left for the purpose in the dead-wood abaft. The screw is 11 feet long and 14 feet pitch, and is intended to make 88 revolutions per minute. The screw is to be driven by a pair of engines of the estimated collective power of 360 horses, working at a pressure of 3 lbs. to the inch.

These engines, with their boilers, will occupy a comparatively small space in the after part of the hold abaft the main mast, leaving a much larger portion of the ship than usual for the purpose of carrying cargo and passengers.

The Great Northern will present the external appearance of a large full rigged frigate with a flush deck.

Her form is calculated for great velocity under canvass, and does great credit to the skill of the constructor.

Without entering into a detailed description of her construction, it may suffice to say, that the frame and outside planking are arranged in the usual manner; and that the ceiling, or internal planking, is arranged diagonally in two thicknesses from the gunwale to the bilge, where it is connected in a peculiar manner with the thick planks at the bilge. This arrangement is expected to prevent any alteration of form from the necessarily unequal distribution of the weights on board with reference to the volume of water displaced at particular parts of the ship.

This point has not been generally attended to in the construction of steamships, and the consequence is, that there is scarcely any steamer to be found that does not very soon after being afloat, undergo a considerable, and often a very perceptible alteration in her sheer.

After the Great Northern was launched, it was ascertained that she had broken her sheer only ths of an inch, instead of several inches, as is frequently the case in vessels built in the usual manner.

In order to show the comparative stiffness and rigidity of his method of building, Mr. Coppin furnished the writer with three models, of the same length, breadth, and depth, and containing pre

Archimedes

cisely the same quantity of materials in each, made from the same plank.

Number 1-A model 6 feet long, 9 inches wide, and 94 deep, planked in the usual mode.

Number 2-A model of the same dimensions as Number 1, planked outside in the usual manner. The inside planking in two thicknesses, was arranged so as to form an internal truss, abutting upon shelf or string pieces, and acting by compression.

Number 3-A model of the same dimensions as the two preceding, and planked outside in the usual manner. The inside planking in two thicknesses, was arranged so as to act by tension only, being without any abutments.

The three models were then loaded carefully as follows:

First Experiment.
Number 1-280 lbs., deflected
Number 2-1120 lbs., deflected
Number 3-2100 lbs., deflected

Second Experiment.

inch, inch, in.

Bee

Beddington Novelty

Ports belonging to. London. Brighton. Portsmouth. South Shields. London.

Great Britain Rattler

Two for the French Government One for ditto

Propellers on the same principle have been fitted to some other vessels by other parties, with various degrees of success. The old river steamer Swiftsure, has been fitted with one, and it is said that a considerable increase of velocity has been obtained. Ericsson's propeller is substantially the same in principle, and is said to answer well. The same remark applies to that patented by Captain Carpenter.

It is not my intention to trespass upon your pages by any further remarks, upon the merits or demerits of the screw propeller, as they have already been brought under the notice of your readers by gentlemen who have devoted much time and attention to the subject.

Mr. Barlow gives six tons per square inch as the ultimate tenacity of yellow pine; whilst a square inch of the same material is crushed by 86 of a ton, or about one-seventh of the weight.

Mr. Coppin's plan is by no means new in principle. Some years since a patent was taken out for building vessels with several thicknesses of plank arranged diagonally; but either from the want of tact on the part of the patentee, or more probably, because vessels so built, were found deficient in transverse strength, the plan was not acted upon to any extent. This I think must have been 25 years About twenty two or three years ago.* since Messrs. Tindale of Scarborough, applied diagonal suspension plates upon the inside planking of some vessels built by them, and soon afterwards doubled several of their vessels with thin planking outside, arranged diagonally, so as to act by tension only; this doubling was found to add so much to the longitudinal strength, as almost entirely to prevent any alteration of the sheer, and in no instance have I been able to discover any indication of straining at the ends of the planks.

Some years since, about 1816 or 1817,

There was a plan for the same purpose, of a much older date than that alluded to by our esteemed correspondent, namely, that of Messrs. St. Barbe and Stuard, the patent for which was taken out February 4, 1796.-ED. M. M.

Ports belonging to. Bristol.

France.

350 horse power. Ditto.

several of the steam vessels built in the Thames had suspension plates introduced upon the timbers under the planking. This plan was adopted by Messrs. John Wood and Co., in the Clyde, about the same time, they having had particular reference to the unequal distribution of the weights in steam vessels, in arranging the plates, and succeeded in preventing that breaking of the sheer which is too often seen in steam boats.

Mr. Oliver Lang, the talented master shipwright at Woolwich Dockyard, was amongst the first to apply the tenacity of iron plates to the strengthening our menof-war. So nearly contemporaneous was its adoption in this form to the same purpose in naval architecture by different individuals, that it is difficult to say to whom the priority belongs. It is highly probable, that having their attention called to the defective construction of our ships in regard to longitudinal strength, they arrived, as they must of necessity have done, at the same conclusions as to the nature and operation of the causes producing the defect complained of, and applied the tenacity of iron to remedy it.

Sir Robert Seppings and others had attempted to remedy it by applying the power of wood to resist compression, to counteract the tendency to hog, or arch.

General Bentham and Mr. Gabriel Snodgrass, were in a certain sense the predecessors of Sir Robert Seppings in the application of timber and iron for this purpose.

Admiral Chapman, the eminent Swedish naval architect, in 1767, published in his great work a plan in which the same principles of construction are adopted in the internal framing of the ship.

In civil architecture, truss framing has been long used; but the practical difficulties in the way of its successful application to naval architecture, and perhaps the prejudice in favour of accustomed practice, have prevented its general use in that department up to the present time.

I am, Sir, yours respectfully,
GEORGE BAILEY.

London, September 20, 1842.

The first column contains the age at which the assurance is effected; the second the annual premiums given by I. M., and the other three the premiums according to the mortality tables and rate of interest indicated, without any addition in the shape of commission.

On comparing I. M.'s premiums with those in the other columns, it will be seen that they correspond most nearly with those calculated by the Northampton Table; that is, the differences between the corresponding premiums are in that case the most regular, although there are, even here, discrepancies enough to show, either that the Northampton Table

cannot have formed the basis of the calculation, or that a different rate of commission has been added to the premiums at different ages. However, the correspondence is near enough to enable us to form a judgment as to the sufficiency of the rates.

I. M.'s premiums (I call them so for brevity) then, it will be seen, with an average addition of about 6 per cent., correspond pretty nearly with those deduced from the Northampton Table. Now, supposing the Northampton Table to give a tolerably correct approximation to the mortality which will be experienced amongst the assured at the ages under

consideration, and that 3 per cent. is the highest rate that can be calculated upon for the safe investment of money (which in the present state of the market is the fact)—I say, making these suppositions, it will be allowed by all who have paid any attention to the subject, that an addition of 6 per cent to premiums calculated on these data is wholly inadequate to provide for expenses of management and risk of fluctuation in the rates of both mortality and interest, to say nothing of profits to members or share-holders. On these grounds, therefore, I think we are warranted in saying that the premiums are inadequate.

But it is well known that the Northampton Table indicates a rate of mortality, especially at the younger ages, (which are just those with which we have at present to do,) far greater than has ever been experienced in any assurance society. By the showing of Mr. Morgan himself, who was the great patron of this table, the number of deaths between the ages of 10 and 20, in the Equitable Society, during an experience of fifty years, were only half those predicted by the Table referred to. And certainly when, as in the case before us, it is the interest of the parties effecting the assurances that the lives put in shall be as good as possible, it were folly to calculate on a greater rate of mortality than other offices have experienced in less favourable circumstances. But the effect of calculating in assurances of the kind under consideration, according to a higher rate of mortality than will actually be experienced, is, to give the annual premiums under their true value, since more will be alive to claim their endowments than the table predicted, and consequently, than the premiums were intended to provide for. It is true that, when the benefit is to be paid for by annual premiums, a compensation to some extent will take place; since, if the assured die off more slowly than was anticipated, more premiums will be received; and it is even possible that in particular instances the compensation will be exact. But an exact compensation at all ages can never possibly take place: since, leaving the rate of interest out of view, the amount of the benefit depends solely on the aggregate mortality between the age at which the assurance is effected, and that at which the benefit becomes due, while the amount of the premium

depends as well on the progressive rate of mortality between the same ages. It will be safer, therefore, to calculate the premiums for such assurances by tables which indicate a lower rate of mortality than the Northampton Table.

Such are the Carlisle and the Government Tables, the premiums derived from which I have given above. It will be seen that these premiums differ but little from each other; while they are, in every case, higher than the Northampton premiums, and generally a mere fraction under those given by Iver M'Iver. Hence, the conclusion becomes still more unavoidable, that the last-named are inadequate. But are the tables from which these higher premiums have been deduced to be depended on, as giving a correct representation of the mortality which will be experienced at the ages under consideration? As regards the Carlisle Table, Mr. Milne, by whom it was compiled, states that, in consequence of the introduction of vaccination, since the observations on which the table is founded were made, the mortality indicated in the table at the early ages is greater than may generally be expected. And the Government Table we may presume to be in a similar predicament. Hence, it will be unsafe to make use of the premiums derived from these tables, without a considerable augmentation; and hence, also, an office which should confine its business to assurances of the kind under consideration, at the rates given by I. M., could hardly fail to be ruined.

It may be satisfactory to some of your readers that I should explain the method by which the foregoing table has been calculated. The calculation was made by means of the formula which I gave in a previous communication, at page 117 of your present volume; and the elements, in the cases of the Carlisle and Northampton Tables, were taken from Mr. Jones's work on Annuities; and in the case of the Government Table, from a table constructed from the data contained in Mr. Finlaison's Report on the Mortality of the Government Annuitants. (Parliamentary Paper, No. 122, 1829.) The formula referred to is,

=

The values of this expression for each value of x, from 1 to x = 10, are the premiums required.

In using the Commutation Tables, not only is the mode of operation more simple, generally, than by any other method; but, when we have a series of values of any given benefit to calculate, we almost always meet with facilities, which, besides materially abbreviating our labour, also afford the means of proving the accuracy of part, at least, of our work. Thus, in the case before us, the numerator of the foregoing expression is constant for all the values of x, and the denominator alone varies. And we observe that the difference between any two successive values of the denominator, (those corresponding to x = 1 and x = 2, for instance,) is N ̊ (0) – N (1.) Now, by the construction of the Commutation Tables, N (0) — N (1) = D (1.) Consequently, if the value of the denominator corresponding to x = 1 be found, that corresponding to x = 2 will be found by subtracting D (1) from the first value; also that corresponding to x = 3, by subtracting D (2) from the second value; and so on for the rest. And the verification is afforded by comparing the value corresponding to x = 10, obtained in this manner, with the same value obtained by subtracting N (20) from N (9). Those who are accustomed to calculations of this kind will appreciate the facility afforded by the mode of operation I have described, as well as the advantage of the final verification. When the denominators are thus found, their logarithms, subtracted successively from the logarithm of the numerator, give the logarithms of the required values of p.

So obvious are the advantages of the employment of the Commutation Tables, for the calculation of the values of benefits depending on life contingencies, that I believe their being so little known and used for this purpose arises from the want of a systematic treatise upon the subject. To contribute in some degree towards supplying this deficiency, I am tempted to offer you a few short papers in illustration of their construction and applications. In drawing them up, I should be largely indebted to Professor de Morgan's able articles in the "Companion to the Almanack," to which I

formerly referred. These articles, however, avowedly contain almost nothing of demonstration; and it is of this deficiency that I chiefly complain, and which I should make it my study to supply.

May I, notwithstanding the length to which the present article has insensibly grown, still beg space for a remark or two on the manner in which Mr. Scott has chosen to solve Iver M'Iver's former problem? Mr. Scott seems to entertain a most magnanimous contempt for the labours of his predecessors in this branch of science. The results of these labours have been published expressly for the purpose of facilitating the enquiries of those who should come after; yet Mr. Scott stubbornly refuses to avail himself of them, and gives clumsy theorems for the solution of particular cases, which may be solved in their utmost generality at one-tenth of the labour, by availing ourselves of the tables which have been published. In finding the value of a temporary annuity for nine years, which was necessary for the solution of the problem referred to, Mr. S. chose to do so (page 114) by a method which involved nine divisions by as many different divisors of seven figures each, and one addition of nine lines; while the value might be found from the published tables, as I showed in my first solution, (page 116,) by two multiplications, one division, and a subtraction. By my second solution, only one subtraction and one division are required for the whole solution. Moreover, had the duration of the annuity been doubled, so also would Mr. Scott's labour, while that by the method I employed would have undergone no increase. If the facilities afforded in calculation by the use of logarithms be not too great to suit Mr. Scott's taste, he will of course, when he has occasion for them, if he act up to his principles, disdain to take them from a published collection, but will insist on calculating them in every case for himself!

Seriously, Mr. Scott ought not to act in this manner. If every one were to do so, and refuse to avail himself of the labours of his predecessors, in matters of mere drudgery, the advances of science would be slow indeed. I trust I have said enough to make this obvious.

I am, Mr. Editor, respectfully yours,
G.

Hermes-street, Pentonville,
September 21, 1842.