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WATCH-GLASS MICROSCOPE.

393

a person whose views were so judicious, riage, rests on springs, and that proand bis mechanical resources so consi- visiou has been made for stopping or derable. There are a number of con- retarding the motion of the machine trivances, some of them very inge- by an invention (not new), the technious, of a secondary nature, which we nical name of which we do not know, have not alluded to. But in looking but which we would call a friction hoop, back over our account, we find we have clasping the rim of a wheel. It opeomitted to mention that the whole ap- rates very effectually.” paratus, as well as the body of the car

WATCH-GLASS MICROSCÓP E.

Sir-Some years ago, I joined For the purpose of holding objects two small Watch-Glasses, of the to be examined, I place a brass pin, same diameter, in a bason of water, turning on a hinge, in the manner by pressing their edges together with represented, on one side of the frame, my finger and thuml), so as to fill and a forceps, with screw, on the them completely. When taken out, other, both of such a length as to set I was then in possession of a single exactly to the focus of the lens. microscope, whose focal length being There is a groove on each side of the 3-16ths of the distance of distinct frame to receive the pin and forceps vision, magnified the surface of an when not used. One principal ohobject 25 times. It then occurred ject ought to be, to make the frame to me, that two such glasses ce- sufficiently thick to protect the conmented together, leaving a small vexity of the glass--a small shagreen aperture to fill them up with pure case would secure the whole. spirit, and cased in a small frame similar to the drawing, would form an

Sir, instrument simple in construction,

Yours respectfully, and excellent as a pocket companion, for the examination of minute ob

Thos. HENRY Bell, jeets, such as plants, insects, &c. Alnwick,

I am,

WORK OF STEAM-ENGINES IN CORNWALL.

From a Return of the Work performed by Fifty-nine Steam-Engines employed in the Cornish Mines, for July, 1825, it appears that six of them accomplished as follows :

Pounds listed one foot Engine and diameter of the high, by consuming Names of the Mines.

Cylinder.

a bushel of coal.

Remarks.

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ADVANTAGE OF THE DOUBLE

CYLINDER STEAM-ENGINE.

Let us proceed, and suppose, without entering into minute detail, that

we have a single (or double) engine [We have already inserted, p. 295, capacities of the cylinders being as

on Woolf's principle, the relative vol. iv., an answer to the inquiry on

1 to 5 (which cylinders we will dethis subject; we select from several

signate by a and b); we raise the other answers the two following, which furnish some useful explana- of 50lb. per square inch; let us

steam in the boiler to the pressure tions.-Edit.]

blow through, and then apply it to

the top of a, whilst, at the same Sir,--Having observed a letter in time, the valves at the bottom of u, a late Number of your Publication, and top of b, are opened; the steam requiring information relative to the which was below the piston of u advantage of applying Steam on rushes into the space above the pisWoolf's principle, and calling on ton of b, and expanding itself into any of “the first engineers” for as- five times the space it previously ocsistance, allow nae, through the same cupied, is, of course, reduced to medium, to attempt a reply. Al. 10lb. per square inch, which acts though I by no means lay claim to with equal force on the top of b and the above rank, “ mine being the bottom of a; therefore the effective last of all the families of Benjamin, force of the steam on the pistons and I the youngest in my father's may be stated at 50 - 101b = 40lb. house,” I contemplate little difficulty on 'd, and 10lb. on b, by which it is in convincing our friend F.J-k-n, very evident, that a great addition of that an absolute advantage is derived power is derived from raising steam by such application, which may be to a high temperature in the boiler, clearly demonstrated by practice or and employing it in that state before theory, mechanics or mathematics. reducing it to a common pressure.

inch;

NEW IMPERIAL MEASURE.

395 Whatever

may

be said of the prin: piston, on account of its having 90 ciple, facts are stubborn things; by square inches more to act upon. facts it may be, and is, clearly de- I believe these engines work with monstrated in almost every case in steam, first, upon the high pressure which this plan has been adopted, piston, at a pressure of about 50lbs. and I feel assured this engine only upon the

square

and the first requires to be fully known for its action of the 'steam upon the low more general adoption; reflecting pressure piston will be nearly of the as it does, infinite credit on the in- same impetus—I say, the first action, yentor, who, with mighty strides, because the pressure will vary as has trod the paths of science, admi- room is made for it to expand, by rably improved this invaluable as- the ascent or descent of the low sistant, and given to the world the pressure piston. When it has exefforts of his genius.

panded into the whole length of the Yours truly,

large cylinder, it is by that means L’AMI DES MACHINES-A-VAPEUR,

brought down to an ordinary pressure, say five or six pounds, upon the

square inch (a proper temperature SIR.-In your instructive Maga

for condensation), which next takes zine, Number 100, a Correspondent place, and a vacuum produced, on requests information relative to

the same principle as in a Watt's Woolf and Edwards's Steam En- engine, by which a further gain of gines. The writer asks how the

Olbs. upon every square inch of the

low steam, after leaving the high pressure piston is effected, by pressure cylinder, gains its

working the steam over again.

power to act on the low pressure one ?

If you think the above will have and further,” Will not the steam

any tendency to settle the controserving the high pressure cylinder

versy between your Westminsterhave as much power to resist the re- bridge-road Correspondent and his turn of the high pressure piston, as

fellow-workmen, your giving it a it will to give action to the low

place in your useful miscellany will

oblige, pressure piston ?

Your obedient servant, I answer, if the two cylinders were of the same diameter, the fact

EDMUND FEARNLEY. would undoubtedly be as it has al- Shipley, near Bradford, Yorkshire. ways appeared to your Correspondent. But this is not the case. In these engines there are advantages, in having the low pressure cylinder eight or ten times the area of the high pressure one. When the steam leaves the high pressure cylinder, it acts with equal force upon the low pressure piston; but there will be a gain of power upon the latter, on account of its additional area.

Let us, for example, suppose two cylinders ; the high pressure one 10 inches area, and the low pressure one

Sir, I beg to offer a shorter solu

tion of T. H.'s problem than your Cor100 inches area; the steam leaving the high pressure cylinder of 18 respondent, Mr. Lake.

Lets solid required, inches, is made to act upon the low

Rr, the greater and less radii of pressure piston of 100 inches; and

frustrum, though there is the same resistance

FE = h, GF a, and LDGE against the former as there is action

e. upon the latter, yet it is evident, on

= 2 . tai. O is equation to well-known principles, there will be generating line GD; but, by Differenagain of power upon the low pressure tial Calculus, any solid of revolution

NEW IMPERIAL MEASURE.

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B.

Now y

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S

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Now =

horse power.

#sy dx (o = circumference of circle). either for my own convenience or that By substitution, solid=". tan. 8 s x , of my friends, by which the labour integrating between sc= a and sc= of calculations, oiten recurring, was a the

greatly abridged, or the operation put a + 13 a3 within the reach of such as were but tan. 0.

3

little accustomed to apply mathema3 a2 h +3 ah + 13

tical investigations to mechanical prin* . tan. 0. 3

ciples. Some of these, which I have

ofien found useful, and which at preNow we have a: ath ::r:R.. a :

hr

sent recur to my remembrance, I shall h :: pr: R

and tan. 6 subjoin, that, if you think them of sufR-r

ficient importance to deserve a place R-1 .. tan. o ; and, by re

in your Magazine, they may, through

that medium, be transmitted to your (R2 + Rr +92) 1 very numerous class of readers. duction, s =

3

Ist. To find an equivalent for the 3 nearly, and s = (R? +Rr power of a steam-engine, expressed in +R), &c. vearly.

The above being worked from first Let a horse power be equal to 200 principles is, I think, more satisfactory pounds, raised at the rate of 2} miles than the former proof.

per hour, as laid down by writers on I am, Sir,

that subject. Yours respectfully,

Let a low-pressure engine, with a A TINMAN. Joad of 10 pounds to the inch, work at

the rate of il strokes per ininute,

8 feet stroke. Then multiply the dia. STEAM-ENGINE RULES.

meter of the piston by its circumference, and ent off two figures from the

right band of the product, we have the (To the Editor of the DicchanicsMayazine.) number of horses' power exactly.

Example.—Let the diameter of the Respected Friend ,-1 have been much cylinder be 28 inches, then will the gratified by the perusal of your useful circumference be £8 inches nearly, and publication, but have received greater

28 x 88 = 2464; whence the engine pleasure from no circumstance con- equals 24. horses' power. nected with it, than from that noble If the engine be supposed to move disinterestedness with which men of with the load of 10 pounds to the inch, the same profession communicate their at the rate of 200 feet per minute, find knowledge to each other. No sooner the power, as before, and increase it by does a mechanic make known his ig- 1-7th part of itself ; thus, 24.64 + norance of any particular subject, and 24.64

28.16, equal 28 horses' power. express his desire to be informed, than 7 generally there are several of his bro- If the engine work at the rate of ther mechanics willing, and often 220 feet per ininute with the same load, eager, to give him the information

find the power as at first, and increase which he requests. I should question

24.64 if another instance could be found of it by À part ; thus, 24.64 + men so ready to possess their goods in 30.7, equal 30% horses' power nearly. common, losing sight of all emolument

2nd. To find the load, on the square and fame, and influenced by the pure inch, of an engine employed iu pumpmotive of benefitting those who are but ing water. too often considered and treated as

Divide 5 times the diameter of the rivals in trade.

pump by 4 times the diameter of the In my youth I took great delight in mechanical and mathematical studies ; multiply by 5, and divide by 3 (or

cylinder; square the quotient, and and although I have, for many years, ceased to be a mechanic by profession, the pounds avoirdupois on each square

annex a cipher, and divide by 6), gives I well remember the pleasure with

inch of the piston for every fathom which I imparted whatever I had met deep, exactly. with in books, acquired by study, or struck out hy my own juvention, to all draw a 10-inch bucket 50 fathoms,

Example.—Let a 40-ioch cylinder why 'showed themselves desirous of

deep. being made partakers of what I considered a treasure. In those days I

10 x 52

Here contrived many simple and easy rules,

= 102760413 lbs.

3 O X4

X

ON THE FRICTION OF CORDS.

397

7.5

which, being multiplied by the depth, 17.5 gives 8.138, &c. pounds to the inch.

14.815, &c. a constant equiva

2 3rd. To estimate the power of an

valent force. engine working expansively.

Example 2.-Let the steam in a highAdd 1 to the hyperbolic logarithm of pressure engine equal 5 atmospheres the number of times to which the steam

(say 75 pounds to the inch); length of

stroke 5 feet; steam shut out after the is expanded; multiply by the force of the steam, and divide by the number of piston hai moved 8 inches.

Here 60:8 = 7.5. times to which the steam is expanded,

75 gives an equivalent force, which, act- And 1 + 2.0149 x =30.149 pounds, ing uniformly throughout the whole stroke, will produce the same effect.

or a constant force of two atmospheres.

N.B. If the steam be let off without Example 1.-Let the force of the condensation, there must be 15 pounds steam first admitted be 171 pounds to to the inch deducted from the equithe inch, and be shut out at the middle valent constant force, for the resistance of the stroke. Then I +6931472 x of the atmospheres.

Hyperbolic Logarithms.
No.
No.
No.

No.
1 0.00000
1.25 .2231435| 34 1.1786549 54 1.6582280 74 1.9810014
1.5 .4054651|| 33 1.2527629 57 1.7047481.71 2.0149030
1.75 .5596157||.3 1.3217558 51 1.7491998|| 7. 2.0476928
2 .6931472| 4 1.3862943 1.7917594|| 8 2.0794415
24 .8109302|| 4+ 1.446918:3 64 1.8325814|| 8.1 2.1400661
25 .9162997|| 44 1.5040774 67 1.8718021 9.2.1972245
23 1.0116008|| 45 1.5581446 61 1.9095425 9.2 2.2512917

3 11.0986123|| 5° 11.6094379|| 7 |1.9459101||10 12.3025851 N.B. The sum of any two or more These rules I have, very many times, logarithms is equal to the logarithin found useful, and to know that they of the product or rectangle of their were rendered equally serviceable to respective numbers, thus, 6931472 + others, would confer a pleasure on 1.7047481=2.3978953, which is the lo- your friend, garithm of twice 5, or 11.

J-L4th. To find the weight of a hollow Ichthyotrophia, 9th Month, 1825. cast-iron cylinder.

To the inside diameter, in inches, add the thickness of metal in inches; multiply by the thickness of metal in

ON THE FRICTION OF CORDS. inches, and hy nine times the length in feet, or three quarters the leugth in Sir, – Professor Leslie, of Edininches; the product (cutting off two burgh, in his work entitled Elements figures from the right handi) will be of Natural Philosophy, page 212, un the weight in cwts., reckoning the the Friction of Cords, says, “If the specific gravity of cast iron to he 7.4. weight balanced a traction of 4 lbs. at

The same rule will also serve for a the end of a semicircumference, it circular plate, considering it has a cy:

would balance 16 lbs. at a complete linder whose insi:le diameter is 0, and circumvolution. length the thickness of the plate. At the end of two turns,. 256 lbs. Example 1.-Required the weight of

three do. 4096 lbs. a pump il inches diameter within,

four do. 65536 lbs. Swe:"" thickness of an inch, length 8 fret.

These conclusions are drawn from Here 11 +.75 x .75 x 8 x 9 = 634.5 ;

theoretical investigation, it is to be whence the weight = 6.345 cwt.

presumed; but, as no theory is entitled Example 2.-Required the weight of

to full credit until it has stood the test a cast-iron circular plate, 6 feet dia

of experiment, I shall take the liberty meter, and 5 inches thick.

of stating the results of some experiHere, internal diameter = 6, thick

ments on this subject, for the purpose ness of metal 36 inches, length = 5

of correcting the conclusions above inches.

quoted, and to prevent practical meThen (+36 x 36 x 5 x = 4860, and chanics' from being misled by such the weight = 48.6 cwts,

high authority.

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