The mode of using Barrett's method has now something of farrago about it: a little discussion may be useful, were it only to awaken attention to the confusion arising from changes made without adherence to the recognised laws of perspicuity.

The farrago to which I have alluded arises out of a struggle between the annuity, as commonly understood, and what I shall continue to call the annuity due. According to the technical meaning of the word annuity, the payment begins to grow at the moment of the grant: thus, a yearly annuity for 12 years, deferred 20 years, begins action at the end of 20 years, and grows the first payment in the 21st year. I shall vary the phrase used in my “Essay on Probabilities” (Cab. Cycl.) by allowing the words “annuity due for x years” to signify an annuity of x payments, the first immediately. Thus an annuity for 12 years, now granted, will in a year become an annuity due, also for 12 years.

The object of this paper is to endeavour to show that the true method of estimating the liabilities of an Insurance Company should be based upon the principle of re-insurance by its own rates of premium, interest being reckoned at 3 per cent.

In submitting the following observations, I feel it necessary, in the first place, to apologise for recurring to a subject which has been so frequently and ably treated by the President of the Institute of Actuaries. But as my method of dealing with this important branch of our business differs in some respects from the plan laid down by that learned writer, I trust I may be allowed to record the present attempt to demonstrate what in my opinion are the true principles which should guide us in determining the liabilities of Life Insurance Companies.

The premium paid on a policy of assurance is divisible into two parts—the first, or net premium, representing the annual contribution absolutely necessary, on a calculation of averages, to provide a stipulated sum on death; and the second being an arranged contribution towards the expenses of the Office.

1. Write down the multiplicand in the usual manner.

2. Write on a separate slip the multiplier with its figures reversed (as in contracted multiplication), being careful to space the figures so that they can be exactly placed over those of the multiplicand.

In a paper read a short time ago before the Institute, I endeavoured to show the inexpediency of using, for the purposes of valuation, tables constructed on the principle which characterizes the Northampton table. I did not intend to pursue this particular branch of the subject further; but, finding that more difference of opinion exists in reference to it than I was aware of, and considering that the practice of making valuations by the Northampton table, and by tables framed upon similar principles, is still carried on to a great extent, I am led to offer a few more observations upon the matter previously to entering upon the consideration of some other questions, the correct solution of which materially depends upon a right understanding of this one.

Public attention has for some time past been earnestly directed to the introduction of the decimal system in our weights, measures, and coins. The nation is generally convinced, that the adoption of such a system would prove of immense benefit—that it would afford great facilities for calculations of all kinds, that it would shorten the work of education, that it would economise labour, and that it would diminish the chances of error. The Society of Arts, and other scientific societies, have investigated the subject in all its phases and bearings, and we have been expecting the speedy adoption of some practical plan which would be certain to confer so great a boon. Unfortunately, the Russian war, the Indian mutiny, and other political events, have rendered it necessary to put aside the consideration of many social reforms, and this, among the rest, shared the same fate. We have bestowed, also, far too much attention to the pound and mil scheme, as if upon it rested the entire question of decimalisation, and thus years have passed without a single step of a definite character being taken.