It is commonly known that in calculating an annuity on three joint lives, two of the lives are made to count as one life of the same annuity value; and that the result is approximately true. Twenty years ago (Phil. Mag., Nov., 1839), I showed that if the law of mortality explained by Mr. Gompertz were accurately true for the whole of life, this substitution of one life instead of two would also be accurately true. I now repeat the same proposition in a more general form.

The extension of life assurance in the United States, and, especially, the more or less successful attempts of English Companies to compete with the American Companies, render an inquiry into the mortality of American assured lives of the greatest interest to the members of this Institute. The question assumes the greater importance, because, from various reasons, the population statistics of the United States have hitherto been, and will for a long period probably continue to be, in a very imperfect state, notwithstanding the talents and skilful labours of the able men to whom the collection of the data in the different censuses has been entrusted, and the readiness of the people to afford the information desired. The marvellous rapidity with which the population has there increased; the vast extent of the country showing such a diversity of soil and climate; the conversion of the country into town districts, or of wild insalubrious localities into lands reclaimed and rendered healthy by the industry of a dense population—are all so many obstacles to prevent our obtaining at present any Government statistics that could be relied on for the discussion of this grave question.

The history of the United Provinces, and of Holland especially, from the close of the Spanish rule down to the establishment of the modern monarchy of the Netherlands, is distinguished for its manifestation of a permanent struggle between different opposite principles. Liberty and authority, municipal principle and state principle, republic and monarchy, the spirit of federal isolation and that of centralization, appear to give battle to each other upon a territory itself with difficulty defended from the waves of the ocean by the watchful industry of its inhabitants.