In forming mortality tables from the experience of assurance or annuity societies or analogous institutions, we deal with individual lives, tracing each throughout his recorded history, from the moment he comes under observation, until he is removed either by death or withdrawal,—and here the word “withdrawal” includes not only lapse or surrender, but the termination of the contract in any other way, as also the closing of the observations at some determined point of time. We therefore have something approaching to accuracy, and the deaths take place among the lives actually observed, there being close relationship between those who are exposed to risk and those who die. With tables of this class the mortality function which first presents itself is the rate of mortality, qx.

With mortality tables formed from census returns and death registers the case is different. We know nothing of individuals, but deal solely with fluctuating groups, and take the lives in the aggregate; and many of the recorded deaths are not those of persons included in the enumerations. For instance, the English Life Table No. 2 was based on the population of England and Wales enumerated at the census of 6 June 1841, and the deaths recorded in the seven years 1838 to 1844; so that many of the deaths took place before the date of the census, and could not have been deaths among the population counted.