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Regarding the Bills of the old Co. of Parish Clerks-they have ceased; but the Co. itself remains, and deserves to be cherished in our remembrance. The difficulties referred to at the foot of the Bill for 1837 increased, as it was but natural they should. The Corp. of Lond. withdrew the allowance it formerly made towards the expense of the Bills. The Co. bowed to decrees it could in no wise control. We have recently visited the old Hall; it is solemn as of yore, and even more silent; but it is not deserted. The printing press is indeed broken up; the printer has long since closed up his last "forme"; but the Master and Wardens (whose courteous reception and frugal hospitality we have to acknowledge) now devote their limited income to the good work of charity; to relieving the poor of that useful fraternity of whom the Co. was orig. composed, and but for whose early labours life ins. might have remained, as for centuries it was, a subject of speculative uncertainty. The B. of Mort. forms the base on which the science of life contingencies has been reared; and on the Co. of Parish Clerks, for several centuries, rested the responsibility of furnishing that Bill.

[It has prob. happened that some of the compilations spoken of in this art. are not strictly B. of MORT., but rather come under the designation of PARISH REGIS. or MORT. OBS. The indistinctness of the early writers on this point we find extremely confusing. Under DEATHS, CAUSES OF, other special forms of Bills will be given. Under MORT. OBSERVATIONS, other special details will be noted, as also under PAROCHIAL REGIS. while under PLAGUES will be found special reference to the Bills at the period of PLAGUES.]

BILL OF PARCELS.-An account given by the seller to the buyer, containing particulars of the goods bought, and of their price.

BILL OF SALE.-An assignment by deed of personal chattels. The instrument may be absolute or conditional.

BILL OF STORE.-A licence granted at the Custom-house to merchants to carry such stores and provisions as are necessary for a voyage, custom free, authorized by 3 & 4 Wm. IV., c. 52 (1833).

BILL OF SUFFERANCE.-A licence granted to a merchant to suffer him to trade from one English port to another without paying custom.

BINARY ARITHMETIC (counting by twos).-A species of arithmetic invented by the renowned Leibnitz about 1703. It is founded on the shortest and simplest progression, viz. that which terminates with the second cipher. In the binary notation, therefore, only two characters are required, I and o, the zero having the power of multiplying the number it follows by two, as in the common notation it multiplies by ten. The No. one is represented by I; two by 10; three by 11; four by 100; five by 101; six by 110; seven by 111; eight by 1000; nine by 1001; ten by 1010, etc. This method of notation, though it may be applied with advantage in the investigation of some properties in numbers, is inconvenient for common purposes, on account of the great number of characters required, even when the numbers to be expressed are small. -Brande. BINOMIAL ROOT, in Algebra, composed of only two parts connected with the signs plus or minus. The term was first used by Recorda, in his Algebra, pub. about 1550. The celebrated binomial theorem of Newton was first mentioned in 1688 -Hutton. BIOLOGY, from the Greek, signifying an account of life.-Another term for signifying Physiology, or the Doctrine of Life. This term was used by Treviranus, of Bremen, in his work on Physiology, pub. 1802-22. Biology includes zoology, anthropology, and ethnology. -Herbert Spencer's Principles of Biology, pub. 1865-67. BIRCH, DR., formerly Sec. and Historian of the Royal So.-He is generally reputed to have been the compiler of a Collection of the Yearly B. of Mort. pub. anonymously in 1759, and containing, in add. to reprints of Graunt's, Petty's, and Corbyn Morris's pubs., "A comparative view of Diseases and Ages," the materials for which are stated to have been supplied by Dr. Heberden; and there was also a T. of Prob. of Life, calculated by James Postlethwayt, Esq. It appears from personal inquiries made by Mr. Milne during the present century of the son of Dr. Heberden, that Dr. Birch cannot have done more than superintend the work through the press-in the case of such a work not a very easy duty, if carefully discharged, as it was. The work indeed is a credit to all concerned. [HEBERDEN.]

BIRD, EDWARD, Man. of F. Department of Royal Exchange from 1830 to 1865. He entered the office in 1802, and passed through the various departments, until he reached the position named. He retired in 1865, having been employed during a period of 63 years in the Corp. He died on 3rd Sept., 1871, in his 85th year.

BIRD, JAMES A., was Sec. of Official and General in 1853.

BIRKBECK LIfe Assu. Co., founded in 1852, with an authorized cap. of £10,000— afterwards increased to £100,000-in shares of £1, "to be paid in full, leaving no further liability." The prosp. said: "This asso. has two distinct departments: one comprising all the transactions of a Life Assu. Co.; the other, that of a friendly so., for assu., relief, maintenance or endowment of members and their kindred, and for the frugal and profitable investment of savings." Again:

To a vast proportion of us life assu, presents the only means by which we can effectually discharge the duties of brothers, sons, husbands, and fathers. That it is of the utmost importance to all will be

readily admitted by those who have seen the results of improvidence; the sorrows, sufferings, and sins of the unprovided; and the bitterness of the dying hour disturbed by reflections upon the unprotected condition of those who speedily become widowed or fatherless. . . . . The B. Life Assu. Co. is, by its peculiar economy and organization, expressly adapted to become the certain and safe resource of all such struggling self-dependent men as will subject themselves to a small present payment, in order that they and their families may in any event be secured against destitution and degradation; and is particularly applicable to the circumstances of members of the Civil Service, who, in the majority of cases, are unable to make provision for their families except by ins.

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The following were among the special features of the Co.: "No forfeiture in case of disability to continue payment after 3 years' prems. have been paid. "Policies are payable immediately on proof of the death of the insured." "The age and insurable interest of the assurer are admitted on every pol." "Pol. may be trans. by indorsement," etc. Finally:

The mechanics' institutes and literary institutions spread over the Brit. dominions afford between 600 and 700 local centres whence the Birkbeck L. Assu. Co. is enabled to diffuse the advantages of the most notable device of our time for improving the tenure of human existence. It is therefore thought that this inst. may appropriately bear the name of the great public benefactor who laboured most successfully to improve the people by creating and gratifying the nobler feelings and capacities of our


Among the trustees of the Co. was William Makepeace Thackeray; while at one period Douglas Jerrold was the Chairman, and Blanchard Jerrold the Sec. Mr. Thomas Walker, B. A., was the Act.

By the year 1854 the Co. had acquired a very fair bus. connexion, chiefly of the industrial class. It issued in that year pol. ins. £86,724 35. 9d., and it paid a div. of 5 p.c. In 1857 the bus. was trans. to the Home Counties Life; and in the same year the joint bus. was trans. to the Whittington.

BIRKMYRE, W. F., the late, was trained in the office of the North British under Mr. Chisholm. In 1861 he was appointed Man. of the L. department of the Lond. branch of that Co. In 1863 he was appointed Act. and Man. of the City of Glasgow L. He died at an early age in 1864. Mr. Birkmyre was an American by birth. He held diplomas from the Inst. of Act. and from the Faculty of Act. He was employed to make the calculations under which the Hartley Colliery Fund was finally distributed. BIRMINGHAM.-This town, which is near the centre of England, and may be said to be the very centre of the metal trade of Gt. Brit., has no very remarkable ins. hist. Several respectable ins. offices have been founded here, and many of the leading offices have branches. There is an efficient fire brigade, consisting of engines supplied by various ins. offices-the Norwich Union engine is under very efficient management. In the 9th report of Reg.-Gen. (1849) will be found some remarkable statistics regarding fluctuations in the number of marriages, consequent upon the depression or advancement of trade. In 1700 Birmingham consisted of 2504 houses, with a pop. of 15,032. The pop. in 1871 was 344,980. The death-rate p. 1000 of the pop. for the last 5 years has been as follows: 1867, 256; 1868, 25'9; 1869, 231; 1870, 230; 1871, 24'9.

In 1857 Mr. Thomas Green, M. R.C.S., read before the Social Science Congress, a paper: The Mort. of Birmingham Compared with that of Lond. and Seven other Towns. The tables extended over a period of 18 years. Birmingham, during that period, contrasted favourably in point of health with Liverpool, Manchester, and Wolverhampton ; but unfavourably with many other places, including Lond. The author says hereon:

It appears that during the last 7 years there have been in Birmingham 3414 deaths-being an ann. average of 492 more than there would have been if the death-rate had been the same as that of Lond. for the same period.

The death-rate of Birmingham during the preceding 7 years, in relation to some of the adjacent towns, had been as follows:


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26.76 per 1000
25'97 99

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In 1865 Mr. W. L. Sargant read before the Brit. Asso. a paper: On the Vital Statistics of Birmingham and Seven other Towns. An abstract of the paper is given in the Trans. of the Asso. for that year. We shall speak of the paper under V. STATISTICS. BIRMINGHAM ALLIANCE FIRE INS. CO., LIM., founded in Birmingham in 1864, with an authorized cap. of £500,000, in 20,000 shares of £25. The Co. was promoted under the auspices of the Birmingham Financial Co., and at once took a respectable position. In 1864 its duty return amounted to £657 9s. 2d. : in 1865 it reached £1506; by 1868 it had reached £1906 11s. 2d. In 1867 the Co. took the name of the Birmingham Fire Ins. Co.; and in 1870 its bus. was united with that of the Lancashire. BIRMINGHAM ALLIANCE LIFE INS. CO., LIM., founded in Birmingham in 1865, with an authorized cap. of £500,000, in 20,000 shares of £25. The Co. was founded upon the basis of the bus. of the Birmingham and Midland Life, estab. 1862; but branches for accident and fidelity guar. were added. The Co. made steady progress. In 1867 it trans. the accident portion of its bus. to the Accident Co. (No. 1), and about the same period its guar. bus. to the European. In 1870 the name of the Co. was changed to Lond. and Birmingham Assu. Co., Lim., where its hist. will be continued. Mr. J. Barclay Bannerman was Gen. Man. and Sec. of the Co.

BIRMINGHAM DISTRICT FIRE INS. Co., founded in Birmingham in 1834; and in 1851 it took the name of the District Fire, under which title we shall speak of it more at large. [DISTRICT FIRE INS. Co.]

BIRMINGHAM FIRE INS. Co., LIM.-See BIRMINGHAM ALLIANCE FIRE INS. Co. BIRMINGHAM FIRE OFFICE Co., founded at Birmingham in 1805, with a cap. of £300,000, in 1200 shares of £250 each. In 1810 it obtained a special Act of Parl., 50 Geo. III. c. xc., An Act to enable the Birmingham Fire Office Co. to sue in the name of their Sec. The Act was not to incorp. the Co. In 1824 the Co. collected in fire duty £5161; in 1834, £7042; 1844, £10, 196; 1854, £14,233; 1864, £14,992.

The Co. was one of great respectability. In 1867 its bus. was trans. to the Lancashire. BIRMINGHAM AND GENERAL.-This Co. was projected in Birmingham in 1854, and went through all the stages up to complete regis., after which we lose sight of it. BIRMINGHAM LIFE ASSU. AND ANNU. OFFICE, founded at Birmingham in 1810, and worked, we believe, in connexion with the Birmingham Fire Office, founded in 1805. In 1810 the Co. obtained a special Act, 50 Geo. III. c. lxxxix., An Act to Enable the Birmingham Life Assu. and Annu. Office to Sue in the Name of their Sec., and to inrol Annu. The Act was not to extend to incorp. the Co.

The bus. of the Co. was small; and in 1826 the Co. ceased to carry on the same. Its pol. were trans. to Provident Life, before any material loss had occurred. The Co. paid the Provident a cash consideration for taking over the risks.

BIRMINGHAM AND LOND. ASSU. Asso.-This Co. was promoted in 1853 by Mr. William Sweeney, Con. Act. We believe the title was afterwards changed to London and Birmingham. The project did not go forward.

BIRMINGHAM AND MIDLAND COUNTIES INS. Co.-An Ins. Co. under this title was projected in 1850 by Mr. E. Oliver, of 6, Temple Row, Birmingham, solicitor, and 6 others, and was completely regis. ; but we hear no more of it.

BIRMINGHAM AND MIDLAND LIFE INS. Co., founded in Birmingham in 1862, with an authorized cap. of £100,000 in 20,000 shares of £5 each, £1 paid. In 1865 the Co. merged into the Birmingham Alliance Life. Mr. J. B. Bannerman was Act. and Sec. of the Co.

BIRT, S., pub. in 1737: Essay to Ascertain the Value of Leases, etc.

BIRTH.-The act of coming into life.

BIRTHS. Many problems regarding births come before actuaries; many more will arise when the next phase of life ins.-that of making a complete provision for prospective families at the time of marriage-shall develope itself. The exact knowledge required by the office before embarking on such an enterprise is accumulating. These increasing facts in the mean time are useful in that not unfrequent branch of business-Ins. against Issue.

It was in 1661 that Graunt, in his Natural and Political Observations, etc., made his famous observation, "that the more sickly the years are, the less fecund or fruitful of children they also be," which (he continued) "will appear if the number of children born in the said sickly years be less than that of the years both next preceding and next following; all which upon view of the tables will be found true, except in a very few cases, where sometimes the precedent and sometimes the subsequent years vary a little, but never both together. Moreover, for the confirmation of this truth, we present you the year 1660, when the burials were fewer than in either of the two next precedent years by 2000, and fewer than in the subsequent by above 4000. And withal, the number of christenings in the said year 1660 was far greater than in any of the three years next aforegoing."

He (Graunt) made many most interesting and sagacious obs. For instance, he was the first to discover that there were more males than females born; but he does not appear to have surmised that female life was of longer duration than male life, and that from this cause there were always more females than males living; indeed, he was led to an entirely opposite conclusion. But his remarks are full of originality, and always suggestive. He says:

The next obs. is that there be more males than females. 1. There have been buried from the year 1628 to the year 1662 exclusive, 209,436 males, and but 190,474 females. But it will be objected that in Lond. it may be indeed so, though otherwise elsewhere, because Lond. is the great stage and shop of business, wherein the masculine sex bears the greatest part. But we answer that there have been also christened within the same time 139,782 males, and but 130,866 females, and that the country accounts are consonant enough to those of Lond. upon this matter. 2. What the causes hereof are we shall not trouble ourselves to conjecture, as in other cases, only we shall desire that travellers would inquire whether it be the same in other countries.

He follows up the subject:

We have hitherto said that there are more males than females; we say next, that the one exceeds the other by about a thirteenth part. So that although more men die violent deaths than women, that is, more are slain in wars, killed by mischance, drowned at sea, and die by the hand of justice; moreover, more men go to colonies, and travel into foreign parts than women; and lastly, more remain unmarried than of women, as Fellows of Colleges, apprentices above 18, etc., yet the said thirteenth part difference bringeth the business but to such a pass that every woman may have a husband, without the allowance of polygamy. Moreover, although a man may be prolific 40 years, and a woman but 25, which makes the males to be as 560 to 325 females, yet the causes above named, and the later marriage of men, reduce all to an equality.

Again :

It appearing that there were 14 men to 13 women, and that they die in the same proportion also; yet I have heard physicians say that they have two women patients to one man, which assertion seems very likely. . . . Now from this it should follow that more women should die than men, if the number of burials answered in proportion to that of sicknesses; but this must be solved, either by the alledging that the physicians cure those sicknesses, so as few more die than if none were sick; or else that men being more intemperate than women die as much by reason of their vices as women do by the infirmity of their sex; and consequently more males being born than females, more also die.

He found out or imagined that he found out-that the proportions of males to females born varied in different districts; for at Cranbrook (he says) there be 20 males for 19 females; in Hantshire [Hampshire] 16 for 15; in Lond. 14 for 13; and at Tiverton

12 for II.

Graunt, reviewing the proportion of births in Lond. compared with the country, arrived at the conclusion that "the breeders in Lond. were proportionably fewer than those in the country," and that the difference arose from reasons of which the following is the substance:

1. All that have business to the Court of the King, or to the Courts of Justice, and all country-men coming up to bring provisions to the City, or to buy foreign commodities, manufactures, and rarities, do for the most part leave their wives in the country.

2. Persons coming to live in Lond. out of curiosity and pleasure, as also such as would retire and live privately, do the same, if they have any.

3. Such as come up to be cured of diseases, ditto.

4. That many apprentices of Lond. who are bound seven or nine years from marriage, do often stay longer voluntarily.

5. That many sea-men of Lond. leave their wives behind them, who are more subject to die in the absence of their husbands.

6. Causes of general unhealthiness.

7. As to the causes of barrenness in Lond., I say, that although there should be none extraordinary in the native air of the place, yet the intemperance in feeding, and especially the adulteries and fornications, supposed more frequent in Lond. than elsewhere, do certainly hinder breeding.

8. Add to this, that the minds of men in Lond. are more thoughtful, and full of business, than in the country, where their work is corporal labour and exercises; all which promote breeding, whereas anxieties of the mind hinder it.

In 1682 Sir William Petty pub., An Essay Concerning the Multiplication of Mankind, wherein he proposed to consider "How many men and women are prolific, and how many of each are married or unmarried." We shall have occasion to speak of this essay more at large under POPULATION.

In 1683 he pub. Another Essay in Political Arithmetic, Concerning the Growth of the City of Lond.; with the Measures, Periods, Causes, and Consequences thereof; wherein he starts the proposition, “That it is possible to increase mankind by generation four times more than at present." Then he proceeds to measure the period in which the "people double," by estimating the excess of births over the burials. Here is a specimen of his method:

I might here insert, that although the births in this last computation be 25 of 600, or a twenty-fourth part of the people, yet that in the natural possibility they may be near thrice as many, and near 75. For that by some late obs., the teeming females between 15 and 44 are about 180 of the 600, and the males of between 18 and 59 are about 180 also, and that every teeming woman can bear a child once in two years; from all which it is plain that the births may be 90 (and abating 15 for sickness, young abortions, and natural barrenness), there may remain 75 births, which is an eighth of the people; which by some obs. we have found to be but a two-and-thirtieth part, or but a quarter of what is thus shown to be naturally possible. Now according to this reckoning, if the births may be 75 of 600, and the burials but 15, then the ann. increase of the people will be 60, and so the 600 people may double in 10 years, which differs yet more from 1200 above-mentioned. Now to get out of this difficulty, and to temper those vast disagreements, I took the medium of 50 and 30 dying p.a., and pitch'd upon 40; and I also took the medium between 24 births and 23 burials, and 5 births and 4 burials, viz., allowing about 10 births for 9 burials; upon which supposition there must die 15 p.a. out of the above-mentioned 600, and the births must be 16 and two-thirds, or five-thirds of a man; which number compared with 1800 thirds, or 600 men, gives 360 years for the time of doubling-including some allowance for wars, plagues, and famine, the effects whereof, though they be terrible at the times and places where they happen, yet in a period of 360 years is no great matter in the whole nation.

In 1686 (perhaps the first ed. a year or two earlier) he pub., Observations upon the Dublin B. of Mort., 1681, and the State of that City, wherein he asserts, as another proposition, "That the Births are the best way (till the accompts of the people shall be purposely taken) whereby to judge of the Increase and Decrease of People; that of burials being subject to more contingencies and variety of causes." Upon this he proceeds:

If the births be as yet the measure of the people, and that the births (as has been shown), are as 5 to 8, then eight-fifths of the births is the number of the burials, where the year was not considerable for extraordinary sickness or salubrity; and is the rule wherby to measure the same, as for example: The medium of the births in Dublin was 1026, the eight-fifths whereof is 1641, but the real burials were 1644; so as in the said years they differed little from the 1641, which was the standard of health; and consequently the years 1680, 1674, and 1668, were sickly years, more or less, as they exceeded the said number 1641; and the rest were healthful years, more or less, as they fell short of the same number. But the city was more or less populous, as the births differed from the number 1026, viz., populous in the years 1680, 1679, 1678, and 1668; for other causes of this difference in births are very occult and uncertain. What hath been said of Dublin serves also for Lond.

Regarding the excess of males over females, he says, "It hath already been observ'd by the Lond. Bills, that there are more males than females. It is to be further noted, that in these 6 Lond. Bills also, there is not one instance, either in the births or burials, to the contrary." Then again, confirming the view of Graunt [it has been said, without

foundation, that Petty and Graunt were one and the same], "It hath been formerly observ'd, that in the years wherein most dye, fewest are born, and vice versa. The same may be further observed in males and females, viz., when fewest males are born, then most dye."

On the question of the proportions of male and female births, there was a good deal of speculation by the older writers. Goodman, early in the 17th century, supposed that more females than males were born. Turgot (French) speculated the other way, and was correct; but he does not appear to have founded his statement upon any data, and it must be regarded only as a guess. Herder (German), writing as recently as 1785, takes for granted that the proportions were about equal. Dr. John Arbuthnot, in his book Of the Laws of Chance, etc., pub. 1692, was one of the first writers who treated of the subject in a really philosophical manner [Phil. Trans., No. 328]. He had made himself fully acquainted with the fact that the male births predominated.

M. Nicolas Bernouilli collected from T. of Obs. [B. of Mort. ?] continued for 82 years -1629 to 1711-that the number of births in Lond. was at a medium about 14,000 yearly; and further, that the number of males, in relation to the number of females, was nearly 18 to 17. Still he seemed to think that chance, rather then Divine decree, played a part in this incident of production. We confess we think his own argument points the other way. He says: "Let 14,000 dice, each having 35 faces-18 white and 17 black-be thrown up, and it is great odds that the number of white and black faces shall come as near, or nearer to each other, as the number of boys and girls do to the tables." His reasoning on this subject is contained in his two letters to M. de Montmort, dated Lond. 11 Oct., 1712; the other, Paris, 23 Jan., 1713, pub. in the Appendix to the Analyse des Jeux de Hazard, 2nd ed. His cousin Daniel Bernouilli returned to the same subject. We have noted his views in our biographical notice of him.

In 1695 the 6 & 7 of Wm. & Mary, c. 6, was passed; and this was the first legislative measure which provided for the regis. of Births. Its provisions were strict. They were not, however, conceived for the good of the people, but to serve the fiscal necessities of the State. Births were subjected to a tax, and the records were to be kept exact, in order that the full measure of the tax might be exacted. [MORTALITY TAX.]

In Natural and Political Obs. and Conclusions upon the State and Condition of England, written by Gregory King, Lancaster Herald, in 1696 [but only pub. as an appendix to an ed. of Chalmers Estimate in 1802], we find many curious statements regarding the births of the people, and the following we regard as worthy of special note, as exhibiting the notions of the best-informed men of that period. He says, "the yearly births of the kingdom being 190,000 souls, those under 1 year old are in all 170,000 :-males 90,000; females 80,000." In regard to the proportions of the sexes at birth he was nearly right. He makes up his total as follows:

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He next found "that in 1000 co-existing persons :

There are 71 or 72 Marriages in the Country, producing 34'3 Children.


Marriages in Towns

Marriages in London

Whereby it follows:

35 2 Children.
376 Children.

1. That though each marriage in Lond. produceth fewer people than in the country, yet Lond. in general, having a greater proportion of breeders, is more prolific than the other great towns; and the great towns are more prolific than the country. 2. That if the people of Lond., of all ages, were as long-lived as those in the country, Lond. would increase in people much faster pro rata than the country. 3. That the reason why each marriage in Lond. produces fewer children than the country marriages seems to be: (1). From the more frequent fornications and adulteries. (2). From a greater luxury and intemperance. (3). From a greater intenseness to business. (4). From the unhealthiness of coal smoke. (5). From a greater inequality of age between the husbands and wives.

And that it may appear what the effect is, of the inequality of ages in married couples, I have collected the following obs. from a certain great town [Lichfield] in the middle of the kingdom, consisting of near 3000 souls. 1. That there is no child of any parents now living in the said town where the wife is 17 years older than the husband, or the husband 19 years older than the wife. 2. That the whole number of children being 1060, the number of those whose mother was older than the father is 228, and where the husband was older than the wife, 832. 3. That one moiety of the whole number of children in the said town is the product of such parents where the husband is 4 or more years older than his wife. 4. That the greater number of children, with respect to any one number of years of difference in age between the husband and wife, is where the husband is 2 years older than the wife, the product whereof is 147, or a seventh part of the whole. 5. That an equality of age in the husband and wife is not so prolific as an inequality, provided that inequality exceed not a superiority of 4 years in the wife, or 10 years in the husband; for the equality of years produced but 23 children; whereas 1 year's inequality in the age of the parents, either way, produced above 60. 6. That of the said 1060 children in the whole town, nearly three-quarters of them are the product of coalitions from 2 years' superiority of age in the wife inclusive, to 6 years' superiority of age in the husband inclusive. 7. That the highest powers in men and women for procreation is, in that town, at 31 years of age in the husband, and 28 in the wife; the produce of the former being 86 children, and of the latter, 83. 8. That one moiety of the said 1060 children are the product of fathers from 28 to 35 years of age inclusive, and of mothers, from 25 to 32. Whence it follows that a just equality, or too great an inequality of age in marriages, are prejudicial to the increase of mankind; and that the early or late marriages in men and women do tend little to the propagation of the human race. Lastly. From a

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