Interpolation, generally considered, is the process of determining numerical values intermediate to a series of other values that are already known, and it is of extraordinary utility in many calculations, and especially in the formation of extensive tables. If, in the direct calculation of a table, the values to be tabulated depend upon a complicated function, difficult of calculation, considerable labour and corresponding risk of error may usually be avoided by computing the values for a certain succession of equidistant intervals, and afterwards determining by interpolation all other values that may be requisite to complete the table and adapt it to the practical purposes for which it is constructed. In such case the method is made use of as a powerful auxiliary at the option of the computer.

The paper commenced with a general view of the effect of emigration upon returns of deaths among the population of England and Wales, followed by an estimate of the extent to which any calculations based upon such returns, and the general census, must be thereby affected. This was followed up by some remarks on the uncertainty attending the statements of ages of the individuals enumerated in the census returns, and the ages returned as at death. A tabular view of the estimated effect of these causes of error upon the expectation of life, derived from the returns, was also given.

The most important practical question arising in an actuary's practice is the following—“By what table of mortality, and according to what process, should the liabilities of a Life Assurance Company be estimated ?” Very wide differences of opinion appear to exist as to the proper answer to be given to this question. Thus, in the Assurance Magazine for January last, are contained two papers, written respectively by Mr. Jellicoe and Mr. Tucker, which bear more or less upon this subject ; and in which very conflicting opinions are expressed by those experienced actuaries.