In order to define the object and scope of the present contribution, it may be well to state at the outset that it puts forth no pretensions to be a complete survey of a subject which embraces in its wide sweep almost the entire field of practical Life Assurance. The author's design is merely to give a brief sketch of the development, from early times, of the systems and practice of Life Offices in ascertaining their liability under Policies of Assurance, and distributing the surpluses brought out by such valuations among those entitled to them; and the idea has been consistently held in view that it is mainly to assist foreign students that each country is asked to give a record and state the lessons of its past experience.