The great value of quadrature formulæ for the calculation of survivorship and other benefits involving three or more lives has been already illustrated in the pages of the Journal. From certain remarks made by Mr. G. F. Hardy and Mr. George King in the discussion which followed the reading of Mr. King's paper (J.I.A., xxvi, pp. 297, 301), I inferred that it would be of interest to examine the errors involved in these formulæ, and to compare the results yielded by them and by other methods of approximation, such as the substitution of an equivalent life. Mr. Sheppard has shown (Proceedings of the London Mathematical Society, xxxii, p. 258) how most of the best-known quadrature formulæ can be readily derived from the Maclaurin Summation Theorem, with expressions for the errors in terms of differential coefficients. In a recent paper (Proceedings of the London Mathematical Society, xxxiv, p. 335), I have obtained similar formulas by direct integration from Everett's Interpolation Theorem, with expressions for the errors in terms of central differences.

The point in this case was whether the Society was liable to be assessed in respect of interest, dividends, and rents, arising from investments in foreign countries.

The Society had large funds invested in various forms in foreign countries, in some of which countries the Society carried on the business of Life Assurance, and in others of which it carried on no business of any kind. It was admitted that only a part of the income arising from these investments was remitted to Great Britain, the rest of such income being either reinvested or remitted direct to other foreign countries for investment, or applied in payment of establishment and other expenses in the country where the interest was earned, or remitted direct to other foreign countries for the general purposes of the Society.