consideration of the male and female children in the said town, and the ages of their parents at the time when such children were respectively conceived, a scheme may be estab. of the powers of generation, and the inclination of the several coalitions towards the producing the one or the other sex, according to the superiority of power in either sex, at the time of such respective coalitions.

In 1710 was pub. New Proposals by the Prolifical So. for Promoting a Contribution towards raising a Monthly Dividend on the Birth of Infants to be born in Wedlock, and living on the second day after their Birth. We shall speak of this So. more at large under POPULATION.

In 1742 Herr Sussmilch pub. in Berlin a treatise On the Divine Decree in the Variations of the Human Race, with regard to Births, Deaths, etc. The work is frequently quoted by Malthus, Price, Milne, and other writers. We do not think it necessary to dwell upon it here. It is often quoted in these pages.

In 1747 a project was set on foot for a General Registry of Births kept at the Herald's Office, on St. Bennett's Hill, near St. Paul's, Lond. The prosp. of the scheme says:

As a General Registry of Births will be of the greatest use in preventing many controversies, and clearing up various difficulties with respect to inheritances and claims of different natures, The King's Heralds and Pursuivants of Arms have thought proper to open a Gen. Regis. of the Births of all Persons, whether natives or foreigners, whom the extensive commerce of this nation may invite to live among us, who shall think fit to apply to them at the Office of Arms.

The Supreme Courts of Judicature being held near this metropolis, a Gen. Regis. of Births from all parts of H.M. dominions collected into one, and ready at hand to be consulted, as in the case of wills, must save great trouble and expence which people are put to when it is necessary to consult such regis. as are now kept dispersed in the several parishes, and which do not comprehend the numerous births of children not baptized in the Estab. Church, or not baptized at all. Proper books will be provided for making the necessary entries, viz., for Lond. and places within the B. of mort.; for the country; and for the colonies abroad. Likewise one for entering the births of persons of any age, born before Christmas-Day, 1747.

There will be daily attendance given, holidays excepted, at the Office of Arms or Herald's Office aforesaid, at the usual office hours, viz., from nine in the morning till one, and from three till five in the afternoon, by a herald and a pursuivant, who are sworn officers; one of whom will make due and exact entries of what is brought before them.

For such who live in Lond., and can conveniently come to the office, one or both the parents are desired to attend there in person; or, in case that can't be done, two persons who were present at the birth, the midwife for one, if convenient, may attend and sign the entry, which shall be witnessed by two officers of arms, in the regis.-book, on paying the fee of half-a-crown; and at the same time an attested certificate of the entry made shall be given upon parchment, and sealed with the seal of the office.

For persons at a distance, they are desired to draw up a certificate, to be signed either by one or both the parents, or by two persons present at the birth, and if convenient the midwife for one, and to go to some neighbouring Justice of the Peace, before whom they are desired to make affidavit of the truth; which certificate and affidavit being transmitted to the office, with the fee of half-a-crown, shall be duly entered by one of the officers in waiting, and the originals shall be filed, or otherwise carefully kept. But if one person present at the birth can attend the office, and bring a certificate signed by one or both the parents, or two persons present at the birth, done in his presence, such certificate shall be enter'd, the person so attending signing the entry in the regis.-book in the presence of one of the officers in waiting. If the time and place of the parents' marriage be also given in, it may be a means of proving those marriages with more ease. But the mother's father's name should always be inserted.

In the 3rd ed. of De Moivre's Doctrine of Chances, pub. 1756, he takes up the reasoning of Nicolas Bernouilli, to which we have referred in this present art., and shows how he had misrepresented the argument of Dr. John Arbuthnot and others. Thus :

Dr. Arbuthnot never said, "that supposing the facility of the production of a male to that of the production of a female to be already fixt in nearly the ratio of equality, or to that of 18 to 17; he was amazed that the ratio of the numbers of males and females born should for many years keep within such narrow bounds"-the only proposition against which Mr. Bernouilli's reasoning has any force. But he might have said, and we do still insist, that "as from the obs., we can, with Mr. Bernouilli, infer the facilities of the production of the two sexes to be nearly in a ratio of equality; so from this ratio once discovered, and manifestly serving to a wise purpose, we conclude the ratio itself, or if you will, the form of the die, to be an effect of intelligence and design." As if we were shown a number of dice, each with 18 white and 17 black faces, which is Mr. Bernouilli's supposition, we should not doubt but that those dice had been made by some artist, and that their form was not owing to chance, but was adapted to the particular purpose he had in view.

It is clear that De Moivre viewed the whole question in the light of this general proposition, which he had laid down, and which is the very converse of the reasoning of many writers, both ancient and modern, "that although chance produces irregularities, still the odds will be infinitely great, that in process of time, those irregularities will bear no proportion to the recurrence of that order which naturally results from orig. design." This argument certainly seems to apply in a remarkable manner to the proportion of births.

In the Phil. Trans. for 1767 (vol. 57), there is a paper by Dr. Thomas Heberden, Of the Increase and Mort. of the Inhabitants of the Island of Madeira. In this island it appeared that for the 8 years 1759-66, the weddings had been to the births as 10 to 468; and to the burials as 10 to 27.5, or 9 to 24'75.

That the numerical progress of a community may be approximately ascertained by means of carefully compiled regis. of its birth, read in the light of its death registers, complied with equal care, has long been known. But in order to be exact, it is necessary that there be no fluctuations in the pop. by means of emigration, or immigration. An instance is recorded by Dr. Derham, in his Physico-Theology [first pub. 1713, but afterwards passing through many eds.], in the parish of Aynho in Northamptonshire-a purely agricultural district-where for a period of 118 years, the births had been to the marriages

as 6 to 1; yet the burials had been to the marriages only as 3 to 1. various instances of this character. [See also Porter, 1833, in this art.]

Dr. Price gives Dr. Price found that in the town of Northampton, for the 40 years 1741-80, the number of christened was in the whole 6326-of which 3218 were males, and 3108 females.

In 1798 the Rev. T. R. Malthus pub. his famous Essay on the Principle of Population, etc., wherein he laid down views regarding the influence of the birth-rate upon the welfare of a community, differing almost entirely from the views of any other writer, either before or since. His work has given rise to a large amount of controversy upon which we do not propose to enter here. [POPULATION.]

In our art. on BILLS OF MORT. various items of information are given regarding Births; and under date 1823 some very remarkable figures are given regarding the births, and proportion of sexes, in the City of Palermo.

In 1827 Herr Hofacker pub. at Tubingen his work: De qualitatibus Parentium in Sobolem prodeuntibus præsertim rei Equariæ, etc., of which, however, but little was known in Europe generally, and that little was obtained by means of an extract from it contained in the Annales d' Hygiène, 1829. The researches of Hofacker were based upon 2000 births in the city of Tubingen, in Wurtemburg. But as his Tables have since been communicated to the Assu. Mag. in extenso [vol. iii. p. 259], it seems unnecessary to repeat them here. They go to show that the sex is determined by the superior age of the male or female parent. He made some researches into a rural pop. of more limited extent than his city obs. Thus in a village there were born in 43 marriages where the wife was older than the husband, 83 boys and 103 girls ; 17 marriages, where the husband was older by 9 to 12 years than the wife, 46 boys and 33 girls; II marriages, where the husband was 50 to 60 years old, 10 boys and 4 girls.

In other villages he found similar proportions; and on the whole his researches led to the conclusion that in cases where the wife is older than the husband, the proportion between the girls and boys is 1031 to 1000.

In 1830, Mr. M. T. Sadler, M. P., pub. his Law of Population: a Treatise in six books, in Disproof of the superfecundity of human beings, and developing the real principle of their increase. His theory, as will be judged from the title of his work, was altogether opposed to that of Malthus.

In 1833 Mr. G. R. Porter pub. his Progress of the Nation; and therein he laid it down that the proportionate number of children born in any country could not be taken as any test of the number of its inhabitants:

For it is well known that in climates where the waste of human life is excessive, from the combined causes of disease and poverty affecting the mass of the inhabitants, the number of births is proportionably greater than is experienced in countries more favourably circumstanced. Frequently, and indeed almost always, in old settled countries, the proportionate number of births decreases with the advance of civilization and the more general diffusion of the conveniences and luxuries of life. In fact, the pop. does not so much increase because many are born, as because few die.

The subject is treated in a somewhat different light by Sang in his Essays on Life Assu., 1852. [POPULATION.]

In a paper by M. Edouard Mallet, entitled Historical and Statistical Inquiries respecting the Pop. of Geneva from 1549 to 1833, which appeared in the 17th vol. of the Annales d' Hygiène Publique, were contained various facts of interest concerning births, etc. For instance, the proportions between_the_marriages and the births from 1814 to 1833 were found to be 1 in 271, or nearly 2 children to each marriage. If 517 stillborn legitimate children were added, the proportions came to be 2.7193 born alive; stillborn, 01429 together, 2·8622 conceptions to each marriage. The writer says hereon :—

This mode of calculating the proportion by the total number of marriages and the total number of births may be questioned, as the regis. do not distinguish the marriages which have proved barren; and the births in a town do not exactly correspond with the marriages in the same town. In Geneva children are born of parents who were married elsewhere, and persons who are married there settle in other parts. Besides, the births which are regis. in one year do not correspond with the marriages celebrated in the same year; therefore the births which took place in 1814 were the offspring of the marriages of the previous year, and the births consequent on the marriages in 1833 will not appear before the following year.

These objections could not be overlooked in considering the fecundity of a pop. for 1 or 2 years only; but in doing so for a period of 20 years their force disappears. As the fruitfulness of the marriages of 1814-15-16 has prob. ceased before 1833; and if the children who spring from the marriages of 1833 are excluded, their number will be nearly balanced by that of the children included from the marriages of 1813.

He next reviews the births of males and females during the years 1695 to 1791, both inclusive. The totals were 68,764, of which 35,022 were males, and 33,742 were females. In one decennial only, 1761-70, did the female births slightly exceed the male births:

The male births were 50'93 p.c. of the total number, and in proportion to the female births were as 103.8 to 100. The female births were 49'07 p.c. of the total number, and in proportion to the male births were as 96'3 to 100. As in the same years there were 65,030 deaths, the births exceeded the deaths by 3734, or 1. On comparing the births and deaths of each sex, the following results appear: Male Births

...

Deaths

...

33,113 29,568

Excess of Male Births ... 3545

Female Deaths
Births

32,457 31,903

In the periods following, the proportion of ann. births to the pop. varied thus: from

160 5 to 1710, 1 in 27; from 1711 to 1730, 1 in 30; from 1731 to 1750, I in 31; from from 1751 to 1770, 1 in 30; from 1771 to 1791, 1 in 33. During the six years, from 1786-91, there were 278 illegitimate in 4352 births, being about I in 15. During the period 1806-12, the births were in the proportion of 1 to 40 of the pop. During the 20 years ending 1833, the births were only in the proportion of 1 in 47 of the pop. During the decennial period 1824-33 the births increased 13.6 p.c.; while the pop. increased 12.5 p.c.

The relative proportions of male and female births varied considerably during the 20 years 1814-33. In the years 1818-20-21, more females than males were born; while in 1832 the males exceeded the females by 57 p.c.! During the decennial 1814-23 the per-centage of males to the whole births was 51:163 p.c.; in the decennial 1824-33, they were 52 684 p.c. On an average of the 20 years, 13 males were born to 12 females. With regard to the illegitimate births, the following fact appeared-the males were in the proportion of 69 to 68 females. In the first 10 years the stillbirths were 1 in 15; in the second, I in 19. This decrease was attributed to improved midwifery. The number of males who were stillborn was greater than the number of females, in the proportion of 4 to 3. The twin births were 1 to 73 of the total births. In the total number of twin children, the excess of females was very nearly equal to that of the males in the total births. Male twins occurred less frequently than female twins; and male and female twins were the most frequent. No triple births were recorded from 1814 to 1833.

At the meeting of the British Asso, held in Dublin in 1835, a Regis. which had been compiled by Dr. Robert Collins, M. D., then late Master of the Lying-in Hospital of Dublin, was presented. It extended to 16,414 deliveries. An abstract of it appears in the Trans. of the Asso. for that year; but the results there given have a medical rather than a statistical bearing. Of 16,654 children, 1121 were stillborn; and 214 of those born alive died-generally on the 8th or 9th day after birth. The Regis. extended over a period of 7 years, commencing Nov. 1826.

In the Trans. of the same Asso. for the following year there appears: Obs. on the Periodicity of Births, showing the total number born in each Month; the number of Premature Children; the Sex, etc.; the number of Stillborn Children, and Children dying; also with regard to the death of the Mothers, and the most important complications met with in Delivery, deduced from the experience of 16,654 Cases. This was indeed a series of most interesting tables deduced from the Registers of Dr. Collins. The following T. presents some combinations of facts of considerable interest.

The following statistics, compiled from the returns of the five leading powers of Europe about the year 1842, are given in the 6th Rep. of the Reg.-Gen. They show not only the number and proportions of births in each country, but the illegitimate births (except in Russia) separately:

In 1842 there was presented to the Brit. Asso.: Report of a Committee of the Brit. Asso. for the Advancement of Science, consisting of Lieut.-Col. W. H. Sykes, F.R.S.; Lord Sandon, M.P.; G. R. Porter, Esq., F. R.S.; J. Heywood, Esq., F.R.S.; Dr. W.

P. Alison, and E. Chadwick, Esq., on the Vital Statis. of very large Towns in Scotland. The Committee had been appointed in 1840. An extensive series of tables was prepared, including some on "Births and Baptisms. The report itself says regarding these:

The inattention which prevails among parents in Scotland in regard to the recording the births of their children in the public regis., even though the parties themselves continue to experience great inconvenience on many occasions on account of the omission, is so very great as to render the statistics of births of no avail to the statist. ...

We need not proceed further-except to say that happily this state of things is now remedied.

In 1848 Dr. Kayser, Prof. of Statistics, at the University, Copenhagen, pub. a treatise: Det Kongelige Medicinske Selskabs Skrifter, in which he treats of fecundity, pop., etc., of Denmark. Instead of fixing the births in proportion to the whole pop., he fixes them in proportion to the whole number of women of the fertile age-which in the northern countries is between 20 and 50 years. He especially mentions the error so commonly committed in indicating the morality of a town or country by the proportion of the illegitimate births to the legitimate. The last number, he argues, is never constant, but depends upon the fluctuation of the marriages; when the marriages increase, the number of illegitimate births will be proportionably decreased; and when the marriages decrease, the number will be raised, although perhaps the real relation is quite otherwise. To compute that proportion, it will be necessary to compare the number of illegitimate births with the number of unmarried women living at the fertile age. In that manner he has computed the proportion at different periods for the towns in Denmark, with a result very different from that arrived at by the method commonly used. Some of his results we shall presently have to notice more in detail. It should be stated that Kayser's obs. were extended over a series of years, partly from 1827-44, and partly from 1830-44.

In a paper on the Vital Statistics of Iceland, read before the Statistical So. of Lond. in 1849 [vol. xiv. p. 1] by Dr. P. A. Schleisner, which was an abstract of his work: Island undersögt fra et largevidenskabeligt Synspunkt af, pub. the same year, the writer says:

Almost all the foreigners who have travelled in Iceland have mentioned the extraordinary fecundity of the nation as something remarkable. It is noticed that families with 20 children and upwards occur frequently. But from such single facts, a general rule for the fertility of a nation cannot be deduced. I have tried to find it out. The fertility of a nation is commonly indicated by the proportion of the children born to the whole pop.

He then examines the theory of Dr. Kayser, as we have already set it forth, and considers it faulty:

It will be seen from the Swedish lists of births and deaths, which contain besides the number of children born, also the ages of the lying-in women, that the fertility is different at different ages, being for instance, in Sweden, highest between 30 and 35 years. Now it may very well happen that two nations, even if they contain the same number of fertile women, may contain a different fraction of them at the most fertile age, and also that the ratios of fertility-if I may so express myself-may differ at the various ages. It will therefore be necessary to construct the tables for the fertility in the same manner as for the mort., unless we follow the method indicated by Moser, who recurs to the marriages and life tables.

He then compares the results of Kayser's obs. for Denmark with those of his own for Iceland, in the several particulars discussed. We can only follow him in his details as to male and female births; thus:

It will hence be seen that the fertility of the Icelandic women both married, and especially unmarried, is a great deal greater than that of the Danish; but that the pop. in point of fertility is not so well composed as the Danish. In Denmark the number of married women out of the whole number of fertile women is 57°4 p.c.; while in Iceland it is only 519 p.c. It will be seen from the above T. that the number of male births exceeds that of female births in a higher degree in Iceland than in Denmark. I have already shown that the prob. lifetime of the Icelandic females in relation to the males is still better than in Denmark; hence it will not excite wonder to find that in the Icelandic pop. the proportion of the males to the females is as 1000 to 1020; while the proportion in Denmark is as 1000 to 1023. The proportion of stillborn children is more favourable in Iceland than in Denmark. It cannot but be apparent that both Kayser and Schleisner are dealing with the results of small populations.

Mr. Saml. Brown, in a paper read before the Inst. of Actuaries in June, 1850, said: "The regis. of the births, which is an important element in ascertaining whether a pop. is increasing or decreasing, is very deficient even still, and has been noticed by the Reg.Gen. with a view to its correction." We are glad to say that we believe most of the causes of error have been corrected.

There is good reason to believe that in England, at least, the rule of an excess of male births is subject to no exception.-Dr. Guy, 1850, Statis. Journ. 13, p. 42.

The following calculation of the Census Commissioners of 1851 shows the influence of bachelorism and old-maidism in retarding the progress of the pop., by keeping down the births: "The Brit. pop. contains a great reserve of more than a million unmarried men, and more than a million unmarried women, in the prime of life, with as many more of younger ages; and if the whole of the pop. were married, the births in Gt. Brit. would,

instead of 700,000, be about 1,600,000 ann., if they bore the same proportion to the wives at different ages as they do now!"

In that year (1851) the births regis. in England and Wales were 615,865; of these 573,865 were the children of married, and 42,000 of unmarried women. The number of married women of the child-bearing age, viz., 15 to 55, was returned at 2,553,894 in that year; and of unmarried women, including widows as well as spinsters, 2,449,669. So that the above figures give to each 1000 of married women, 224 children born annually; and to each 1000 unmarried women, 17 children born annually! Upon which the Census Commissioners remark that, " 186,920, or 1 in 13 of the unmarried women must be living so as to contribute as much to the births as an equal number of married women! From these, or similar statistics, it has been calculated that one out of every fifteen English men and English women now living was born illegitimate!

In a letter communicated by Herr Hopf, of Gotha, to the eds. of the Assu. Mag., in 1852 [vol. iii. p. 255], occurs the following passage, embodying some ideas which we regard as original :

The proportion which the births bear to the numbers of the pop. commonly is a much more uniform one than that of deaths. I some years ago collected the facts in reference to this question, which, with respect to Prussia, have led me to the following results: In the years 1816 to 1843, during which period the pop. of Prussia increased from 10 millions to 15 millions, the average proportion of the births in this country amounted to 4'088 p.c. of the pop. a year, and that of the deaths to 2'886 p.c. But while the mort. of one year rose to 3'549 p.c., or exceeded by 22'95 p.c. the above-stated average proportion, and that of another year lowered to 2'515 p.c., or fell short by 12'85 p.c. of the same average; the utmost fluctuations undergone by the births were between 4'487 and 3652 p.c., or 9'77 p.c. above, and 10'68 p.c. below the average proportion. The deaths, therefore, required for their fluctuation a scope of 36 p.c. of the regular ratio, whereas the births varied only 20 p.c.; and the former proved much less constant than the latter, though human will is allowed to exercise an influence on births which it cannot exercise on deaths. But this will Providence has limited by the action of instinct, the effects of which we see are far more uniform than the working of the law of mort. Considering this, assu. for BIRTHS, when estab. on a large scale, might be granted with greater safety than DEATHS. Regarding the proportions of the sexes born, he remarks as follows:

It is a fact that 5 to 6 p.c. more boys than girls are born; but the cause of this fact does not seem to be as yet sufficiently fixed. Hofacker, a German, and Sadler, have indeed found that from marriages up to a certain age of the married persons, there will be got so much the more boys, the more the age of the husband exceeds that of the wife. When it is therefore considered that, at least in Germany, the husbands on an average uses to be by 5 to 6 years older than his wife, this difference of age would be sufficient to make good the excess of the male births. Yet this difference of age, instead of being the true operative cause of the fact in question, is, in my opinion, only another parallel exterior fact, unable to account for the other. We first find that the illegitimate show a smaller proportion of the excess of boys-in Prussia there are among natural children only 103 boys to 100 girls-and yet we are not entitled to suppose the difference in the ages of the parents of natural children to differ materially from that of the parents of legitimate ones.

Another most striking abnormity occurs with the Jews, who amounting in Prussia to about 200,000, make at present about 1p.c. of the whole pop. of the kingdom of Prussia. Among this race, according to facts collected from a period of 15 years, the proportion between births of girls and births of boys being 100 to 11121, the male births were prevalent in a degree prob. never heard of among any other race. . . . We must therefore think ourselves justified in drawing the inference, that with the Jews the difference of age in married persons is smaller than with Christians; which being acknowledged, the above-mentioned excess of male births must appear still more strange, and is in no accordance whatever with the statements of Hofacker and Sadler, whose obs. were limited to the Christian pop. How is this abnormity to be accounted for?

In 1853 Mr. Samuel Brown contributed to the Assu. Mag. [vol. iii. p. 17] a paper, On the Influence of the Ages of the Parents at the time of Marriage on the Sex of Children, and on the Prolificness of Marriages. In this paper reference is made to many of the facts already here noted, and much additional light is thrown upon the points treated of. In 1855 Dr. Guy read before the Brit. Asso., at Glasgow, a paper, On the Fluctuations in the Number of Births, Deaths, and Marriages, and in the Number of Deaths from Special Causes, in the Metropolis during the last 15 Years, from 1840 to 1854 inclusive. The author says:

In reference to the return of births, deaths, and marriages, it will be sufficient to state that while there is reason to believe that the number of marriages and deaths is truly reported, the reported number of births, in consequence of the regis. of births not being compulsory, has generally fallen short of the actual number, especially in the first years of the series. This will have to be borne in mind when I come to speak of the fluctuations in the number of births. . . . The births which amount, on an average of the 15 years, to 32,028 in the million, have fluctuated between a minimum of 30,348, and a maximum of 33,736-the first number having been regis. in the first year, the last number in the last year of the series. The mean fluctuation in the intervening period has amounted to nearly 2 p.c. In distinguishing the births and deaths as male and female, we have occasion to observe that both the mean and extreme fluctuations in births and deaths are somewhat greater in females than in males. As the differences, however, are not very considerable, it will suffice to have pointed out the fact.

Dr. Guy points out that while the deaths in Lond. for the 5 years 1840-44 inclusive fluctuated as 2.87, the births only fluctuated as I 34-the one amount being more than twice as great as the other. In other words, the causes, whatever they may be, which, by their combined operation from year to year, brought about the ascertained number of births, were nearly twice as uniform in their operation as those causes, whatever they be, which issued the ascertained number of deaths.

The English schedule is defective, as it does not show the age of the father and mother at the birth of the child; but it may be inferred, from the Swedish returns, that not more than I in 8 women who bear children is under the age of 20, or above the age of 40.— 14th Rep. of Reg.-Gen., 1855.