The past session of Parliament has witnessed the passing of an Act for the regulation of Life Assurance Companies in the United Kingdom, which, while introducing great changes in the law, still stops very far short of the system of legislation which has been for several years in operation in a few of the United States of America, and which is warmly approved of and urgently recommended for adoption by some persons in this country. The present may therefore be considered a fitting time for reviewing what has been done and considering whether any further legislation is desirable, and if any, of what nature it should be.

The development of the nth differential coefficient of a function in terms of the finite differences is involved in the expansion of the multinomial . A general expression for the coefficient of each power, to the seventh inclusive, is given in De Morgan's Diff. and Int. Calculus, p. 264,—but the extremely intricate character of such general expression renders it desirable to obtain a more convenient practical method of computing these coefficients to any extent that may be required.

Dr. T. N. Thiele makes the following remarks in reply to those we prefixed to his adjusted table of mortality given in the last number of this Journal:—

I must consider the constant difference of about 0·1 after the age of 50 between my adjustment and the numbers of living, which follow from the observations, but are not directly observed, and therefore not independent of each other, as the probabilities of living are, as an agreement completely satisfactory. The apparent disagreement I consider to be the result of one observation (52–53), where the observed probability of life disagrees strongly with the numbers of the other adjacent ages, and is not compensated by the following numbers disagreeing sufficiently in the opposite direction. Whence in comparing the calculated probabilities with the observed no systematical disagreement appears in these ages, as the following table shows; but if the numbers of living are compared, every other adjustment must show a disagreement of the same kind at the age of 50 as mine.