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CIRCULATING DECIMALS.

and bringing down double the quantity of an area, but I should not call that longgas.” If it brought down six times the work ; that is, stall and pillar work. I quantity of gas, a proper well-managed have seen walls of coal worked 400 or quantity of air continually kept in mo- 500 yards in length. Does Mr. Mitcheson tion round long-work, would have swept think the northern stone roofs would fall it away. But the yard or Bensham in that length behind him ? I know they coal should be worked before the next would, though I also know that a rock under it.

roof is not ihe best roof for long-work. I should very much like to know how The first sinking that takes place in longMr. Buddle's long-work was began; upon work, after a sufficient quantity of coal what plan it was opened; how wide and is taken from under, to allow the strata to long it was when it grinded the coal to settle down, if the roof is very strong, powder; whether the roof broke down shale or rock, often causes great confusion, at all behind him before he gave it up? and a novice in the trade would be soon I say nothing of the mode of working inclined to abandon ii. But an old longthe thick coal in Staffordshire that is worker knows how to manage the weight not long-work ; one thing only I would to his own advantage, ever after, in workobserve,-some of the boys employed ing the mine.' Why did not ihe Comnow on that magnificent vein of coal will mittee procure the opinions of some be rummaging it over again for what is Shropshire long-workers? In that district left behind by their present mode of the system of coal-getting is wholly longworking it. Mr. Buddle, speaking of the work, whether the roof be stone, clunch Bensham seain of coal, says, “ I found it clay, or even sand ! prodigiously fiery, so much so, that the

I a am, your obliged servant, coal itself afforded gas enough to light

THOMAS DEAKIN. the pit. I drilled a hole into

Blaenavon, May 5, 1836. the coal, and stuck a tin pipe into it, and lighied it, and I had immediately a gas. light.” Now, sir, that proves nothing at all extraordinary, because I have seen Sir,– Your correspondent, G. C. L., p. much greater intimations of fierceness 43, is somewhat hasty in his assertion, than that, and the mine as sweet and

that I have taken but a partial view of clean of gas, at the time, as a house. I the question I proposed and answered, on have seen oftentimes, when the colliers circulating decimals. have been making a cutting across the

The rule I gave may be applied geneseam about six or seyen inches wide and rally, though in some cases it requires a three feet into the solid coal, a lighted knowledge of several properties of circandle has been put into the cutting, and culates, some of which I referred to in the gas would ignite immediately and fill my former communication.

The ex the cutting with flame, which would fre- ample attempted to be worked by G.C. L. quently keep burning till it was brushed may be considered as one case of the rule, out. No one in the mine cared a fig for aud that proposed by me as another, such incidents as this, because they knew though this is almost a distinction with. a current of air was passing along the

out a difference ; for, in his example, the face of the work, which would not suffer

1 the flame to come out of the cutting.

denominator of the decimal is

0584 + Mr. G. Mitcheson, on being asked if he thought the principle of long-work

17, as found by him and the numerator, could be applied to the northern collieries,

38235+

=6}: hence, the fraction is said, that " in many places in the North 05882+ they had a post or stone roof that would

61 13 stand forty or fifty yards upon an area ;

The attempt to find the denohe did not think that long-work could at

17 all be practised there, for it would never minator hy the part next in value, rebreak down behind them, and there would minds me of the school-boy, who, if he be ten times more space for foul air than obtain the "answer,” heeds not how it there is now."

has been procured. According to this witness the stone In order to avoid complex fractions, roof will stand forty or fifty yards upon if, by the first part of the rule, it is found

34

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that the decimal is a mixed circulate, the given part may be multiplied by that power of 2, the index of which is the number of terminate figures ; this product, divided by the part of the least value, will give the numerator and the denominator found by the rule, being multiplied by the same power of 2, will give the required denominator.

It is with regret that I am forced to observe, that your correspondent does not appear to have sufficiently considered the subject; in the second paragraph he says,

“ if we take any numerator for the

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fraction we shall always find the same 43'

culate of the figures, and the other figures constantly recur.”. This is not tig, a mixed circulate of 17 figures, in

which t is a terminate number prefixed correct, the circulates of consists of two

43

to
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the part therefore forming the cirseries, of 21 figures each, hence •0232, &c. does not recur in every multiple of

culate does recur with every multiplier. the same, as may be readily seen by try

Having adopted an original method ing it with either 2, 3, 5, 7, 8, 12, 15,

for exhibiting the circulates of any frac&c. the products of which will be a series

tion, which affords, a ready means for complementary to .0232, &c. The same

examining their several properties, I subfigures can only recur by every multiple join the circulates of when the number of figures in the series

as an example. 34

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34ths.

1 | 27 | 15 | 31 | 21 | 23 | 9 | 5 | 33 | 7 | 19 | 3 | 13 | 11 | 25 | 29
01 7| 4 9 61 6 2 1 9 21 5101 3

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1 | 10 | 15 | 14 | 4 | 6 | 9 | 5 | 16 | 7 | 2 | 3 | 13 | 11 | 8 | 12

17ths.

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In these tables the upper lines are the which is m-1; and this always happens numerators, or successive remainder, in when m is a prime number, or any other findiug the circulate by the common me- number not divisible by 2, 2n, 5, 5n. thod; and the bottom lines the circulat. ing series. The middle line is the ter

a

For example: forms one series of 6 fiminate figures; these arise from all

7 fractions whose denominators are divisi. ble by 2, 24, 5, 5n, and they possess the gures,

four series of 13 figures, 53'

69 same property as the series, viz. half being complements to 9 with the other

three series of 22 figures, and two of 1 half. By the arrangement, the com

figure. When m is divisible by 2 or 5, menciug figure of the series is placed

one added to the number of figures that under its respective numerator.

circulate, completes the amount m-1.

All the circulates formed from any a When is exhibited in the form of a denominator m, as above, are multiples

of each other; consequently, if in the circulating decimal, a series of figures application of the first part of my rule equal to m-1 is either produced, or two the series are found to recur without emor more series, the sum of the figures in bracing every figure produced by the

m

m

year old.

MORDAN AND co's NEW PATENT PEN.

111

maker, 11, Leathersellers' Buildings, multiplication, the fraction will con.

London Wall, answering precisely to the

subject of the present comment. The sist of more than one series, each of

hardship of individuals losing their ins which must be found either wholly, or in

ventions, through an incapability of as, part, to discover where the series is of

certaining what had been before invented ihe least value decimally.

and privately made use of, has been al. I have not had time to investigate the

together removed by the alterations in rulės given by G.C.L., which may be

the law of patents; the public, however, correct, though the first one, upon which

have a just right to benefit by the over, the others depend, has an inconsistency

sight of patentees where the opportunity in its expression; for if .999, ad infini

exists of information. It is a matter of tum, is to be divided by the given num

surprise that 'gentlemen so long in the ber, there cannot be a last reinainder :

field of invention, and bona fide manu. he probably means that the division is to

facturers into the bargain, as Messrs. Mor, be made until the figures recur; if so, it

dan and Co., should have put theinselves is fortunate for him that the answer to my

to the expense of attempting to secure question, which he has chosen to illustrate

what appears to be nearly, if not quite, a

15 his rule, happened to be = to the re

43

Sir, your obedient servant,

SCRUTATOR (pro bono publico). 14 2

+ else the division 5 30'

HANCOCK'S STEAM-CARRIAGES. might have extended almost ad infinitum.

Mr. Hancock still continues to run his To your mathematical readers, I would

steam-carriages on the Paddington-road suggest the following subject of investigation since the numerators, and like- with uninterrupted success. No accidents wise the series, follow a law of progress

have happened, nor any derangement of sion, rules remain to be discovered for the machinery, unless the breaking of a finding the value of any term, the nature

chain pulley may be so called, which was of the ratio, the place of the term, &c.

immediately replaced by another. The These inquiries, if investigated, would

" Infant," which Mr. H. yesterday (Friopen a most extended field for analytical day) brought from Stratford, for the purdiscovery.

pose of working on the Paddington-road, Yours respectfully,

is the first steam-carriage that ever ran ANTHONY Peacock.

for hire, which it did on the same road April 30, 1836.

about six years ago, and a fortnight before Sir Charles Dance commenced

running on the Cheltenham-road with MORDAN AND Co.'s New PATENT PEN.

Mr. Gurney's drag. The “ Infant" seems Sir,

It is a great pity that patent spe- in excellent condition, and apparently culators, before patenting a thing, do not not any the worse for the occasional give themselves the trouble to ascertain working it has had since its birth. whether a similar production to it has The rate of travelling during this week been, in any shape whaiever, previously

has been about the same as last; averagbefore the public. The want of this very ing one hour and ten minutes from the pecessary precaution exhibits itself in the

City to Paddington and back, a distance instance of the three-nibbed metallic of nine miles. Of this time upwards of pen, advertised in different journals, and one-fourth is consumed in stoppages for exbibited (per engraved card) in various coke, water, and

passengers. From Monstationers' windows, as a recent patent of day morning, 10 Thursday 12 o'clock, sixMessrs. Mordan and Co.

teen single trips to Paddington were perAt p. 31 of a pamphlet on metallic formed, and forty-six to Islington. The pens, by J. Carstairs, * 'will be found the

number of passengers carried was 711. description of a metal pen, the invention We understand the carriages will conof a Mr. James Gowland, chronometer. tinue to run daily, in the morning from

9 to 12, and in the afternoon from 3 to 6 • Simpkin, Marshall, and Co. 1835.

o'clock.

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able labour were able to strike through some cover. ings of fint, when they discovered a vein of ore, almost pure lead, and in three days have not raised less than three tons, worth 201. a-ton. It is expected, without exaggeration, that for six months to come they will gain 1001. a.week by their own manual labour, exclusive of the tribute payable to the proprietors; but fears are entertained that their good fortune inay cause the death of some of them from over exertion, as they are not to have any assistance. Botstone within balf a mile of the famed Ecton mine, from which the Duke of De. vonshire amassed so large a fortune; and what is very singular, these three men have been working at the first-named mine near one year, earning not more than 12s. each a week, and have frequently blasted within a yard of the place where the treasure has been discovered. The face of the vein is not six yards from the surface.-Stafford Paper.

Mr. Thomas Sheriff, Westbarns, East Lothian, has invented a plough, for which he has been awarded a premium of tive guineas by the East Lothian Society. The property of this implement is to cultivate the subsoil, in opposition to the system of trenching, which was lately introduced into East Lothian, and the tendency of which was to turn down the rich vegetable mould, and raise up the subsoil, in many, nay, in most cases, always the inferior, Íts construction is simple, and every common plough can be coaverted into a subsoil plough at pleasure, and at a trilling expense.

It is only calculated to operate successfully on a subsoil whioh does not afford much resistance; but a plough bas been invented in Stirlingshire, which, with a proper application of strength, will culti.vate the most stubborn clay subsoil that exists.Farmers' Magazine.

Communications received from A SubscriberMr. R. Roberts-Mr. Lunt.

An Old Subscriber" is informed, that we are always willing to publish the particulars of useful inventions without payment. His order on town for cash has been destroyed.

Errata.- In a few impressions of our last Num. ber, p. 95, col. 2, line 8 froin bottom, for “ 11,” read "9,"-and line 6 from bottom, for“ 11," read “ 12."

The Supplement to Vol. XXIV., containing Ti. tle, Contents, Index, &c., and embellished with a Portrait of Mr. Walter Hancock, C.E., is now published, price 6d. Also the Volume complete in boards, price 98. 6d.

NOTES AND NOTICES.

Preservation of Animal Substances.-A pamphlet published at Florence gives an account of a strange discovery by Geralamo Legato, the accuracy of which is attested by the principal professors in that city. It appears that Legato, while traversing the des sis of Africa in 1820, for the purpose of per. fecting a map, discovered in one of the hollows which a whirlwind bad ploughed up, a completely charred human body, the flesh and bones of which were in goud preservation. It struck him that the process of charring could only be effected by the scorching sand, and that if the heat of the sand bad in this instance effected the completo disicca. tion and carbonization of animal substances, it might be possible to effect something similar by artificial means. On his return to Italy, he commenced bis experiments, and at length succeeded in imparting to the limbs and bodies of animals solidity, and indestructible durability. By this, whole bodies, as well as individual parts, acquire a thoroughly firm consistence, which is more decided according as the respective parts are harder or softer. The skins, muscle, nerves, veins, fat, blood, all undergo this change without its being necessary to remove the intestines, which assume the same consistence. At the same time the colonr, form, and character, in general, remain un changed ; no smell is perceptible, and both joints and limbs remain tiexible and moveable as when alive. When bodies have acquired this consistency, neither damp air, moths, nor water can effect them. The weight is but slightly diminished. Not a hair is lost; on the contrary, they are rooted more firmly than ever. Birds and fishes lose neither skins, scales, nor colours, and in like manner insects and worms remain perfect in every respect. Legato's cabinet contains many specimens of this novel and singnlar discovery. One of the most re. markable is a table composed of 214 pieces joined to. gether. The observer would take them for so many different kinds of stone, and yet they are nothing moye than portions of the human members.Scotsman.

Colossus Redivivus.-An Englishman has lately erected on the banks of the river Theiss, in Hungary, a mill in the form of a colossal man. The head is the dwelling-house, the eyes serving for windows, and the nose for a double chimney. The machinery is placed in the body, and set in motion by a stream of water from a canal in the form of an immense bottle, which the monster is emptying into his mouth.-Times. How is the water raised into the botile?-Q.

New Percussion Gun.—The Wirtemburg papers occupy themselves much about experiments made with a percussion gun, of the inven'ion of Duke Henry, by means of which an able soldier can fire eight or ten shots in a minute.

Wonders of Mechanism.—The Hague Journal states, that a Dutch artilleryman, named Vander Boll, having 1 st both hi. arms below the elbow, by an explosion, the sculptor, J. F. Freit, of Flushing, has contrived and executed for him two artificial fore arms and hands, with which he can feed himself, put on his clothes, perform all other ordinary offices, and even write.(?) The poor man was also deprived of one of his eyes, but for this we suppose no substitute can be found ! - Guernsey Star.

Sampson Twigg and Co., a firm of three labour. ing men, obtained permission to work in a mine at Botstone, in this county, the property of Messrs. Gaunt and Challinor, of Leek, and to take the minerals, subject to a certain tribute to the proprietors, for six months to come. The mine is at the bottom of a stupendous mountain. The men began at the bottom of the hill, and alter consider.

Patents taken out with econoiny and de. spatch ; Specifications, Disclaimers, and Amende ments, 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, Peterbo-
rough-court, between 135 and 136, Fleet-street.
Agent for the American Edition. Mr. O. Ricu,
12, Red Lion-square. Sold by G. W. M. RaY.
NOLDS, Proprietor of the French, English, and
American Library, 55, Rue Neuve, Saint
Angustin, Paris.
CUNNINGHAM and SALMON, Printers,

Fleet-street.

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