1. The development of this paper involves the consideration of certain arithmetical, mechanical, and photo-electrical technicalities, but the ultimate aim is a very simple one and it may therefore be advisable to state it at once. The ultimate aim is to persuade the whole civilized world to abandon decimal numeration and to use octonal numeration in its place; to discontinue counting in tens and to count in eights instead.

It is over 20 years since the surrender values and paid-up policy amounts of ordinary policies were made a subject for discussion in this Hall. Industrial surrender values have been recently discussed. This paper is therefore primarily concerned with ordinary policies. In practice a company can grant whatever scales of surrender values or paid-up policies it may choose, provided it does not depart from any written, verbal or implied obligations to its policy-holders. There are, however, certain principles of equity to which consideration should be given, and it is along these lines that the problem is investigated.