The principal difference between the accounts of an insurance ecompany and those of an ordinary trader lies in the fact that the trader buys before he sells, while the insurance company sells before it buys, that is to say, the insurance company first receives the money on any transaction, and afterwards pays out. From this it arises that the trader keeps account of his liabilities by book-keeping and ascertains his assets by taking stock, while the insurance company keeps account of its assets by book-keeping and ascertains its liabilities by taking stock. There are certain classes of trade, chiefly brokerage, where there is either no stock, or a stock not needing stock-taking, in which the trader can keep account both of his liabilities and of his assets by book-keeping, and has thus a far better knowledge than he otherwise would of the sources and the progress of his profits. The purpose of this paper is to suggest that an insurance company, including even a life office, may keep accounts of both assets and liabilities by book-keeping methods, and may thus have clear information as to the sources and progress of its profits.

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.