The records of the Colony of Victoria afford a field for scientific enquiry in many directions, and questions of interest to the physician, the economist, or the actuary, are to be found therein. Its separate existence is but of thirty years' duration, as it was on 1 July 1851 that the Queen's proclamation was issued erecting it into a separate colony, to be called after her Majesty's name.

Many social and economic questions concerning the colony have already been considered; and no longer ago than 1879, the present Government Statist, Mr. Henry Heylyn Hayter, read an exhaustive paper before the Statistical Society. The object of the present enquiry, however, has, so far as I am aware, not received previous attention; and as it is one of strictly professional and scientific interest, it is hoped that it may be appropriately considered by the members of this Institute.

That object is to deduce from the registered vital statistics of the colony a mortality table exhibiting the actual rate of mortality which has been experienced ; and to compare that table with other standard tables, in order to note the effect of the different conditions of life prevalent in Victoria. For it is to be expected that a colony, whose geographical extent is only slightly inferior to that of Great Britain, whose difference of temperature between summer and winter varies less than that of Lisbon or the favoured Riviera, and whose population is far greater than any other Australasian colony, would possess special characteristics calculated to mark their effect on the rate of mortality of the people.

Mr. John Finlaison's method of graduation (Journal, vol. xxi, page 50) deals with an irregularity, which, for convenience, may be assumed to be unity, in the following manner:—It diminishes the irregularity to a small fraction on its first appearance at one end of the formula; conducts it along the formula by easy stages, as over a double inclined plane; and dismisses it gently at the other end. The method has the advantage of simplicity in working and check, but it is correct to first differences only.

Mr. Woolhouse's method is correct to third differences, and the irregularity glides over a curve; but the application of the formula requires sustained attention.

The object of this paper is to combine the facility of the one method with the smoothness and correctness of the other.

Let S be the sum of nine numbers, u0 to u8, increasing by third differences,

the central term,

whence .