Since the last article on the settlement of fire-claims under average policies appeared (April, 1857), a very important change has been adopted. The third clause of the Liverpool floating policies, known under the title of the “independent liability clause,” has been introduced, by the common consent of nearly all the Insurance Companies, and made part of the conditions of all London mercantile floating policies. The alteration is, beyond all doubt, a very considerable one in its practical effect. It will change entirely the mutual relation of the Companies in very many cases of joint insurances, and, if very great care be not taken at the outset, introduce no small share of doubt and difficulty in the relation of the Offices with the assured. It may, therefore, be worth while to offer a few remarks at the present moment on the change actually effected by the recent alteration of the average clause, and then make some practical suggestions as to the regulation of claims under the altered form of policy.

In the course of an actuary's practice, the question not uncommonly arises—What is the value of a life interest, accompanied by a policy of assurance on the same life ? The most obvious course for solving this question is to value the life interest and the policy separately—the former by the well-known formula . With regard to the policy, it is not so clear how it should be valued. If valued on the same principles as the life interest, the value of a policy for £1 would be 1 − (p + d) (1 + A); but this formula is quite inapplicable, for it gives a negative value for many years to a policy, and almost always a much smaller value than the surrender value allowed by the Office. There is, therefore, apparently no choice but to take the value of the policy at the latter amount.

The idea of periodic or discontinuous functions was primitively introduced by Euler, and has since been the subject of extended investigation by M. Fourier, who has made some new and important applications of it in. his mathematical theory of heat.

As the forms above referred to are now numerous, and in constant requisition, we have thought that, by collecting some of them together and putting them into print, we might be affording certain facilities for, and leading the way to, more uniformity of practice in this particular than has hitherto been attainable. We, accordingly, append such specimens as we have been able to get together, and shall be obliged to any of our readers who will afford us the means of adding to their number, or who will suggest any improvements in their construction. Most of those now given have been in use for many years amongst some of the older Companies. It is quite possible that amongst those of more recent date better forms are rife, and we shall be very glad if the publication of these prove the means of bringing such to light.—Ed. A. M.

The returns of the various Insurance Companies are published in some of the United States, so that if all the facts were fully stated as required, a fair estimate could be formed of the extension of the business of the Companies from year to year, with their premiums, capital, reserve, &c. Those of the commonwealth of Massachusetts are given agreeably to the requirements of Acts passed in 1837 and 1842. In 1850, the requirement of returns from the mutual Fire Insurance Companies was repealed by an Act of May 3rd in that year.