It has been, I believe, considered an axiom that payment of Life Assurance premiums should be made in advance, or in other words, that under any sound system of Life Assurance, the premiums paid must never be less than the value of the risk incurred from the outset upon the basis of calculation adopted, and this appears as a fundamental principle in all the published formulas for the determination of the values of any interests involving Life Assurance. The methods that are described in the following pages necessitate a departure from the existing practice in this respect, and it is therefore essential, in the first place, to justify so important a change.