tied in some circumstances even a greater chance, that the woman shall be the sur vivor of a marriage, and not the man ; and this difference cannot be accounted for merely by the difference of age be tween husbands and their wives, without admitting the greater mortality of males. In the district of Vaud, in Switzerland, it appears, that half the females do not die till the age of 46 and upwards, though half the males die under 36. It is like wise an indisputable fact, that in the be ginning of life, the rate of mortality among males is much greater than among females. From a table formed by Dr. Price, from a register kept for 20 years at Gainsborough, it appears, that of those who lived to 80, the major part, in the proportion of 49 to 32, are females. M. Deparcieux, at Paris, and M. Wargentin, in Sweden, have further observed, that not only women live longer than men, but that married women live longer than sin gle women. From some registers exa mined by M. Muret, in Switzerland, it ap pears, that of equal numbers of single and married women, between 15 and 25, more of the former died than of the lat ter, in the proportion of two to one. With respect to the difference between the mortality of males and females, it is found to be much less in country parishes and villages than in towns ; and hence it is inferred, that human life in mates is more brittle than in females, only in con sequence of adventitious causes, or of some particular debility that takes place in polished and luxurious societies, and especially in great towns. From the ine quality above stated, between the males and females that are born, it is reasonable to infer, that one man ought to have but one wife ; and yet that every woman, without polygamy, may have a husband ; this surplus of males above females being spent in the supplies of war, the seas, &c. from which the women are exempt. Per. haps, says Dr. Price, it might have been observed with more reason, that this pro vision had in view that particular weak ness or delicacy in the constitution of males, which makes them more subject to mortality ; and which consequently ren ders it necessary that more of them should be produced, in order to preserve in the world a due proportion between the two sexes. That this is a work of Providence, is well made out by the very laws of chance, by Dr. Arbuthnot, who supposes Thomas to lay against John, that for 82 years running, more males shall be born than females ; and giving all allowances in the computation to Thomas's side, he makes the odds against Thomas, that it does not so happen, to be near five mil lions of millions of millions of millions to one ; but for ages of ages, according to the world's age, to be near an infinite number to one. According to M. Kerse boom's observations, there are about 325 children born from 100 marriages. M. Kerseboom, from his observations, esti mates the duration of marriages, one with another, as in the following table. Those whose ages, taken together, make 40, lire together between 24 and 25 years.
50 22 . . 23 60 23.. 21 70 19.. 20 80 17 . . 18 90 . 14 . 15 100 12 .. 13 " Phil. Trans." No, 468.
Dr. Price has shown, that on De Moi vre's hypothesis, or that the probabilities of life decrease uniformly, the duration of survivorship is equal to the duration of marriage, when the ages are equal ; or, in other words, that the expectation of two joint lives, the ages being equal, is the same with the expectation of survivor ship ; and, consequently, the number of survivors, or (which is the same, suppos ing no second marriages) of widows and widowers, alive together, which will arise from any given set of such marriages constantly kept up, will be equal to the whole number of marriages, or half of them (the number of widows in particu lar) equal to half the number of mar riages. Thus, the expectation of two
joint lives, both 40, is the third of 46 years, or their complement, i. e. 15 years and 4 months ; and this is also the expec tation of the survivor. That is, suppos ing a set of marriages between persons all 40, they will, one with another, last just this time, and the survivors will last the same time. In adding together the years which any great number of such marriages, and their survivorships, have lasted, the sums would be found to be equal. It is observed further, that if the number expressing the expectation of sin gle or jointlives, multiplied by the number of single or joint lives whose expectation it is, be added annually to a society or town, the surh gives the whole number Eying together, to which such an annual addi tion would in time vow: thus, since 19, or the third of 57, is the expectation of two joint lives, whose common age is 29, or common complement 57, 20 marriages every year between persons of this age would, in 57 years, grow to 20 times 19, cr 380 marriages always exi sti ng together. l'he number of survivors also arising from these marriages, and always living together, would, in twice 57 years, in crease to the same number. Moreover, the particular proportion that becomes extinct every year, out of the whole num ber constantly existing together of single or joint lives, must, wherever this num ber undergoes no variation, he exactly the same with the expectation of those lives at the time when their existence commenced. Thus, if it were found, that a nineteenth part of all the marriages among any body of men, whose numbers do not vary, arc dissolved every year by the deaths of either the husband or wife, it would appear, that 19 was, at the time they were contracted, the expectation of these marriages.
Dr. Price observes, that the annual ave rage of weddings among the ministers and professors in Scotland, for the last twenty-seven years, has been 31; and the average of married persons, for seventeen years, ending in 1767, had been 667. This number, divided by 31, gives 214, the expectation of marriage among them ; which, he says, is above two years and a half more than the expectation of marri age would be, by Dr. Halley's table, on the supposition that all first, second, and third marriages, may he justly considered as commencing, one with another, so early as the age of 30; and lie has proved, that the expectation of two equal joint lives, is to the expectation of a sin gle life of the same age, as two to three: consequently, the expectation of a single life at 30, among the ministers in Scot land, cannot be less than 32.25. If we suppose the mean ages of all who marry annually to be 33 and 25, the expectation of every marriage would be nineteen years ; or, one with another, they would be all extinct in nineteen years the mar riages which continue beyond this term, though fewer in number, enjoying among them just as much more duration as those that fall short of it enjoy less. But it appears from the observations and ta bles of 31. Muret, that, in the district of Vaud (dividing half the number of married persons, viz. 38,328, by the an. nual medium of weddings, viz. 808) the expectation of marriage is only 23i years : so much higher are the probabilities of life in the country than in towns, or than they ought to be, according to De Moivre's hypothesis. See PRICE's AN NUITILS.