table of Deparcieux will readily suggest itself,. that as the observations on which it was founded were made from picked lives, they can hardly be supposed to represent the general law of mortality. Mr. Finlaison, on the other hand, at the conclusion of his Report, after a very extensive examination of not fewer than twenty-two sets of observations, gives his opinion, though he carefully limits himself to a mere opinion, "that there is very little, if any, advantage at all, in favour of selection," and that picked and chosen lives (such as are presented to insurance offices) are not superior in longevity to the rest of the same rank in society, from among whom they are so chosen. If, however, we admit that the table of Deparcieux represents a select mortality which was most probably rather below the general mortality in France in the middle of the last century, the result of a comparison of the respective expectations of life given by it, and by M. Demonferrand's life table of 1837, is in favour of an increased vitality amongst the French population, for its conclusions accord with those which are supplied in the present day by a table for those departments of France where the mortality is most rapid, in which the rate is raised above the average by the returns from Paris and the other great towns.

The English life tables, which exhibit results

most closely corresponding to those at which Deparcieux had arrived, are the Carlisle Tables, published in 1815 by Mr. Milne in his "Treatise on Annuities." They were at that time the only life tables, applicable to the mass of the people, which had been formed from the necessary data, namely, the enumerations of the living from amongst whom the deaths occurred at every age, excepting those of Sweden and Finland, already alluded to, as compiled by M. Wargentin in 1755, from which countries a subsequent series of returns was published by M. Nicander in 1801. Dr. Heysham of Carlisle had kept an accurate register of the births and of the deaths at all ages during a period of nine years, from 1779 to 1787, in the two parishes which comprehend Carlisle and its environs, and had distinguished the sexes. During the same interval, two enumerations of the population of these two parishes had been made in 1780 and 1787 respectively, in both of which the ages were distinguished, and the sums total of both sexes. The tables constructed from these data, as may readily be supposed, afford a far higher expectation of life than the Northampton Tables; and though the observations were only carried on during so short a space of time as nine years, yet this circumstance is of less importance, as during the twenty-two years commencing with 1779, as

Mr. Milne has shown, the proportion of the annual average number of deaths to the mean number of the people, was the same as in the first nine years, namely, 1 in 40. The expectation of life at birth, which the Carlisle tables exhibit, is rather more than 38 years. Whether, therefore, we contrast the mean duration of life, or the rate of mortality, as furnished by these tables, with those which the last observations in England and Wales afford, in either case we find an evident improvement; the expectation of life at birth being at present rather more than 41 years, and the rate of mortality 1 in 46.

When the mean duration of life is said to be augmented, it must not be supposed to imply that the term of human existence is in any way extended, but merely that a greater number of individuals attain a mature age- for instance, the age of 45-55.

LECTURE IV.

THE most important object to which a National Life Table can be applied, is without doubt the determination of problems connected with the efficient state of the population, such as the proportion of males capable of bearing arms, the numbers whose labour is available for different branches of industry, and the proportion of infants and old people for whose support the labour of the efficient portion of the population must be taxed. The secondary use to which they have been applied, and which in reality led to the study of such contingencies, was the determination of the value of life annuities, pensions, and other financial transactions. It was for this latter purpose that Halley may be said to have invented the form of the life table in 1693, when he presented to the Royal Society of London an "Estimate of the mortality of mankind drawn from various tables of the births and funerals in the city of Breslau, with an attempt to ascertain the prices of annuities upon lives." (Philosophical Transactions Abridged, vol. iii. p. 510.)

Halley selected the bills of mortality of the city of Breslau as furnishing the least objectionable data, for the calculation of a life table, because "the births exceeded a little the funerals, and the confluence of strangers was but small;" and although he was well aware that he wanted the number of the whole people to ensure the necessary accuracy in his calculation, yet he considered it to give a more just idea of the state and condition of mankind than any thing then extant. Amongst the manifold uses of it which he pointed out, was that it "showed the chances of mortality at all ages, and likewise how to make a certain estimate of the value of annuities for lives, which had previously been effected by an imaginary valuation." The form in which a life table on Halley's principle is constructed may be very briefly stated. If 100,000 persons be the assumed number born alive, which is termed the base or radix of the table, the relative numbers living in each consecutive year till the whole number is exhausted must be ascertained. Thus the age at which the table terminates will vary with different observations. In the English life table of 1841, the last survivor of a given 100,000 lives did not expire till the 105th year. Upon adding up the column of the relative num bers living, in the English life table for example, the sum of their lives amounts to 4,165,890