MORTALITY, LAW OF. In this article we intend to confine our velem to sonic, account of our present knowledge, theoretical and practical, of the laws which are found to regulate mortality among mankind in this country.
Uncertain as is the life of any one individual, it is now very well known that if two different numbers of individuals, at or near the same age, be taken, the number that will be left at the end of a few years will be nearly the same, if they exist during that time under similar circumstances. No tables, however different the station and circumstances of the person from whose lives they are made, differ from one another by anything like the amount which might be sup posed likely by one who turns his thoughts rather to the existence of one individual than of a large number. A little consideration will make the probability of something like permanence in the distribution of mortality very great d priori. That harvests fluctuate in goodness is very well known ; but it is also obvious that if the fluctuations upon a whole country had been as great as those upon an individual field, the human race must long ere this have been starved off the face of the earth. If, in the same manner, the mortality of races had varied as much as that of families, it is impossible that the population of any country could have gone on in a gradual and regulated state of increase; or supposing that large fluctuations had compensated each other, the con sequence must have been such a disproportion of the numbers living at different ages as it never has occurred to any one to imagine possible.
The law of mortality, theoretically speaking, is a mathematical relation between the numbers living at different ages ; so that, having given a large number of persons alive at one age, it can be deduced by the law what number shall survive any given number of years : prac tically speaking, it is, in the absence of such a mathematical law, the exhibition in a table of the numbers surviving at the end of each year. Thus, DE MOINRE'S HYPOTHESIS (namely, the supposition that out of 88 persons born one dies every year till all are extinct) is an asserted theoretical law of mortality ; while the Carlisle table, presently given, is a practical one.
If y represent the number of persons living at the age of x, out of a certain number a at a certain previous age (usually the time of birth), then if a line varying with x be made the abscissa of a curve, and another varying with y its ordinate, this curve may be called the curve of mortality. Its form, as deduced from a given set of observations, may lead, by comparison with known curves, to an equation which, more or less accurately, connects y and x.
Besides De Moivre's hypothesis, others have been given, the principal of which we shall notice in order.
A curve following a mathematical law may be drawn through any points, however great their number or irregular their distribution; but the greater the number of points, the more complex will be the equation of the curve. With an equation of a high degree (the tenth, perhaps, or the twelfth), any given table of mortality might be very nearly represented; but such complexity would be useless, and it has there fore never been attempted. Similarly, by using area of different curves, a near representation might be attained ; but such a method, being practicable in many different ways, would not possess the interest attaching to one simple and uniform law, and would only attract attention by offering facilities for the actual Calculation of life. contingencies.
In 1765 Lambert presented an equation of the following form, tu representing very closely the London table (e is the base of Napier'E logarithms) :— y = 10000 — 6176 ax ?• 13x} a being = 1 : 13•682, and 11 = 1 : 2.43114, and y being the number surviving at the age of x, out of 10,000 born. This form, if it conk be made to represent other tables, by an alteration in the constants would be one of great practical utility ; but we are not aware of any attempt having been made to extend it.