In 1869 a table taking a far wider range was compiled, known as "Actuaries' Experience Table No. 2." It comprised the experience of twenty English and Scotch offices, all over twenty years old. It treats of 146,847 lives, which on an average had been under observation for ten years, and records 23,856 deaths. This table was not graduated until recently, and is only beginning to come into use.
About the same time Mr. Sheppard Homans published the "American Experience Table," based principally on twenty-six years' experience of the Mutual Life Insurance Company of New York. For the very young and old ages where the data were insufficient, he also made use of other American and English statistics. This table has been adopted as the official standard for New York and many other States.
The exact numbers and other details that served as a foundation for all these mortality tables have been given rather fully, at the risk of wearying the reader. The object has been to indicate the difficulties of obtaining them in a reliable and sufficient form, and on such a scale as to furnish trustworthy averages.
A little reflection will show that large numbers must be observed for a long term of years, to have deaths occur for every single year of life, and in the proper proportion for each age. Take as an illustration the Carlisle table based upon 1,840 deaths in eight years, which would average 230 deaths per year. According to the present mortality of England, about forty per cent. of the deaths of the whole population occur among children under five years old, forty per cent, between the ages of five and sixty-five, and twenty-per cent, in old age, between sixty-five and one hundred years. Apply these percentages to the 230 deaths at Carlisle, and they would give 92 persons dying under five years old, 92 between five and sixty-five years, and 46 between sixty-five and one hundred years of age. For the last thirty-five years of life only 46 deaths would be likely to take place, because, while the percentage of mortality is high, the number living at those ages is very small. But, when 46 deaths are distributed among thirty-five years of life, it is apparent that they are not likely to prove regularly divided among them. At some ages, and they may be the very highest, no deaths at all may occur. We know, however, that it is not in the course of nature that in any one year of life no human being should die, and properly ascribe it to the small number and the short space of time observed. Here the mathematician steps in and determines, from the insufficient data gathered, what the probable percentage of deaths would be for every year of life, in large communities living under similar conditions.
In illustration of what has been said, and as both interesting and instructive, the actual percentage of deaths comprised under the "Ungraduated Actuaries' Experience Table No. 2" is herewith given in graphic representation:
The table shows the remarkable fact that, out of so large a number
