Lapas attēli
PDF
ePub
[blocks in formation]

to the temperature of the external air and sea, it took more than ten days in the tropics before the hold was heated again to the tropical standard.

VENTILATION OF MINES.

Sir, I have read the numerous important and interesting extracts in your valuable Magazine, from the evidence taken before the Parliamentary Committee, on accidents in mines, with some degree of attention; and perceive that the grand desideratum in the opinion of all parties examined, and others who have observed on the subject, is a better ventilation than has been hitherto effected.

*I notice, too, that the air-pump has been tried, though in what manner has not been stated in the details I have seen, but evidently without any important

result..

My present object is, therefore, now to suggest an application of the air-pump, in a manner which I think would be found to effect the object desired; viz. a complete ventilation of the most extensive mine.

The simplicity of my plan is such, that any person conversant with these matters will be immediately able to form a judgment of its practicability; and, although I have no practical knowledge of mining, I feel theoretically some degree of confidence that it will produce the desired effect.

My plan is this: on the top or the mouth of the shaft, over the most remote part of the mine, let a double-barrelled air-pump be erected, with a pipe of leather to descend to the bottom, and thence to that part which may be found contaminated with bad air. The end of the pipe, which may be eight or ten inches wide, should be left open, and kept distended throughout its whole length by small hoops at convenient distances. All apertures at the top of the shaft through which the pipe descends, should be closely stopped and made air-tight; and all others, wherever they may be found, except the principal shaft. By this means, when the pump is put in motion, the air in the immediate neighbourhood of the mouth of the pipe would necessarily be taken away through the pipe, and its place supplied by that surrounding it; and finally, the whole atmosphere

of the mine would be put in motion, and supplied with pure air from the mouth of the great shaft of the pit.

A double-barrelled pump might be proportioned to the extent of the mine; say each cylinder to contain 30 gallons, which would take out one hogshead at every stroke of the engine; and supposing it made 40 strokes in one minute, it would remove 2,400 hogsheads of air in one hour. This would be sufficient to keep the atmosphere of the pit perfectly salubrious. I think the working of the pump a few hours a day would be suffi cient for the purpose.

[ocr errors]

This contrivance is so simple, that it requires no further explanation; and if you will oblige me by giving it a place in your widely circulated Magazine, its merits, if it possess any, will soon be appreciated by those whom it may more immediately concern.

[ocr errors]
[merged small][merged small][ocr errors]

Sir, It appears to me a matter of surprise that none of your mathematical readers ever took notice (at least none have been published) of a question you inserted from me, in the 18th voluine, respecting circulating decimals. I am the more persuaded that the subject is altogether new and original, from the fact that, in most cases, some one of your readers is ever ready, sometimes too ready, to correct the unfortunate wight who, in full anticipation of the honours due to an inventor, has communicated to your pages a new discovery of something which the aforesaid readers can prove, or at least attempt to prove, is as old as the hills.

The question is as follows: "Given 3488372+ a part of a decimal circulating series, required the whole of the series and its equivalent vulgar fraction."

The solution of this question depends upon, as I have before observed, one among several newly-discovered, or rather observed, properties of circulating decimals: some of these I noticed prior to, and others just after, the appearance of a communication on the

subject in your 9th volume from Mr. Utting, which was followed by some others, the most interesting of which was a notice of the late H. Goodwin, Esq.

The property to which I allude is, that every decimal circulate is formed by a continuity of combined geometrical progressions, of every ratio from two upwards to one less than the denominator of the portion from which the series is produced. A knowledge of one of these ratios, which I have named the circular multiplier, or ratio, enables us to form the series in the shortest possible space of time, and by what may appear singular, beginning at the end: thus to find the decimal circulate of put down unity on the right hand, and multiply it by 3 (the circular multiplier for this series); place the product unit figure on the left of the 1, then multiply it by 3; and again place the unit's figure of the product to the left of the former figure: continue to repeat this operation until the figures recur, and the result will be the decimal circulate 0344827586 206890551724137931. To solve the

given question, multiply the part given by 2, 3, 4, 5, &c., until among the products some of the given figures are found to be repeated: these will generally be combined with some of the unknown part of the serie, which may therefore be united to the given part: this additional part being multiplied, will furnish more of the unknown figures of the series, and by continuing the operasition the recurrence of the same figures will show where the series is completed. If unity be divided by five or six figures loof the series, where it is decimally of the least value, the quotient will be the de ́nominator of the fraction; this denominator multiplied by five or six of the "given figures will give the numerator. In the present example, it will be found that when 3488372 is multiplied by 4 in the product 3953488, the first four figures are repeated, combined with 395.

The

part known will now be 3953488372: this, or rather the new part, multiplied by 194, adds three more figures to the series; viz. 581. Repeating the works we at last obtain 348837209302325581395. for the whole of the series where 0232 is of the least decimal value: therefore,

[blocks in formation]

In many examples the work may be facilitated, and considerably abridged, by the assistance of some other properties, particularly that one noticed by Mr. H. Goodwin; viz. that every decimal circulating series has a complementary part.

Although I have no doubt that the ratio of the circumference and diameter cannot be expressed by any finite number to one, yet as the two, considered separately, are of finite dimensions, they must be capable of being expressed by two finite numbers, which two numbers are the numerator and the denominator of the fraction equivalent in value to the decimal series expressing the ratio; this decimal series is already known as far as 132 places of figures; hence it appears to me probable, that by some of the newly observed properties of decimal circulating series, the whole of the series may be found, and from it the vulgar fraction equivalent thereto. Since, however, the decimal circulate of a fraction, whose denominator is a prime number, may consist of as many digits as the number expressed by the denominator less 1, the iminense number of figures in the series may present an almost insurmountable obstacle towards its attainment, without, however, affecting its possibility, if means can be devised for overcoming that difficulty.

Judging from what I have read upon the subject, it appears to have been very little studied, and if the attention of a few minds were directed to it, I feel assured that some very important results, as to the nature of the combination of numbers when multiplied by other numbers would be obtained, decimal numbers differing only from whole numbers in being decreasing instead of increasing series.

I am, Sir,
Yours respectfully,
ANTHONY PEACOCK.

January 20, 1836.

[blocks in formation]

+b: a.

1

b

1

::

b

:: a

Again, let us suppose that the engine and train had run a certain distance upon a level, so as to obtain a maximum speed, then if with this velocity they begin to ascend a plane of the above inclination, and if the steam could be brought up and maintained at such a pressure, that the pull exerted on the ascent should be to that on the level, as a + b: a, it would evidently follow that the initial velocity would be permanent during the whole ascent; but it is practically known that

this is not the case: for it is now a wellestablished fact, that an engine cannot exert the same pull at high velocities as it could do at lower velocities; or, as Mr. Robert Stephenson says, "at high velocities the steam does not act so efficiently upon the pistons as at lower velocities." This being granted, it follows that although the steam is brought up to the same pressure in heginning the ascent (with the maximum velocity), as that which would be required to move the load up the ascent from a state of rest, the velocity in the first case will gradually decrease until it becomes uniform; and this last acquired permanent velocity will be equal to the full speed obtained when starting from a state of rest.

In both cases the power exerted by the engine is supposed to be the same. This being premised, let S be the length of the ascent in miles, V the initial velocity in miles per hour, and the acquired permanent velocity, then § (V +v) will be the average variable velocity per mile an hour, from the beginning of the ascent to the place where the velocity becomes uniform, and § (} (V + v) +v)

=

V + 3y

4

will be the average velocity

per mile an hour over the whole ascent;

and S

V+3 v 4

4 S V+3 v

will be the

time in hours, or part of an hour, in moving up the whole ascent.

But to determine v, we must have recourse to an experiment, which, in this case, is easily done; suppose the time in moving up the ascent was observed to be h hours or part of an hour, then we have 4 S the equation h From which V+3 v

[blocks in formation]

Consequently (V+0)

[merged small][subsumed][ocr errors][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small][merged small]
[blocks in formation]

SAFETY OF LEAD PIPES PROTECTED BY TIN.

(Extract of a letter from Mr. G. Chilton, dated New-York, June 23, 1834.)

Dear Sir,-Observing, in a late number, a notice of Ewbank's patent tinned lead pipes, and having had many applications for information concerning the danger attending the use of metal pipes for conveying water, beer, cider, &c., 1 have been induced to subject the pipes of Ewbank to a few trials, for the purpose of ascertaining whether, from the occasional contact of acids, any deleterious solution of lead would attend their ordinary use. It is well known, that the common beer pump, with a leaden pipe, has frequently given to the liquor a dangerous impregnation, especially after remaining stagnant for a time, and the beer in a sour state. The substitution of block tin would remove the apprehension of danger, but its greater price offers a strong temptation to the use of lead. It appears to me that the lead tube lined with tin will answer the ends of cheapness, safety, and durability. I would therefore invite your attention to the following experiments, which, if you think them of any importance to the public, you may insert in your Journal. Experiments. Various portions of lead tube, coated, some with pure tin, and others with different alloys of tin and lead, were bent into the form of a semi-circle, and filled with vinegar of different degrees of strength. After standing, some a month, and others six weeks, with occasional disturbance, the

I observe that this poorest of mathematicians, but most dogmatic and arrogant of all living prigs, has, after being beaten to his utter confusion and disgrace, in the controversy of his own provoking in the Mechanics' Magazine, started a Journal of his own, in order that he may have all his own way, and be no more troubled with such inconvenient antagonists as truth, honesty, and commonsense. I cordially wish him in his new character and career all the success he deserves; and beg, at the same time, with equal cordiality, to congratulate the readers of the Mech. Mag, on a capital riddance.-I, M.

clear solutions were tested, first with sulphate of soda, and afterwards with bihydro-sulphuret of ammonia. The application of the first of these tests, namely sul, soda, produced no alteration in any of the solutions, from which it must be inferred that they contained no lead.

The application of the second test produced, as was anticipated, a brown precipitate of sulphuret of tin. In the same manner, two fresh pieces of tube were filled with a strong solution of common salt, which remained in contact for some time. The solutions when assayed with the same tests, showed that nothing but a little tin was dissolved.

It appears that in all these cases, which I regard as galvanic effects, the tin was the most oxidable metal, although, when not under the influence of polar arrangement and in the open air, lead appears to oxidiate sooner than tin. It is scarcely necessary to remind you that results similar to these were obtained thirty years ago by the celebrated Professor Proust, at Madrid, who undertook for the Spanish Government an extensive series of experiments on the different alloys of lead and tin, with the express view of determining whether the popular prejudices against the coating of copper vessels with an alloy of tin and lead, which is the common practice, was ill or well founded. Nothing can be more satisfactory than the conclusions he drew from his labours, namely, that as, in all his numerous experiments, neither lead nor copper were dissolved, there is little reason to fear the solution of lead from the tinning of our kitchen utensils. may just mention here, that I am in the habit of cleaning out my soda fountain every spring with dilute muriatic acid, which uniformly dissolves the oxide of tin without touching the copper, which I am persuaded will remain as securely as the sheathing copper in Sir Humphry Davy's great experiment, and for the American Journal of

same reason.

-

Science and Arts.

TUNNEL UNDER THE OHIO.

I

A writer in the Cincinnati Journal recommends the construction of a railroad under the Ohio river, opposite that city. The following is an outline of the plan :

The railway is to consist of two semiellipses, one above and the other under

16

TUNNEL UNder the oHIO.

neath. The height of the upper arch to be 10 feet, and the lower 3 feet, and 24 feet in width inside, making the ellipse 13 feet high and 24 feet wide in the clear. The arch to be composed of cut stone masonry 2 feet thick. This arch is to be buried in the ground just sufficient to protect it from the action of the river. A floor composed of timbers laid lengthwise, on the bottom of the arch, and covered with planks, forms the carriageways and side-walks. The carriageways to be each 8 feet wide, and the side-walks each 4 feet wide. The sidewalks are a little raised above the carriage-ways. The stones composing the arch are to be cut so as to form segments of the ellipses, and laid in hydraulic cement, and made as near water-tight as practicable. Notwithstanding all the care that may be taken in the construction, yet with a pressure, in time of high water, of 4,375lbs. upon each square foot of the arch, the water will percolate through in such quantities as to require an engine to keep the road dry. It will of course be necessary to light the interior when opened for travel.

Between high and low water marks, there is a difference at this place of about 63 feet, and allowing the top of the arch to be 7 feet below low water in the bed

of the river, and placing the bottom of the arch at each end, at high-water mark, will make the total descent 83 feet. It

is thought that 1 foot ascent in 12 feet horizontal distance is the greatest inclination the road will admit; consequently, the length of the inclined arch, from high-water mark to the bed of the river, will be about 1,000 feet; and allowing also that the bed of the river at low water is about 1,000 feet wide, will make the total length of the road 3,000 feet.

The only difficult point in executing the work will be in excavating the earth and rock below low water. It is quite practicable, however, in a dry season, at comparatively small expense, to enclose a space with a frame of timber and plank, made water-tight by placing bags of earth around the outside, aud pump out the water with an engine placed upon a flat boat, until theexcavation is completed and the arch formed within the space enclosed. Then by moving the same coffer dam its length farther along, another space can be enclosed, and the work completed in the same manner,`

[blocks in formation]

Total cost of 10 feet of the roadway....563 20 Which being multiplied by 300, for the length, will give 169,860 dollars for the total cost of the arch and flooring. If to the above we add the probable cost of pumping the water and excavating the earth and rock for the roadway, and of covering the arch over again 3 feet deep, it will make the total expense not less than 210,000 dollars. To which should be added 20,000 dollars for superintendence and expenses of the affairs of the company, &c. There can be no doubt that the stock in such an undertaking will yield a handsome profit.

It will be observed that a roadway, constructed upon the above plan, leaves the river entirely unobstructed; that the arch is completely out of the reach of injury from the river; that it is perma nent, solid, and will last for ever; and that it involves but a trifling expense to keep it in order for constant use.

Patents taken out with economy and despatch; Specifications, Disclaimers, and Amendments, prepared or revised; Caveats entered; and generally every Branch of Patent Business promptly transacted. Drawings of Machinery also executed by skilful assistants, on the shortest notice.

LONDON: Published by J. CUNNINGHAM, at the Mechanics' Magazine Office, No. 6, Peterborough-court, between 135 and 136, Fleet-street. Agent for the American Edition, Mr. O. RICH, 12, Red Lion.square. Sold by G. W. M. REYNOLDS, Proprietor of the French, English, and American Library, 55, Rue Neuve, Saint Augustin, Paris.

CUNNINGHAM and SALMON, Printers,
Fleet-street.

« iepriekšējāTurpināt »