The present paper was undertaken on happening to peruse very lately Messrs. Gray, Smith, and Orchard's laborious and useful work, entitled Assurance and Annuity Tables, according to the Carlisle rate of Mortality, at 3 per Cent. In the introductory section of that work, when referring to the larger Tables V. and VI., containing the single and annual premiums for survivorship assurances, it is there very justly remarked, “Considering the frequency with which occasion arises for the functions here tabulated, and the tedious nature of the operations requisite when their values have to be formed from other tables, it may, at first sight, seem surprising that complete tables of them had not been formed long ere now; but the wonder will cease when it is farther considered that, until recently, there had been pointed out no other method of forming them than the tedious operation just referred to.

To trace the succession of events which have given rise to the duplex system of assurance in this country, known as the Participating, and Non-participating, would not be altogether uninteresting or unprofitable. There is little doubt, that the immoderate premiums required at the outset by the few who were disposed to embark in the then novel speculation of life assurance, suggested the idea of mutual association, as a means of achieving the same objects on more advantageous terms; and thus the participating system owed, to a certain extent, its origin to the non-participating.

It has frequently been remarked, that however varied and uncertain may be the occurrence of the events to which the life of a single individual is exposed, the average return in a large mass of persons is so regular, as to be predicted with confidence within very small limits of error. On the uniform happening of these events under similar circumstances, or the discovery of the laws by which they are governed, the actuary depends for the application of the theories of probabilities to the many useful purposes for which they may be rendered available.

It has frequently been remarked, that however varied and uncertain may be the occurrence of the events to which the life of a single individual is exposed, the average return in a large mass of persons is so regular, as to be predicted with confidence within very small limits of error. On the uniform happening of these events under similar circumstances, or the discovery of the laws by which they are governed, the actuary depends for the application of the theories of probabilities to the many useful purposes for which they may be rendered available.

The interest which the Members of the Institute of Actuaries take in all matters relating to assurance, has induced me to present a few statements which exhibit the loss upon marine risks under certain classifications; and at the request of their valuable and talented secretary, I lay before them the data upon which tables for assuring the following benefits were constructed by me in the early part of last year for a projected company.