195

Eggs, 11

Ellison’s Bricks, 151

Endemic Diseases, 289

Enteric Fever, 91, 224, 300

Epidemic Diarrhœa, 26, 225, 302

Epidemic Diseases, 289

Erysipelas, 110, 305

Excreta, 165

Exercise, 249

Expectation of Life, 346

F

Farcy (see Glanders)

Farr’s Formula, 347

Fats, 6

Favus, 276

Fermented Drinks, 55

Filaria, 278

Filters, 97

Filtration, 95

Fire Grates, 159

Fish, 11 Dangers of, 26

Flax, 270

Fleas, 277

Flesh Food, 9

Floors, 217

Flour, 16

Flukes (see Trematoda)

Fomites, 299

Food, 4 Diseases due to, 23 Heat value of, 32 Preparation and Preservation of, 38, 43 Relation of, to Mechanical Work, 36 Variations from Climate, Age, &c, 29 Vegetable and Animal, 31

Forests and Climate, 229

Formalin., 44 and Formaldehyde as disinfectants, 326

Fortin’s Barometer, 238

Fruits, 21

Fuel, 161

Fungi, 20

G

Gaertner’s Bacillus, 25

Galton’s Stove, 155

Gas Stoves, 157, 161

Gelatin, 9

Gin, 63

Glanders, 304

Glaisher’s Tables, 241

Glucose, 21

Gluten, 15

Gout, 28, 59

Goux System, 194

Graveyards, Air of, 118

Green Vegetables, 20, 42

Ground-water, 222

Gully-trap, 167, 180

H

Habits, 247

Haffkine’s Cholera Vaccine, 228

Hardness of Water, 79, 90

Heat, kinds of, 159

Hendon Disease, 27

Heredity, 245

Hermite Process, 191

Hopper-closets, 170

Hot Water Supplies, 163 Pipes, 162

House Construction, 209 Drainage, 165 Materials of Construction of, 205 Position of, 201 Refuse, 198 Slops, 165

Humidity, absolute and relative 235 Measurement of, 240

Hydatids, 279

Hydrocarbons, 6

Hydrophobia, 305

Hygrometers, 101, 240

I

Idiosyncrasy, 246

Illuminants, 115

Immunity, 287

Incubation Periods, 287

Infantile Mortality, 342

Infective Diseases, 284 of Animals, 24

Infectious Diseases, Hospitals for, 320 Notification of, 338

Influenza, 309

Insects and Disease, 281

Intermittent Downward Filtration, 192

Iron in Water, 83

Isobars, 231

Isolation, 319

Isothermal Lines, 230

J

Jenner’s Discoveries, 293

K

Koch’s Postulates, 285

L

Latrines, 174

Laveran, 282

Lead in Water, 82, 90 Workers in, 108

Lice (see Pediculi)

Liebig’s Extract of Meat, 10

Life Capital, 347 Tables, 345

Linen, 270

Lysol as Disinfectant, 327

M

Macaroni, 17

Main Sewers, 183

Maize, 18

Malaria, 91, 224, 307

Mallein, 304

Malt, 18, 62

Malted Bread, 17

Margarine, 15

McKinnell’s Ventilator, 149

Metabolism, 6

Measles, 297

Meat, 9 Diseased, 24 Tinned, 25 Parasites in, 23

Meat Poisoning, 25

Metchnikoff’s Theory, 289

Meteorological Observations, 237

Metallo-keramic Joint, 177

Miasm, 285

Microbes (see Bacteria)

Microscoporon Audouini, 275

Milk, 12 and Disease, 26, 296, 299, 301 Boric Acid in, 44 Souring of, 274 and Tuberculosis, 311

Mineral Waters, 47

Mortar, 206

Mosquito, 282, 308

Moule’s Closet, 195

Mountain Climate, 228

Mutton, 10

N

Natural Ventilation, 147 Relative value, 154

Nematoda, 278

Nitrogen, 274

Nitrates in Water, 81

Nitrification, 192, 220

Nitrogenous Foods, 5

Notification of Consumption, 314 Infectious Diseases, 318, 338 Trade Diseases, 337

O

Oatmeal, 17

Obesity, 28

Occupation and Mortality, 343

Offensive Trades, 120

Oidium albicans, 275

Oils, 46

Onion, 20

Over-feeding, 28

Oxygen in Air, 100

Oxygen Absorbed, 86

Oxyuris, 278

Oysters and Disease, 291

Ozone, 101

P

Pan-closets, 169

Pandemics, 289

Parasites, 276 in Meat, 23

Pasteur-Chamberland Filter, 98

Pasteurization of Milk, 13, 312

Pediculi, 277

Personal Hygiene, 245, 257, 260

Pettenkofer’s Method, 126

Phagocytosis, 287

Phosphorus, in Food, 5 Workers with, 108

Phthisis, 225, 310

Piles, 248

Plaster, 212

Plague, 281, 305

Pneumatic System, Liernur, 183

Poisson’s Formula, 349

Population, Density of, 343 Estimation of, 336

Pork, 11

Porter-Clarke Process, 95

Portland Cement, 206

Potato, 20

Privy or Midden System, 196

Proof Spirit, 64

Proteids, 5

Propulsion, Ventilation by, 153

Puerperal Fever, 306

Q

Quarantine, 320

R

Rabies (see Hydrophobia)

Rainfall, 235

Rain Gauge, 242 Water, 67 Pipes, 166

Rats and Plague, 306

Registration of Births and Deaths, 337

Relapsing Fever, 28, 300

Respiration, 102, 113

Rest, 257

Rheumatic Fever, 225, 306

Rickets, 28

Ringworm, 275

Rivers, 72

Roasting, 38

Roofs, 208

Rum, 63

Rye, 18

S

Saccharomycetes, 275

Sago, 19

Salts as Food, 7

Saprophytes, 286

Scarlatina or Scarlet Fever, 296

Schools, Closure of, 322

Scott Moncrieff Process, 192

Scrofula, 316

Scurvy, 2, 27

Seasonal Incidence of Diseases, 289

Sea Relation to Climate, 229

Sebaceous Glands, 260

Semolina, 17

Septic-tank, 193

Sewage—Disposal of, 190 Dry and Wet Methods of Removal of, 197

Sewers, 183, 184 Air of, 117 Problems as to flow in, 187

Shell-fish and Disease, 291

Sheringham’s Valve, 151

Shone System, 186

Sinks, 167

Silk, 270

Sleep, 258

Slop-closets, 174

Small-pox, 2, 292

Smoke Nuisance, 160 Test, 181

Soap, 261

Soil, 219 Diseases in Relation to, 224 Drainage of, 226

Soil-pipe, 174

Spices, 46

Spirits, 63

Springs, 68

Starch, Detection of, 19

Starvation, 27

Statistical Fallacies, 349

Steam as Disinfectant, 329

Stoves, 157, 161

Streets, Width of, 203

Sugar, 21

Sulphuretted Hydrogen, 112

Sulphurous Acid (Disinfectant), 325

Summer Diarrhœa, 225

Sunshine Recorders, 243

Sweat Glands, 260

Sweating Sickness, 1

Sylvester’s Method, 150

Synoptic Map, 231

Syphonic Closet, 172

T

Tannin, 49

Tape-worms, 279

Tapioca, 19

Tea, 30, 47

Temperature of Rooms, 158

Tetanus, 304

Thermometers, Maximum and Minimum, 239

Thermometers, Dry and Wet Bulb, 240

Thrush, 275

Tight Lacing, 267

Tinea, 276

Tobacco, 54

Tobin’s Tubes, 152

Toxins, 286

Trades and Disease, 107, 118 Offensive, 120

Traps, 179

Trematoda, 277

Trichina Spiralis, 23

Trichophyton, 275

Trough-closets, 174

Tuberculin Test, 311

Tuberculosis, 309 Prevention of, 314

Tuberculous Meat, 24

Typhoid Fever (see Enteric Fever)

Typhus Fever, 300

V

V-shaped Depressions, 233

Vaccination, 293

Valve-closets, 170

Variola (see Small-pox)

Veal, 10

Vegetables, 20

Ventilation, 132 Methods of, 146 Problems as to, 137 By Propulsion, 153

Ventilation by Introduction of Warmed Air, 155 Of Mines, 156 Of Drains, 178

Vermicelli, 17

Vernier, 238

Vinegar, 46

Vital Statistics, 335

W

Wall-paper, 214

Walls of House, 210

Wanklyn’s Ammonia Process, 86

Warming of Houses, 159

Wash-out and Wash-down Closets, 172

Waste-pipes, 166

Water, 65 As food, 8 Analysis of, 84 Classification of supplies of, 73 Constant and Intermittent Services, 76 Enteric Fever and, 72 Hardness of, 79 Impurities of, 78, 89, 90 Sources of, 66 Storage and Delivery of, 74 in Soil, 222 Purification of, 94

Water-closets, 168

Water-gas, Carburetted, 115

Water-test of Drains, 182

Weather Forecasting, 234

Weissman on Heredity, 246

Wells, 69

Whiskey, 63

Whooping Cough, 298

Widal Reaction, 301

Willich’s Formula, 347

Windows, 216

Winds, 131, 230, 243

Wines, 62

Wool, 269

Wool-sorters’ Disease, 274

Work, Amount done, 252 Relation of Food to, 36

Wort, 62

Writers’ Palsy, 252

Y

Yellow Fever, 305

Z

Zygophyta, 275

FOOTNOTES:

[Footnote 1: While the addition of animal fat like margarine raises the melting point, rape-seed oil and other vegetable oils lower it.]

[Footnote 2: The fat to be analysed is saponified with soda or potash, and then the fatty acid set free by hydrochloric acid. If water be now added, 11 or 12 per cent. of the fatty acid will be dissolved, if the fat is butter; less than this if it is a mixture; and not more than 5 per cent. if no butter is present in the fat.]

[Footnote 3: Freshly made; of which 1 c.c. = ·00001 grm. of N₂O₃]

[Footnote 4: Made by dissolving ·395 grm. of KMnO₄ in 1,000 c.c. of water. Each c.c. of this solution =·0001 grm. of oxygen available for oxidation.]

[Footnote 5: Caused by the liberation of iodine. Thus—

K₂Mn₂O₈ + 8 H₂SO₄ + 10 KI = 6 K₂SO₄ + 2 MnSO₄ + 8 H₂O + 5 I₂.]

[Footnote 6: Of the strength of 1 grm. of crystalline sodium thiosulphate to 1 litre of water.]

[Footnote 7: In practice one has frequently to be contented if the CO₂ does not exceed 1 part per 1000 of air; and if the room is clean and free from dust, this higher limit may be accepted.]

[Footnote 8: The damp-proof course should have been shown close under the plate carrying the floor joists.]

[Footnote 9: Some bacteria form in their interior minute _spores_, by means of which they are able to resist ordinary destructive agents. These spores again develope into bacteria.]

[Footnote 10: Furthermore, it is stated that when at rest on a plane surface the Culex assumes a position with the axis of the body more or less parallel to the surface; while the Anopheles, under the same circumstances, has the axis of its body more or less at right angles to the surface.]

[Footnote 11: This is diphtheria attacking the larynx]

[Footnote 12: From “Elements of Vital Statistics,” by A Newsholme.]

[Footnote 13: This was written before the figures for the period 1891-1900 were available; but the method adopted is the same, substituting the death-rates, etc., for the later period.]

[Footnote 14: The death-returns greatly understate the actual death-rate from this cause.]

[Footnote 15: There is no general agreement as to the exact sense in which the words _average_ and _mean_ should be used. They are used here interchangeably.]