Notwithstanding the very large amount of leasehold property, which in the course of every year is bought and sold in this country, and notwithstanding the extensive transactions—of almost hourly occurrence—in the public market, in Government and other temporary Annuities, the subject of the rate of interest which any given purchase will yield the buyer is very imperfectly understood, even by those most deeply interested in the inquiry, unless they happen to be at the same time well versed in actuarial computations.

Let be the given function, then, by a well known theorem

the integral of which, since u0, δu0, δ2u0, &c., are constants, and

will be

which differs from (A) only by the coefficients of δu0, δ2u0, &c, being shifted each one place to the left.

Having been favoured by Mr. W. T. Thomson with a copy of his large Table, “Carlisle 3 Per Cent.,” and believing that the insertion of a notice of such laborious and useful computations as are brought together in that extensive work is in accordance with the objects of the Assurance Magazine, I beg to offer a brief explanation of some of the most important features of the Table; and such notice will afford an opportunity of referring to particulars which it appears desirable to annex to those submitted in my former paper.

We have been favoured by Mr. Thomson, the Actuary of the Standard Life Assurance Company, and one of the Vice-Presidents of the Institute, with a copy of certain cases submitted to Mr. Edward Sang, and of his opinion in reference thereto. The matters to which they relate are of so much practical importance, and the learning and ability of Mr. Sang are so well known, that we gladly avail ourselves of Mr. Thomson’s kind permission to publish them, and feel we need offer DO apology to our readers for giving them entire.

Considering the undeniable importance of a conformity to correct principles in carrying out the processes which must he resorted to for the purposes above mentioned, it is not a little remarkable that no work exclusively on the subject has hitherto appeared. If we except Mr. De Morgan’s and Mr. Sang’s Essays and the Observations scattered through the writings of Mr. Babbage, Mr. David Jones, Mr. Samuel Brown, and one or two others, we believe it may be truly said that scarcely any allusion to it is to be found.

Until within a very recent period the doctrines of probability have been applied to scarcely any great public purpose except the Assurance of human life. In that particular department of knowledge, a number of labourers have been for many years busily occupied in gathering the facts, endeavouring to classify events, and trace some general laws. In later years, researches have been extended into the effects of different classes of diseases upon health and longevity. Still more recently, the calculations of fidelity risks, of railway and other accidents, of bankruptcy, and of other circumstances affecting the person of an individual, or his commercial dealings, have been made with a view of proving their capability of being estimated for Insurance.

It would be very difficult to select a more simple idea, couched in more simple terms, than that conveyed by the expression ‘Total Loss.” It would not be easy to find an idea which has wandered farther from its radical, and has by development undergone greater transformations than that of ‘Total Loss,’ according to the doctrine as now expounded.

The new Stamp Act does not, as perhaps might have been expected, set at rest the much disputed question, whether the assignment of a chose in action requires an ad valorem stamp. The clauses in the schedule to the new act, upon which the question will depend, and which immediately follow the words “conveyance and mortgage,” are word for word the same as those in the schedule to the 55 Geo. III., C. 184, and hence it will remain abstractedly in the same position as before. A strong opinion has been expressed that in every case of such an assignment, whether by way of mortgage or upon a sale, the ad valorem stamp is necessary, and assuming that the points depend upon the construction of the word property in the statute, it is argued that “whatever is dealt with as property, and is the subject of sale or mortgage, is property within the meaning of the act, and that the instrument by which the transfer is effected is chargeable with the ad valorem duty, unless expressly exempted.”—(Tilsley, Stamp Laws, 248).