Some years ago I had the honour of reading before this Institute a paper which, though mainly devoted to a study of surrender values, treated such surrender values as purchases by life offices of reversions. On that occasion I stated that sound British companies could well afford to repurchase their own acceptances at 6 or even at 5 per-cent. Subsequent experience has done much to confirm me in the opinion then expressed, but I did not then, nor do I now assert that offices should on such terms purchase other reversions than their own policies; and I trust it will not be thought wasting your time, if I preface this paper by enumerating a few considerations which seem to indicate that the present market price of reversions gives, comparatively, a return none too high to an investor. Such market rate I take to be 5 per-cent in the case of an investor who does not stand, or, what is the same thing, arrives at his price as if he did not intend to stand, any risk of loss, whether through longevity of life tenant or death of reversioner.

All our empirical knowledge depends not only upon the exactness, trustworthiness, and frequency of the observations on which it is founded, but quite as much upon the possibility of drawing general conclusions from the observations. The great variety of form in which the results of observation appear, even independently of the diversity of the nature and the method of observation, will easily explain why the range of the conclusions to be drawn from the observations, differs widely according to the field of the science to which they refer. While the natural philosopher must be satisfied with the mere knowledge of a fact in a field which has not previously been investigated, he goes in other realms of science far beyond this first step of observation; he obtains an explanation about the causes of the phenomenons and the connection of the forces and the laws which govern the events that come under his observation. Such explanations cannot in general be drawn directly; they require a number of intermediate steps in which the observed result has to be critically examined and analyzed into its single elements. The proceeding to be adopted for this purpose depends upon the nature and form of the observation, and it would be a mistake to suppose that we can follow the same method for all kinds of observation.

The strict analogy which exists between these two classes of annuities has doubtless received the consideration of the majority of students, but I am not aware that it has ever in print had that attention which it deserves; and at any rate our usual text books hardly even refer to it. Although it is shown, in the short but suggestive article of the late Prof. De Morgan (vol. iv, p. 277), in the most general way, that years, or periods of time, may be interchanged with any other kind of status whatsoever, whether certain or contingent; yet, as successive statuses are almost exclusively spoken of, the less complex cases are liable to escape notice. Under these circumstances, the following brief notes may not be thought superfluous.