tion 0.149: that is the death-chance of a newborn infant under the given law of mortality. As 851 of them survive, 0-851 is the fraction to express the probability of living; it is the life-chance. Now 851 + ·149 = 1 = lifechance death-chance. This probability is often expressed thus: the chances are 851 to 149 that a new-born child will live a year. The value of 11. payable if the child should live a year is 178. (8517.); the value of 11. payable on the death of the child is 3s. (1491.); the chances in favour of life being greater than the chances in favour of death. The lives may be looked at with a view to determine the persistency of the life-force; which is such in the present case, that 851 live out of 1,000 during one revolution of the earth; at the age of twenty it is such that 992 out of 1,000 men live a year. The proportions vary under varying conditions, but these variations do not accurately denote the vital force, which is only correctly measured on the scale of mortality.

"The mortality is determined by the ratio which the deaths bear to the years of life.* The men living, and the time expressed in years, multiplied into each other, produce the years of life with which the deaths are compared. A year of life is the lifetime unit.' It is represented by one person living through a year; or by two persons living through half a year. A regiment of an average strength of 1,000 men during three years represents 3,000 years of life; and if the deaths in the three years are 60, the rate of mortality is thus 60 expressed: m = =02; or the mor3000 tality is said to be at the rate of two per cent. per annum. The 100 years of life are a fixed quantity; and as it is found that under various circumstances, and at different ages, the rate varies from 1 to 2, 3, 4, 5 up to 50, this scale serves to measure the life-force, or the complementary death-force, in the same way as the centigrade scale of the thermometer serves to measure heat. A thermometer is not a convenient measure of heat unless at all temperatures it contains the same quantity of mercury,

XX.

*See introduction to English life table, pp. xiv. to

and unless each degree measures equal expansions of the mercury. If the mercury escapes, a correction is required to give the expansion of equal quantities of mercury at every degree of temperature. In observing with the barometer, the measure is adjusted at both ends, so as to give the exact height of the column above the mercury in its well.

"So, to determine the rate of mortality on a strength of 1,000 men joined by no recruits, it is necessary to take their mean strength during the whole period of observation; for if one man dies at the end of a week, 999 only remain afterwards exposed to risk, and if the numbers are reduced at variable intervals to 990, to 985, to 911, to 700, to 600, and so on, it is evident that the years of life in the same time will be less than the years of life in a regiment which obtains a recruit for every casualty. All that is required in such cases is to take the observations so as to give the true years of life; and the ratio which these years of life bear to the deaths is the exact measure of the mortality. It is evident, on the other hand, that such a measure is not supplied by a comparison of the deaths in a year, for example, to the living at the beginning of that year. The results by this method are only strictly comparable when the deaths are in the same proportion and occur in the same periods of the year.

"By the English life table 1,000 infants followed through their first year of age yield nearly 903 years of life; and the mortality is at the rate of

=.16559.

149 903'

or, more correctly,

It is 16 559 per cent.

149,493 902,781 per annum. The probability of dying is 149493; and upon the erroneous assumption that this is the rate of mortality it would be 14.949 per cent. per annum; less by 1.610 than the true rate, with which it should never be confounded.

"At other ages than the first year the rate of mortality serves to give the probability of living a year, and thus supplies the fundamental elements of a life table. The difference between the rate of mortality (m), and the probability of dying (p), becomes less in proportion as the two fractions diminish; for upon the hypothesis that the deaths in a year occur

"II. MORTALITY AT DIFFERENT STAGES OF LIFE.

"The Mortality of Infants.

"As there are difficulties in determining the ages of the oldest people in the population, so there are great difficulties in determining the rate of mortality among infants, from the want of exactly observed facts. The infants in the first year of life are to some extent mixed up with infants in the second year of age; and their numbers fluctuate from year to year, owing to fluctuations in the births, and the mortality from zymotic and other diseases, so that the years of infant life cannot be accurately deduced from decennial enumerations of the infants living at the date of the Census. Again, the mortality diminishes so rapidly after the date of birth, and at such various rates under different conditions, that it is necessary to subdivide the first year into months, and even days, to get results exactly comparable. The still-born children in England are not registered; and a certain number of infants that breathe for a short time are, it is believed, to save the burial fees, interred as the stillborn are buried, and so escape registration. Upon the other hand, the deaths of premature children born alive are registered; and they amounted to 45,814 out of 626,340 deaths of infants under one year of age in the six years (1858-63) that they have been distinguished from infants dying of debility. The recognized proportion is 7.315 per cent., so that to obtain the rate of mortality among children born at the full term of nine months, the premature children, if we had the means, should be struck out of the account both of the living and dying. This is impossible in the present state of statistical observation. But it happens that these deaths of premature children serve as probably more than a sufficient set-off against the infants of full term dying soon and escaping registration.

"The age of man is reckoned from the date of birth; but before that date the foetus has lived its intra-uterine life, and the instant in VOL. I.

which the sperm-cell and germ-cell intermingle is the true time of the embryo's origin. Respecting the rate of embryonic mortality there is little definite information; but it is probable that as the mortality in the first year of breathing life rapidly increases as we proceed backwards from the twelfth to the third, second, and first month, the same law prevails during embryonic life, until we arrive at the destruction of an immense proportion of the spermatozoa and ova which are provided to secure the continuation of the species. This question well deserves the attention of the Obstetric Society, and is intimately connected with abortions, miscarriages, and still-births.

"From a table inserted in the English life table showing the estimated numbers of males and females surviving each month, and the annual rates of mortality in each month; it will be observed that the rate of mortality rapidly declines month by month; and that the mortality of boys in every month exceeds that of girls, so that at the end of the first year the number of boys does not greatly exceed the number of girls.

"The mortality of infants in France was such in the first year as to reduce 1,000,000 to 820,065, according to the experience acquired by following the births in 1856-60 for the twelve months following. The deaths were 179,935, and the probability of dying, 0.179935. The French returns show the deaths in the first week of life; and by the returns of 1856 the mortality was at the rate of 154 per cent. per annum in the first seven days, 120 in the second seven days, and 54 in the sixteen days following. The mean births were 927,226; the deaths in the three periods were 27,002, 20,517, and 20,618, making 68,137 deaths in the first month of life. So out of 1,000,000 births 29,121 die in the first week, 22,128 in the second week, and 22,236 in the sixteen days following. In England and Wales the deaths of 2,374,379 infants in the first year of age were registered in the twentysix years 1838-63; and of the number 1,329,287 were boys, 1,045,092 were girls. 996,680 deaths at the same age were registered in the ten years 1851-60; of boys 557,213, and of girls 489,417. Nearly 100,000 infants died annually; in the proportion of about 56 boys to 44 girls.

34

"Causes of Death in Infancy: Age 0-1. "The causes of death are necessarily obscure. The small organs are not fully developed, and the functions are often not easily explored. Of the subjective symptoms no information is supplied by the little patient.

"When the zymotic diseases are fully developed they are distinguishable in infants. Whooping-cough was fatal in infancy; but the bowel complaints were nearly three times as fatal as whooping-cough. Thus in the ten years 5,027 boys and 4,114 girls died annually of diarrhoea, dysentery, or cholera. From all zymotic diseases, 11,442 boys and 9,956 girls died annually. Of scrofula, phthisis, and hydrocephalus 3,547 boys and 2,723 girls died annually. The convulsive diseases and other affections of the brain and spinal cord were fatal to 12,448 boys and 9,171 girls of the first year of age annually. The diseases of the lungs were less fatal. 607 of the boys and 532 of the girls died by accidental or other violence yearly.

"Nothing is known in our statistics about the still-born, as they are not at present registered, on the ground that it is difficult to distinguish them from abortions and miscarriages. But the difficulties are not insuperable; and in many ways the facilities of burying stillborn children unregistered throw open the gate of temptation to crime.

"Children under Five Years of Age: 0-5. "Note.-The rates in the text show the deaths to 100 living, unless another basis is indicated.

"By the English life table, the mortality, it will be seen, decreases rapidly after the first year of life. The annual mortality of males per cent. in each of the first five years of age is 18-326, 6.680, 3.624, 2·416, and 1.799; of females 14-749, 6·436, 3.603, 2-450, and 1-785. The mortality of males by the life table under five years of age is 7.014, of females 6-125. During the ten years, 1851-60, the mortality of males of ages (0-5) in somewhat different proportions was 7.243 per cent., of females 6.274 per cent. The proportions. of the first and second year's children are higher in the increasing population than they are in the life table. When the mortality by each cause is treated of, we may take, to avoid

fractions, 1,000,000 males living a year for basis; then to that number the annual deaths by zymotic diseases were, by small-pox, 1,047; typhus, typhia, and typhinia inclusive, 1,401 ; measles, 2,847; whooping cough, 3,246; scarlatina, 4,311; diphtheria, 431; cholera, diarrhoea, and dysentery, 5,625; making, with others, 22,420 deaths out of 1,000,000 boys by all zymotic diseases, against 21,772 out of the same number of girls. Whoopingcough was more fatal to girls than it was to boys in the proportion of 4,003 girls to 3,246 boys; so was typhus or typhia; all the other zymotics were more fatal to boys than to girls.

"Cancer was fatal to few children; and the deaths were probably from soft cancer (fungus hæmatodes). There were many deaths from scrofula and phthisis. Hydrocephalus killed boys in the proportion of 2,915 to 2,162 girls; other diseases of the brain in the proportion of 12,169 boys to 9,479 girls. These brain diseases constitute a sixth part of the mortality of the young boys, and between one-sixth and one-seventh of the mortality of girls.

"Convulsions in infancy is the capital head under which these affections accumulate. Like diarrhoea, convulsion is the result of teething, local irritations, poisons, zymotic action in the early stage, before the development of its characteristic symptoms. The nerve-force is thrown into motion by a great variety of causes; and the convulsion of the muscles is so striking a symptom that it overwhelms all others, some even more dangerous in their essence.

"The heart and lungs-the great seats of the circulatory and respiratory systems-are intimately connected. Death ensues when the heart does not beat. The stoppage of the breath, or anything to prevent the access of oxygen and the expulsion of carbonic acid, is fatal. Thus from the affections of the respiratory system we have a mortality of 11,296 boys and 9,499 girls per million. The lung and the brain diseases of girls are equally fatal. The diseases of the digestive organs produced a mortality of 1,470 boys and 1,121 girls. The maladies of the urinary organs, of the organs of generation, of the joints (excluding scrofula), and skin are rarely fatal in childhood. The violent deaths are nearly as fatal as the idiopathic diseases of the digestive organs, for 1,451 boys, 1,188 girls, per million

living died annually by violence. Under other causes are included premature births, atrophy, and debility, malformations, teething, as well as cases in which the causes are unspecified. There are 16,579 annual deaths to a million boys, and 13,885 deaths to a million girls, from a group of causes, including malformations, premature birth, atrophy, debility, and other ill-defined developmental diseases.

"Mortality of Children (0-5) in different Districts.

"Death in childhood is an unnatural event, inasmuch as the regular series of development of the human structure from the germ-cell to the perfect man in his prime, and in his last. declining stage of existence, is interrupted. But life at all ages depends upon so many conditions, and is exposed to so many risks, that

out of given numbers living some die at every age, and we can only take for a practical standard the lowest authenticated rates of mortality.

"Thus in the 63 healthy districts of England the annual mortality of boys under five years of age was at the rate of 4.348, and of girls 3.720 per cent.; the mean being 4.034. 28 districts have been selected, showing the low annual rate of mortality 3.348 for the mean of the rates of the two sexes: the boys dying at the rate 3.576, the girls at the rate 3·120.

"The 28 districts are found in all the regions of England and Wales, from the northern limits of Northumberland to the New Forest on the Southampton Waters. The mortality was at the annual rate of 2.317 in Bellingham; 2-593 for boys, 2.040 for girls. This rate is slightly exceeded in the adjoining district of

Rothbury, also on the border of Northumberland; and in Bootle north of the Duddon on the coast of Cumberland. The mortality among the families of the British peerage has been investigated with much care and ability by Mr. A. H. Bailey and Mr. A. Day.* They confined their investigation to the peers, the children of peers, and the children of the eldest sons of peers living in the present century. The numbers existing on December 31, 1855, were 4,282; 2,283 males, and 1,999 females. The mortality of peers' children under five years of age was at the rate of 2.069 per cent.; among boys under five years of age 2.227, girls 1.882. The number of facts for the peerage is small; as the deaths of boys were 274, of girls 196; or 470 in the aggregate. For Bellingham the deaths of boys in ten years were only 112, of girls 82; 194 in the aggregate. The districts of the lowest mortality are very thinly peopled, but there is no reason to suspect that any of the deaths are unregistered. And the mortality only proceeds gradually step pp. 305-326.

* Assurance Magazine, vol. ix.,

by step up to 3.500 in many other districts. Dr. Joseph John Fox, in a valuable paper on the vital statistics of the Society of Friends, found that by the returns in the Annual Monitor' the mortality under five years of age in 1842-52 was at the rate for boys of 3·190, of girls 2.383.† This mortality differs little from the mortality of the peerage. Another return makes the mortality of the boys of Friends 5.598, of the girls 4.733. The mortality of 1,087 children of the clergy has been investigated by the Rev. John Hodgson, M.A., who procured returns in 1829 and 1858 from the parents; the mortality of the boys was at the rate of 3.729, of the girls at the rate of 2.302 in the years under observation; making the mean mortality of the sexes 3.027.

Very different are the rates of mortality among children in 151 districts; where the