The subject of this paper has on two previous occasions been brought before the Institute; namely, by Mr. Jellicoe on 26 November 1855, and by Mr. Baden on 27 March 1871. The former of these gentlemen stated that, at the time his paper was written, a great diversity of opinion existed among actuaries, as to the proper method to be adopted in advising upon the proportions in which a settld fund should be divided by mutual consent between the life tenant and the reversioner; and so far as can be judged from the discussion that followd the reading of the latter paper, a similar diversity still existed then. One point, however, was clearly establisht by the discussion, namely, that Mr. Baden was quite mistaken in supposing that, because Mr. Jellicoe's conclusions had not been publicly calld in question, therefore they wer generally accepted by members of the profession.

As a wish has been expressed for some further information as to the manner in which a base fee created by the conveyance of a tenant in tail may be converted into a fee simple, it is proposed to consider the question in the following pages.

It is well understood, that an estate in tail is an estate in fee inheritable by heirs special, namely by lineal descendants generally as heirs, or such descendants of a particular class, and that a tenant in tail may convert such an estate into a fee qualified to last so long as there shall be issue inheritable under the entail. Such a conversion may be made by any conveyance sufficient to pass a fee, and will in any such case bind the heir until entry by him,(a) but if enrolled in Chancery in the manner required by the Act for the Abolition of Fines and Recoveries will, notwithstanding the want of the consent of the protector of the settlement, wholly bar the issue in tail, leaving the estate absolute during their existence, and liable only to be defeated by the failure of issue, and then by the entry of the remainderman. When the protector consents in the manner prescribed by the Act, there is no base fee, but the estate tail is converted into a fee simple and the remainders are absolutely barred.

The Northampton Table has played such an important part in the life insurance transactions of this country, and is still used to such a considerable extent, that a short explanation of the method by which it was constructed, may not even at the present day be without interest to the actuarial profession. In many ways we are greatly indebted to Dr. Price, and in the writer's opinion anything emanating from him is well worthy of our consideration. It is to be hoped, therefore, that no further apology need be made for the following remarks on one of his most important works.

Problem VIII—To construct a table for the formation of Survivorship Assurances.

A survivorship assurance on (x) against (y) is an assurance payable at the end of the year in which the combination (x. y) is dissolved, provided the dissolution is caused by the death of (x).

The only treatise of any value on this subject that I am acquainted with is a paper by Mr. Peter Gray, in vol. xiv of the Journal of the Institute of Actuaries. Considering the magnitude of the pecuniary interests frequently involved in transactions of the nature referred to, it is somewhat surprising that Mr. Gray's valuable labours have not, ere this, been followed up by contributions from other writers on the doctrine of Interest and Annuities. This, I think, is much to be regretted,—and must form my apology for the following attempt to add something to what Mr. Gray has given us.