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This last method is most important, for it shows that, on the assumption of losses payable at the end of the year, the value at the beginning of the year of the insurance is the product of the probability of death, the discounted value of $1 due at the end of the year and the sum insured.

The foregoing are "net premiums," which means that nothing has been added for expenses or contingencies.

Historically, one-year term or natural premium insurance was not the earliest, though, because of its simplicity, it is first to be considered here. Current cost insurance was the earliest form, but no care was taken to apportion the cost correctly. Insurances for short terms, less than a year, one year or more than a year, were also granted at an early period, but without developing the principles for computing the values of such insurances. Even whole life insurance, for level premiums or for a single premium, preceded whole life insurance by renewable one-year term insurances, each at its own appropriate premium.

Sheppard Homans, a very eminent American actuary, devoted a- large part of his lifetime to an attempt to introduce and popularize the renewable one-year term or natural premium system of life insurance. The demand for cheap insurance was then very great, as, indeed, it always has been, and numerous societies and orders, operating on unjust systems of apportioning the costs, were supplying this demand.

The history of Mr. Homans' experiment, which was made through the Provident Sayings Life Assurance Society, which he founded and which has successfully survived, though the natural premium plan which it