Director Sam L. Rogers of the Bureau of the Census published tables of vitality statistics[120] to show expectation of life at all ages for the population of New England, New York, New Jersey, Indiana, Michigan, and the District of Columbia (these being the mortality death registration states) on the basis of the population in 1910 and the mortality for three years. They are like life tables of insurance companies with the exception that they are based on the whole population. According to these tables the average expectation of life for males at birth is 49.9 years; for females, 52.2. Expectation of white males reaches its maximum at the age of 2 (57.7 years). At the age of 12, it is 59.2 years; at 25, 39.4; at 40, 28.3; at 50, 21.2; at 60, 14.6; at 70, 9.1; at 80, 5.2 years. During the first month of life the death rate of native white boys is nearly 28 per cent higher than that for girls. The twelfth year seems to be the healthiest for the native whites and thereafter there is continuous increase in the death rate. Expectation of life is not the same as saying that a man has an even chance of living that number of years, because expectation represents the average remaining length of life at any given age in a stationary population. A native white male child at birth has one chance in two of reaching sixty. At the end of his first year he has more than an even chance of reaching sixty-four. At forty-two he has an even chance of attaining seventy. At all ages women live longer than men and expectation in the country at all ages is distinctly greater than in the city. R. Henderson’s work[121] sets forth the theoretical relations with reference to the duration of human life, describing those mortality tables that have had the greatest influence on the development of the science of life contingency and its applications in this country. The author establishes a connection between mortality tables and mortality statistics and tells how to interpret the latter. The methods of constructing mortality tables from census and death returns and from insurance experience are then taken up. The writer deals only with life contingencies and not at all with monetary applications and gives us a new table. “The present value of a sum of money payable at death cannot be properly calculated in assuming it to be payable at the end of a definite period equal to the expectation of life.” Nor can the present value of a life annuity be calculated by assuming it to be certainly payable for that period.