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 inch; 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, ventor, 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

JOlbs. upon every square inch of the steam, after leaving the high

low pressure piston is effected, by pressure cylinder, gains its power

working the steam over again. 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 pressure piston ?

oblige, I answer, if the two cylinders

Your obedient servant, 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

NEW IMPERIAL MEASURE. 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


----E. 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,-1 beg to offer a shorter solu. 100 inches area; the steam

tion of T. H.'s problem than your Corleaving

respondent, Mr. Lake. the high pressure cylinder of 10

Let s = 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

= 0. upon the latter, yet it is evident, on Now y = x . tao. 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 =.

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. tan. 0.


duction, s =


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

greatly abridged, or the operation put

a + h3 - a3 within the reach of such as were but · s'= g. tan. 0. 3 = little accustonied to apply mathema- ;

tical investigations to mechanical prin*. tan. 3 a? h +3 ah + 13

ciples. Some of these, which I have Now we have a: ath ::r:R.. a :

often found useful, and which at pre

sent recur to my remembrance, I shall

hr h :: r: R-pi. a= " , and tan. 6 subjoin, that, if you think them of suf

ficient importance to deserve a place :. tan. 0 = "-"; and, by re

in your Magazine, they may, through

that medium, be transmitted to your . (RP+R r + 2) l very numerous class of readers.;

Ist. To find an equivalent for the Now a = 3 nearly, and s = (R2 + Rr power of a steam-engine, expressed in + R), &c. vearly.

horse power. 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 . lain, 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 circumfereuce, and ent off two figures from the

right band of the product, we have the (To the Editor of the Mcchanics' Magazine.) 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 88 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 { part ; thus, 24.64 + – men so ready to possess their goods in 30.7, equal 303 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 piathematical studies ; multiply by 5, and divide by 3 (or

cylinder; square the quotient, and and although I have, for many years, annex a cipher, and divide by 6), gives ceased to be a mechanic by profession, the pounds avoirdupois on each square 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 Example. -Let a 40-inch cylinder struck out hy my own invention, to all draw a 10-inch bucket 50 fathoms who 'showed themselves desirous of deep. being made partakers of what I considered a treasure. In those days I

10 x 5 2 5. contrived many simple and easy rules,

hers 7x4 * 3 = 102760417 os.



397 which, being multiplied by the depth, 17.5 = 14.815, &c. a constant equivagives 8.138, &c. pounds to the inch.

3rd. To estimate the power of an valent force. engine working expansively.

Example 2.-Let the steam in a highAdd I to the hyperbolic logarithm of pressure engine equal 5 atmospheres

(say 75 pounds to the inch); length of the number of times to which the steam

stroke 5 feet; steam shut out after the is expanded; multiply by the force of

piston had moved 8 inches. the steam, and divide by the number of times to which the steain is expanded,

Here 60:8 = 7.5. 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 1+.6931472 % of the atmospheres.


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Hyperbolic Logarithms.
No. 1
No. 1

No. 1
1.25 .2231435. 37 1.1786549 54 11.6582280| 74 1.9810014

405465 11 31 11.2527629.| 51 11.7047481|| 71 12.0149030
1.75 .5596157|| 33 1.3217558 1.7491998 75 2.0476928

.6931472 4 1.38629431 6 11.7917594|| 3 2.0794415
.8109302 44 1.446918:3|64 1.8325814 8-1 2.1400661

,9162907 47 1.5040774 61 1.8718021) 9 2.1972245
23 1.0116008|| 45 1.5581446 63 1.9095425 9 2.2512917

3 1.09861231 5 11.6094379|| 7 1.9459101110 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-L-. 4th. 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 inches, and hy nine times the length in

ON THE FRICTION OF CORDS. 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 insiile 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 iucbes diameter within,

four do. 65536 lbs. Swa:"" thickness of an inch, length 8 feet.

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 Erample 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.

...........14 lbs.

6 lbs.

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Ist. I took a cord of 392 feet to the 8th. I then applied the line used in es, pound, to which I attached a weight of periment 2nd to a glass cylinder of four. one pound, and applied it to a cylinder inches diameter, loaded with the same of dry ash-wood, turned in a lathe constant weight of one pound, and 1.75 inches diameter, and ascertained found the traction, the force of traction necessary to raise At half a turn .... this single pound weight, and found, one and a half ..... when the cord was in contact with half two and a half ......... ..9 the circumference of the cylinder, the From the above experiments, when force required was............ 2 lbs. due allowance is made for the stiffness at one and a half turns..

of the cord, and for the weight of so at two and a half....

much of the cord as necessarily formed at three and a half............66 part of the load to be raised, it will, I

2nd. I then tried, upon the same ash trust, not be difficult to see that the cylinder, another line, very Aexible, of resistance may be considered as in92 feet to the pound, loaded with one creasing as the second power or square pound, as before, and the force of trac- of the number of turos, and not accordtion observed was, .

ing to the high power assumed by At half a turn................24 lbs. Professor Leslie. one and a half turns ......10

I am, Sir, two and a half ..........30

Your obedient servant, three and a half ..........83

B. Bevan. 3rd. I next took the line of 92 feet to the pound, loaded with oue pound, upon a cylinder of cast iron, rough

WHY DOES A RAZOR CUT BETTER from the foundry, of 4.5 inches dia

AFTER BEING DIPPED IN HOT meter, and found the traction to be, At half a turn....

WATER? one and a half ............98 4th. Applied the same line to a cy.

[We insert the following letter, rather linder of cast iron, turned but not

for the purpose of inviting discuspolished, of one inch diameter, and sion on the subject of which it treats, found the traction to be,

than as approving entirely of the exat half a turn................ 24 lbs.

planations given by the writer. Some one and a half ......

of his inferences, we think, will be two and a half ............23

found illogical, at least.-EDIT.] three and a half..........56 5th. Upon the same cylinder I tried Sir,-In answer to your Corresponda new stiff cord of 114 feet to the pound, ent's (Novaculus) question, "Why and found the traction,

does a razor cut better after it has been At half a turn....

., 2 lbs. dipped in hot water?" In general one and a half ..

... 6

terms, I would say, that as a sheet of two and a half ....

sand-paper is cut by a pair of scissars three and a half ...

with greater difficulty than a sheet of 6th. My next experiment was upon similar paper, but not sanded. The

razor, before being dipped, has obstruca glass cyliuder, of 10 inches diame tions in itself to overcome, but which ter, with the above-named flexible line

become removed by the water. This of 92 feet to the pound, and found the

opinion is the necessary conclusion to

be drawn from the fact, namely, that traction,

fire causes bodies to suffer loss of eleAt halt a turn................13 lbs.

mentary matter universally, and com. one and a half ......

municates nothing whatever to them. two and a half............53

In order to illustrate the case, it is three and a halt..

necessary to divide it into two parts, 7th. Upon a glass cylinder of .95 viz. first, as respects fire being hot; inches diameter (as in experiment 6th), secondly, as to whether fire takes from l'used the stiff cord used in experiment bodies, or communicates matter to 5th, and found the traction,

them. At half a turn..............

...1} lbs. First, As to fire being hot, the conone and a haif ......

trary is the fact there can be no such two and a half ......

thing in nature as a hot body, because three and a half ......

there is no such thing as an element four and a half ......

hot, sui generis; and because matter


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INQUIRY, ETC. being inert, is incapable of changing tact with or in the neighbourhood of it. its like from hot to cold, and from cold Aud as fire can act but uniformly, that to bot. Inertia implies unchangeable- is, cannot draw to it and propel from ness, as, where there is no power or itself at the same time, it is concluability, there can be no change of sive there is nothing communicated by essence; and therefore heating aod it to bodies ; and that what is taken çooling unalterable matter, by matter for radiation, is the effect of the abwhich is inert, is highly irrational to straction which the air suffers by fire, imagine.

or by bodies that have been rendered * In the pext place, The means we pos- deficient of some species of matter by sess, by which we become acquainted fire, by which these act on the thermowith heat, must convince that fire has meter as they have been acted on nothing whatever in common with by fire. keat. Thus, when the hand is applied From which it would seem, that to an ignited coal, it is not the flesh the deficient state of the water causes which feels, as, without nerves, there the sated (cold) razor to suffer loss of would be no feeling excited, even were electric matter, and from the teeth of the flesh burnt. Neither do the nerves its saw-edge some of the like, that may feel; for, when separated from the be compared to grains of sand or to brain, and in all other respects remain- saw-dust, which, by sticking between ing uninjured in the body, neither pin the teeth of a saw, prevent it cutting nor pincers applied to them can pro- with the same facility as when they duce seusation. Sensation, then, is are removed. confined to the sensorium, which may

I remain, Sir, be the brain-an organ that does not

Your obedient servant, come in contact with the external body,

T. H. PASLEY. which we suppose hot. Hence it is manifest that heat consists in sensation ouly, with which what is material can have no similitude, and that it is from

INQUIRY. imagining the external body to be in a state similar to the seusation that we conclude the body is hot. The term No. 154.-ART OF TURNING, heat, in short, only applies to sensation, feeling, or when health is con

Sir, I should be obliged to any cerned.

of your readers to favour an amaSecondly, Fire takes matter from teur turner with the best apparatus bodies, and imparts none to them. for elliptical turning, and also with This is the fact, notwithstanding it is the mode of turning cubes with opposed to universal opinion. Wood, mathematical truth. I am inpaper, linen, damp clothes, fuel, and formed it has been done so corall combustible bodies, are deprived of rectly as to produce a degree of matter by fire; so, when indecom

cohesion sufficient to suspend no posable bodies suffer physical change by fire, without loss of weight, it may

less than six pounds weight. be justly inferred that they also have

I am, Sir, been deprived of matter, although it may be only electric matter; for fire,

Your obedient servant, it will be granted, cannot act otherwise

TURNSCREW. than similarly on all bodies. What fire takes from water is visibly collected on the bottom of vessels before ebullition takes place, in the form of bubbles, that cannot be made to ascend in.

ANSWERS TO INQUIRIES. the water as long as the vessel is in contact with the fire. The denuded state of air, as respects vital matter,

No. 145,-WISD-LATHE. in which combustion is carried on Sir, If your Correspondent, the oxidation, by fire, of metals in air “ E. B.” is in the habit of visiting

and the decomposition of water by iýnited iron, wherein what the water is

y London, he may see a beautiful, deprived of the iron, which is fire, ac

horizontal mill at Battersea. The quires, amounts to a demonstration sails consist of a large wheel, ex-: that fire takes some species of matter actly like an undershot wateror other from whatever may be in con- wheel, only nuuch longer in the di

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