4. LAW OF MORTALITY. By this term is expressed the proportion out of any determinate number of human beings who enter on a given year of age, that will die in that year. Every observation on the duration of life presents certain numbers, which, by recorded facts, are found to pass through each year of age, and also shows how many have died or failed to pass through every year of age. Those numbers, by the rule of three, are converted into the proportions who would die at each age out of one million of persons, if such a number had commenced it. Suppose, then, a million of persons to be in existence at the first year of age; suppose a million to be in existence at the second year of age; suppose a million to be in existence at the third year of age; and in this manner suppose an equal number to be in existence at the commencement of each and every year to the extreme term of human life. Now, the proportions that by actual observation are found to die at each and every year out of the million that were alive at the commencement of it, form separately the law of mortality for each year, and collectively for the whole of life. 5. DECREMENT OF LIFE. Assuming, as before, that a million of male children are born alive (for the still-born must be excluded from the calculation) if it be found that 180,492 would die in the first year, it follows that the difference, namely, 819,508, will enter upon the age of one year. Suppose the law of mortality indicate that the proportion that will die, out of a million, between the age of one and two, is 30,000; it is plain that the number who would die out of 819,508 will by the rule of three be 27,863, and consequently that the residue, namely, 791,615, will remain alive, and so enter on the age of two years. This method being pursued through each and every age to the extreme term of life, when none of the original million survive, the result is a table of mortality in the form in which it is commonly presented in the works of writers on this branch of science. In the table thus constructed there is a column containing the number of living persons who, out of the original million, lived to enter upon each and every year. Of this rank of numbers the difference between each term and its next succeeding one, is the number who die in that particular interval: that number is the measure of what is technically called the decrement of life for that particular year, and the whole of the decrements for each and every year taken collectively is termed the decrement of life. The decrement of life, then, is not only not the same as the law of mortality, but is carefully to be distinguished from it. The law of mortality is derived from observing the number who die out of one and the same number which is always supposed to enter on each and every year. The decrement of life constitutes a rank of numbers arising out of the successive deaths; that is, out of the original million in the first year; out of the survivors of that