The present effort does not profess to be complete. It deals with the main problems that come before the Consulting Actuary in connection with Staff Pension Funds, but does not go into the details of what may be called the fancy benefits which are occasionally met with. The solutions of the general problems here given will, however, indicate the methods to be applied in attacking other, and sometimes more complex, questions, which, when the principles have been grasped, will not present serious difficulty.

The volumes of the Journal contain numerous theoretical investigations dealing with the changes produced in Policy-values by alterations in the basis of valuation, and a number of interesting and important results have been obtained, of which the most valuable have been embodied in the Text-Book, Part II, Chapter xviii, Articles 39–72. These investigations are almost entirely based upon analytical transformations of algebraical expressions for the Policy-value. Fruitful as this method has been, and elegant as are many of its processes and results, it yet labours under certain serious disadvantages. From the nature of the method it can be applied only to the limited class of benefits—practically confined to ordinary Whole-Life and Endowment Assurances, with uniform Premiums and Benefits—which admit of the Policy-values being expressed in an algebraical form involving only one class of function, e.g., ax, Ax or Px: so that relations which are really of very wide generality remain undemonstrated, except for those particular classes of Assurance. Again, demonstrations based upon a particular mathematical formula for the Policy-value are not easily modified to meet changes of conditions which, though slight in themselves, may render the fundamental formula completely inapplicable: while abstract analytical demonstrations are both harder to grasp in the first instance, and harder to reproduce or adapt when subsequently required, than are demonstrations based upon more concrete considerations.

Insurance Companies are sometimes asked to lend on a prospective interest under the will of a living person. In most cases, such an expectancy would of course be quite out of the question as a security; for besides other circumstances that may arise to defeat it, there is the possibility that the person who has executed the will may change his mind, or get rid of all his property in his lifetime. But in certain circumstances the chance of realizing such an expectancy may be materially increased. For example, the person who has made the will may become lunatic and incapable of dealing with his property or making a testamentary disposition of it. The property would then be placed in the custody of a trustee or the Court, and, subject to a proper allowance for his maintenance, would be kept intact till his death or recovery. And, if there is strong evidence that there is practically no chance of the lunatic recovering his reason, the prospective interest can almost be regarded as an ordinary contingent reversion to fall in on the death of the lunatic, if the beneficiary survive him. In such circumstances, the prospective beneficiary may desire to raise a loan on his interest; and life offices are sometimes approached in this connection. Though, as the writer shows in the following remarks, such an expectancy cannot form a mortgage security, even when the chances of its realization are as favourable as those mentioned above, it may be useful to examine the chief points that come up for consideration in a proposal of this sort, and the reasons for which it should be declined.

Under the Act of 1617, cap. 16 (of the Scots Parliament) and subsequent Acts, all deeds relating to land require to be registered, such deeds ranking according to the date on which they are registered and not according to the date of signature. There are other kinds of Registration in Scotland, notably for Preservation and Execution. Under this the principal writs are retained in the permanent custody of the Registrar, an extract (official copy) being furnished which has the same validity as the original. In the case of Registration for Publication, with which this note deals, the deed, bearing a Certificate of Registration by the Keeper of the Register, is in due course returned to the persons registering.