Hence, the foregoing present values will be more conveniently represented by v, v2, v3, . . . . vx, respectively. It is obvious that the present value of any other sum, will be found by multiplying the present value of £1, due at the end of the same number of years, by the number of pounds in that sum. Copious tables of the present values of 17., due at the end of any number of years, from one to one hundred, together with their logarithms, are given in Mr. Jones's work, Part I.

is

The indications of the mortality table are represented as follows. The number shown by the table to attain to any age denoted by the letter, with the age attached as a suffix. Thus, lo, la, la, la, ,, &c., denote the numbers who attain the successive ages, 0, 1, 2, 3, x, &c., respectively. These symbols will, of course, denote different numbers in the case of different tables. Thus l。, repre

£1.....

£............

2 years.

3 19

senting the number alive at birth, which is called the radix of the table, will, in the case of the Carlisle Table, be equal to 10,000, and in that of the Northampton Table, to 11,650; and the values of the other symbols will in like manner vary. But the great advantage of the use of symbols is, that we have no need to distract ourselves with their particular values, until we reach the final solution of the problem with which we may be engaged. Also, since the number who die in any year of age, that is, who enter upon that year and do not live to complete it, is equal to the difference between the number who complete that year and the number who completed the previous year, these decrements, as they are called, will be represented as follows:— lol, is the number who die in their 1st year.

2nd

3rd

ath (x+1)th

Sir,-As I was shutting my windows a few days ago, to keep out the visible and tangible particles of a metropolitan fog, the blackening influence of which, even the town sparrows bear witness to, when compared with their congeners in the country, I could not help thinking what a benefactor indeed, (I do not mean to the sparrows), Mr. Williams would be, if he could improve the combustion in our common grates, in the same degree as he has improved furnaces on a large scale.

It must be evident to every one, that has

ever poked a fire, that large quantities of unconsumed gas, as well as smoke, are constantly escaping, only to add to the murky atmosphere without, so common here in the cold seasons of the year; gas in fact constitutes the greater part of what we commonly call smoke and I believe it is also incontrovertible, that none of the most improved stoves hitherto invented, have succeeded either in burning all this gas, or in preventing the generation of smoke, during the combustion of that part of the gas which they do burn: yet surely when this object

has been attained in a furnace, we might expect to find it also attainable in an open grate. Mr. Williams's exact principle could not perhaps be brought into action, but might not an equally efficient one? Even burning all the gas would be a great improvement.

The origin of the form of our present grates has been evidently more a desire to fit them for throwing out heat, than any consideration with regard to attaining a perfect combustion: till of late years, all that was thought to be necessary, was to "put your combustibles in a convenient place, set fire to them, and let them provide themselves with air." Now on looking at a common fire-place, (particularly when a fire has been lately replenished), we perceive at once that almost all the smoke comes from the back and sides of the grate, and that the gas will not burn well in either of those situations; burning, when it does ignite, generally with a lambent Jack o' lantern flame, ready to die away every instant, from want of air; whereas the gas evolved in the fore-part of the grate burns brilliantly and without intermission. This seems to suggest that the grate should be all front, (being an Irishman, Sir, you know I am privileged-so no criticizing, if you please), or at least that such a state of things is a desideratum to be approximated to, as nearly as may be, without disregarding other requisites. perhaps is already the case in several newly invented grates, as far as the sides are concerned, but I do not think I have ever seen a grate in which the back admitted a good supply of air.

This

I have said nothing, Sir, as to any means of preventing bona fide smoke, and for a good reason, because I am not aware of any; experiments in these matters require such "appliances and means to boot," that it is not everybody that can try them; but it would be well worth the while of any of your readers who have it in their power to

do so. Perhaps this may meet the eye of Mr. Williams, and induce him to turn his attention, if he has not done so already, to this branch of a subject upon which he has already thrown so much light; even if it were only in pity to us poor metropolitans, condemned for half the winter to have the sun no brighter than a new copper penny. I am, Sir,

Your obedient servant,

R. W. T.

P.S. I may take this occasion, Sir, to remark that your note appended to your correspondent "M.'s" last letter on the crank, would have been quite sufficient to stop any reply on my part, had I intended making one; but I beg leave to assure you,

that, even had you not come forward at all, I should have made no attempt to answer suchair-drawn daggers as were there aimed at me, they being but

"a false creation

Proceeding from a crank-oppressed brain."

THE TREASURE SHIP "LE TELEMAQUE."

We learn from the Journal du Havre, that the works for the salvage of Le Télémaque are steadily advancing. The little town of Quilleboeuf is quite alive with shareholders and speculators, who daily arrive, to satisfy themselves as to the progress of the undertaking, and to watch the market for shares, which mount in price as the long-buried wreck gradually rises from the sand.

The works having sufficiently advanced, the process of weighing was commenced on the 14th of October; and after every thing was tightened up, a stress of above 600 tons was applied, by means of powerful screws acting between the bridge raised on the vessel and the large platform constructed on the rocky bed of the river. The experiment was anxiously watched by all present, and no small uneasiness was felt by some, who saw the enormous timbers bend and creak, while the wreck appeared still as firmly fixed in the sand as ever. After about twenty minutes' screwing, the operations were suspended, and the vessel left to the operation of the current under this great strain. In about six hours the timbers had straightened; and when the screws were then again applied, the wreck, with the vast superincumbent mass of iron and timber, yielded to the force, and, once free from the suction of the sand, the whole, though of very great weight, became perfectly manageable.

The current having thus done its work in loosening and clearing the wreck, it became necessary to protect the works from its force, and additional piles were accordingly driven, to form a small breakwater, in case of storms. The weighing has also proceeded as fast as due precaution would allow; and by the close of last week, a workman had walked along the wreck, having the water only to his waist.

It will still demand some days to raise the Télémaque entirely above low water mark, to support her from beneath, and then to cut through all the chains and timbers to open and discharge her. The interest felt in France, now that the engineering question has been solved, is unprecedented. The demand for the shares is very great; but though a few may be picked up at from 107. to 207. each, the majority of the holders refuse to sell under one thousand francs for the hundred franc share.

RAILWAY REFORM.

Sir, I noticed with some surprise, in the last Number of your Magazine, a communication signed "George Cumberland," under the head of "Railway Reform," detailing what he is pleased to term "A New Plan of working "a single railroad with as much efficacy as a double one," viz., by "sidings" or "turn-outs," to which he has applied the term " sinuosity." The plan is by no means so new as your correspondent seems to fancy. It has been applied, for many years, to the colliery railroads in South Wales, and various parts of the kingdom; but I am not aware that it has ever been used on railways for passenger traffic. Indeed, it must be evident to all persons acquainted with the practical working of railways, that this "new plan" is quite inapplicable to passenger railways. Had it not been so, it is not probable that engineers would have overlooked one so advantageous.

I am, Sir, your obedient servant,
T. DYNE STEELE.

October 31, 1842.

FILTRATION OF WATER.

Sir,-In your correspondent "W. H.'s" letter of October 15, it is stated, respecting the purification of water, that a very efficient filter may be made for less than 1s. 6d. It would oblige me much, and, no doubt, many others of your readers, if he would state how it is constructed; and, at the same time, whether it will take away the lime with which water, more or less, is impregnated, and which must be more or less prejudicial. I am, Sir, yours respectfully, A SUBSCRIBER.

22, Young-street, Manchester. October 28, 1842.

NEW PLAN FOR THE SUPPLY OF LONDON WITH PURE SPRING WATER.

Sir, I have seen in the Mechanics' Magazine a discussion, upon certain observations made by the Rev. James Clutterbuck, on the periodical drainage and replenishment of the subterraneous reservoir in the chalk basin of London. I have read also various opinions and counter opinions on the subject, by some ingenious and very clever men, the general scope of which was to show that the deep wells, in and round London, will and do admit, of being nearly exhausted of water by the end of each week, and that if a large quantity is taken from any one locality, the other wells distant from that locality, are drained by it. If so, then, not a much greater supply of water could be obtained by adding to the number of deep wells in and round London.

A great deal has been said likewise of late about the quality of the water supplied by different water companies, to the overgrown and still increasing metropolis, and about the necessity of purification by filtration or some other means.

Now, if there really be a necessity of a bet. ter supply of pure water to the metropolis, I beg leave to propose a plan, that will most certainly afford a plentiful supply, and which could be carried out to such an extent, that the supply would become immense.

I propose not to meddle with the lower springs that are below the London clay forma. tion and the chalk, but to collect the water from the upper springs, that form themselves at a certain depth from the surface of the earth.

I would commence operations with the basin of the Thames, above London, in the most convenient place, to form a surface reservoir. From that reservoir, I would carry a subterraneous archway up the valley, and parallel with the river Thames, but not communicating with it, nor following its windings, though approximating closely to it in some places. The river Thames of course rises against the stream; therefore the archway, by driving it up the side of the stream, would, by and by, be as deep as the bed of the river Thames, which I consider would be deep enough for my purpose. I would continue this arch-way drift still onwards; but not level as before, allowing it to rise as the bed of the river rises, and taking care always to be as low with it, as the bed of the river. By that time a large stream of water would be going out through the arch-way into the reservoir, and the supply for London would in a measure be commenced.

Let the drift-way be then continued up the vale of the Thames, and let lateral drifts from it be also made wherever any strata is intersected, that is likely to afford a large supply of water. The system might be thus extended to such a magnitude, that a great part, if not all London might be supplied by it, and as more and more water was wanted, it would only be necessary to continue the arch-way drift up the basin of the Thames to any distance, until the supply was enough.

A drift-way of 4 feet in width and height, would discharge an immense volume of water into the reservoir, on account of the rise that would be in it, from that level part of it, where it had first become as low as the bed of the Thames. For from that place the drift would rise as the bed of the Thames rises; consequently, the arch-way at the reservoir would discharge itself full of water, with a pressure behind it, from the drift-way rising far up the valley of the Thames.

The expense of the drift-way, per mile, would not be great. The pits down to it would be shallow, by keeping the drift near the side of the Thames, viz., to the depth of the bed of the Thames. A few of the pits might be left but covered over; the greater part of them should be filled up. The little damage done to the land, during the operation, would be made good behind, as fast as the drift was carried forward.

I have read of many hundreds of thousands of pounds being expended by Water Companies; but the whole of them would not produce such a supply of pure spring water as would result from the above plan. Besides, very little land would be damaged, and a great deal of land would be benefited by the drainage. I do not know how the vale of the Thames is situated with regard to London, for I never was there; but I should think the reservoir should be placed so far up the vale of the Thames, that the water should flow from it into London, without having to be pumped up by engines.

I believe such a drift would not cost so much money per mile as would an open canal, taking in the expense of land, aqueducts, bridges, &c., and it would be much less objectionable, for many obvious reasons. It would not interfere with any existing establishment; it would not be liable to inundation by land floods, nor be dependent on the irregular supply of surface water; it would receive its supply from the pure springs in the bowels of the earth.

I am, Sir, your obedient servant,
THOMAS DEAKIN.

Blaenavon, October 17, 1842.

GAS FROM SOAP-SUDS.

A few years ago the immense quantity of soap-suds employed in the city of Rheims in preparing woollen stuffs was entirely lost. M. Houzeau Muiron conceived the idea of extracting from them the fatty matter, and of making an important application thereof. In fact, by submitting them to a regular purification, he has obtained a limpid oil, with which he succeeds in preparing the soaps in demand in commerce, while the residue of this purification serves for the advantageous production of a gas for lighting a part of the city.

The soap-suds collected in the shops, where they have become saturated with grease and the impurities of the tissues, are poured together into a large basin, which is capable of containing about 3,000 gallons. To decompose them, there is poured upon them 308 pounds of muriatic acid, or 154 pounds of sulphuric acid, first diluted with its own weight of water, and the mass is rapidly

agitated until the decomposition is complete.

Shortly afterwards a froth is seen to form, which at the end of twelve or eighteen hours is sufficiently well separated from the water upon which it floats. Four-fifths of this water is then run off, containing about one per cent. of sulphate of potassa, which is utilized either by evaporating it in dryinghouses, or by running it off upon dry earth exposed to the air, which, when sufficiently charged with the salt, is washed. Directly after this operation, the basin is filled again with a fresh portion of soap-suds, which float the fatty matter and permit it to be run off into a side tub. The product obtained is a mixture of unaltered oil, the acids, animal matters, and a large quantity of water, which forms with them a species of hydrate. This water is disengaged by injecting several times into the mass a current of steam, which heats it and facilitates its evaporation. The fatty matter is then run off into a boiler, where it is submitted to a rapid ebullition, aided by continual agitation, which drives off the last portions of water. The product contains twenty or twenty-five per cent. of impure matters, which colour it and render it turbid. To purify it, it is poured into basins of copper and mixed with two per cent. of concentrated sulphuric acid. After two days the limpid oil comes to the surface, while the impurities are precipitated to the bottom.

The oil is carefully separated, and the deposit, when filtered through cloths in a press, gives still a large quantity of oily products, which are added to the preceding and made into soap by treating them with common soda.

The residuum is black and very thick; from it M. Muiron produces the gas for lighting; but before introducing it into the retort, he liquifies it by means of the empyreumatic oil obtained in the preceding operation.

The gas thus prepared is purified by lime, and the water from the washing contains sufficient cyanide of calcium for the preparation of Prussian blue from it, by treating it with sulphate of iron and washing the precipitate with muriatic acid.

This gas possesses a considerable lighting power, and in order to apply it to the lighting of the establishments scattered throughout the city of Rheims, M. Muiron has contrived a manner of transporting it, at the same time simple, economical, and free from danger.

F. BOUDET.

Jour. de Pharm. et de Chim., May, 1842.

ECONOMY OF FUEL IN RAILWAY ENGINES.

The Commissioners for the Management of the Public Railways in Belgium, have lately directed much of their attention to the practicability of lessening the consumption of fuel in steam-engines. It is calculated that the heating of the boilers alone consttutes nearly one-half of the whole expense of the trains on railways. The system partially introduced of late is based on the principle that every head engineer shall be liable for the quantity of coals which he consumes. An account has accordingly been opened with each of them, in which the number of miles he traverses, and the precise time during which the locomotive is detained at the stations, are entered. Every three months, a Board of Engineers investigates the account, and determines the maximum, quantity of coal which ought to be allowed. The difference which is found, after deducting the actual consumption from the maximum fixed, shows the amount of saving effected; and upon this difference the engineer becomes entitled to a premium of twenty-five per cent. on each hectolitre. Orders, varying from one to five hundred hectolitres, are delivered to the engineer once a month; and these orders are his warrant for the receipt of coals at the several stations. There is another advantage, too, in this regulation; the detention at intermediate stations does not exceed the time allowed; for the whole cost of the fuel, which a prolonged detention occasions, becomes a charge upon the engineer, let the cause be what it may. The quantity of fuel requisite for getting up the steam forms the item of a separate account with the engineer; and the plan has this collateral recommendation, besides-that it is a test of the care and trustworthiness of the parties employed.

NOTES AND NOTICES.

Pearls.-Letters from Norway mention that there have been found in the bed of the great stream that runs through Jedderen, in the diocese of Christiansand, and which from the excessive heats became dry, a great number of bivalve shells containing pearls, some of which were so large and fine that they were valued at 607. a piece. At the beginning of the 17th century, when Norway was annexed to Denmark, the government took the pearl, fishery of this stream into its own hands, and the finest pearls were sent to Copenhagen to be deposited in the crown treasury. After this, the produce of the fishery became so low, that it did not pay the expenses, and it was abandoned. It will now probably be resumed.

Average Altitudes.-At a sitting of the Berlin Academy of Science, of the 11th July last, H. Von Humboldt read a long memoir, upon the methods by which the comparative and average heights of continents might be ascertained. From the calculations of the learned gentleman, it appeared that the average height of Europe was 615 feet, of North

America 648 feet, South America 1,035 feet, and of Asia 1,053 feet. The whole of these calculations were grounded on the assumption that each chain of mountains was to be taken as a bilateral horizontal prism, and that each high level should be considered as a plain, and should be brought down to a comparison with the level of the surrounding country. A careful calculation proceeding on this footing, gave as a result that the mass of the Andes' chain in South America, including the whole of the flat portion of the eastern borders, and the beautiful wooded heights uniformly distributed on those plains, and of which the level portion is exactly one-third larger than the upper levels of Europe, is only 486 feet higher than the average height of the latter quarter of the globe.

Steam Navigation said to be invented by the Spaniards -A letter from Madrid, published in the Commerce French paper, contains an account of the discovery in the Royal archives of Salamanca, of authentic documents, proving what has heretofore rested on vague tradition. The following extract is from a register kept by the Minister of the Marine:

"In 1542 Don Blasco de Garray, captain in the navy, (Capitaine de Vaisseau,) submitted to the examination of the Emperor Charles V. a machine moved by the steam of boiling water, by which ships, however large, could proceed on a calm sea without oars or sails. The Emperor ordered that a trial should be made, which took place in the Roads of Barcelona on the 17th of June, 1543, and succeeded perfectly. This experiment was tried with a vessel of 200 tons burden, named Santissima Trinidad, commanded by Captain Don Pedro de Learga, who had arrived at Barcelona with a cargo of wheat. The Emperor Charles V. and his son, afterwards Phillip II., Don Enrique de Toledo, the Governor Don Pedro de Cardona, the Grand Treasurer Ravago, the Vice Chancellor Don Francisco Gralla, a great number of other distinguished persons of Castile and Catalonia, and numbers of naval officers, some on shore and some on board the vessel, were present at the attempt. The Emperor, the Princes, and the other illustrious personages, were astonished at seeing the ease with which the machine moved the vessel; but the Grand Treasurer Ravago thought it right to advise that the invention should not be adopted in the vessels of the State, because, according to his opinion, the machine was too complicated, and would be too expensive, and there would be reason to fear an explosion of the boiler." "The special commission ordered to report on the experiment, confined themselves to stating, that a vessel moved by steam had first completed three leagues in two hours, and then a league in an hour, and that it could be made to move twice as swiftly as a common rowing galley. The Emperor did not pay any more attention to the invention of Don Blasco de Garray, but he presented him with 700,000 maravedis, and promised to raise him successively to the higest rank in the Spanish navy. The late M. Raynouard, of the Académie Française, has left among his papers a ballad in honour of Garray, which was sung in the streets of Barcelona in 1542."-Times. [All this we have seen before; it is of most plausible circumstantiality; but, nevertheless, until we have something better than the authority of an anonymous "letter from Madrid," for the existence of the "authentic document," said to exist in the Royal archives of Salamanca, and for the correctness of the version here given of them, we must take leave to consider the whole affair as but an ingenious fiction.-Ed. M. M.]

INTENDING PATENTEES may be supplied gratis with Instructions, by application (postpaid) to Messrs. J. C. Robertson and Co., 166, Fleet-street, by whom is kept the only COMPLETE REGISTRY OF PATENTS EXTANT from 1617 to the present time).