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A R T S, SC I E N C E S,

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T R E A T I S E S or S Y S T E M s,

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The H I s To R Y, T H E o R Y, and P R A C T 1 c E, of each,
according to the Latest Discoveries and Improvements;

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Including ELUCIDATIONS of the most important Topics relative to RELIGION, MoRALs,
MANNERS, and the OEconoMY of LIFE :

A Descr IPTI on of all the Countries, Cities, principal Mountains, Seas, Rivers, &c.
throughout the Wo R L D ; -

A General HIST ORY, Ancient and Modern, of the different Empires, Kingdoms, and States;
- + A N D
An Account of the L1 v Es of the most Eminent Persons in every Nation,

from the earliest ages down to the present times.

Compile i from the writings of the § Alithers, in several languages ; the woff approved Dićionaries, as well of general science as of its £arti-
cular branches ; the Franjačions, journals, and Men:irs, of learned Societies, both do home and abroad: the MS. Leółures of
Eminent Professors &n different science: ; and a variety of Original Mlateriuls, furnished by an Extensive Correspondence.

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Strength of



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S T R TRENGTH. of MATERIALs, in mechanics, is a sub

jećt of so much importance, that in a nation so emiment as this for invention and ingenuity in all species

Importance of manufactures, and in particular so distinguished for

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Strength of

its improvements in machinery of every kind, it is somewhat fingular that no writer has treated it in the detail which its importance and difficulty demands. The man of science who visits our great manufactures is delighted with the ingenuity which he observes in every part, the innumerable inventions which come even from individual artifans, and the determined purpose of improvement and refinement which he sees in every workshop. Every cotton mill appears an academy of mechanical science ; and mechanical invention is spreading from these fountains over the whole kingdom: But the philosopher is mortified to see this ardent spirit so cramped by ignorance of principle, and many of these original and brilliant thoughts obscured and clogged with needless and even hurtful additions, and a complication of machinery which checks improvement even by

its appearance of ingenuity. There is nothing in which

this want of scientific education, this ignorance of principle, is so frequently observed as in the injudicious preportion of the parts of machines and other mechanical structures; proportions and forms of parts in which the strength and position are nowise regulated by the strains to which they are exposed, and where repeated failures have been the only lessons. - *, It cannot be otherwise. We have no means of instruction, except two very short and abstraćted treatises of the late Mr Emerson on the strength of materials. We do not recolle&t a performance in our language from which our artists can get information. Treatises written expressly on different branches of mechanical arts are totally silent on this, which is the basis and only principle of their performances. Who would imagine that PR1 ce’s BRITIs H CAR. PENTER, the work of the first reputation in this country, and of which the sole aim is to teach the carpenter to erect folid and durable strućtures, does not contain one proposition or one reason by which one form of a thing can be shown to be stronger or weaker than another ? We doubt very much if one carpenter in an hundred can give a reason to convince his own mind that a joist is stronger when laid on its edge than when laid on its broad fide. We speak in this strong manner in hopes of exciting some man of science to publish a system of instruction on this subjećt. The limits of our Work will not admit of a detail : but we think it necessary to point out the leading principles, and to give the traces of that systematic connection by which all the knowledge already possessed of this subject may be brought together and properly arranged. This we shall now attempt in as brief a manner as we are able.

The strength of materials arises immediately or ultimate. ly from the cohesion of the parts of bodies. Our examinaVol. XVIII. Part I.

imaterials arises from


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tion of this property of tangible matter has as yet been very Soength of partial and imperfeót, and by no means enables us to apply tot mathematical calculations with precision and success. The various modifications of cohesion, in its different appearances of perfeót softness, plasticity, dućtility, elasticity, hardmess, have a mighty influence on the firength of bodies, but are hardly susceptible of measurement. Their texture also, whether uniform like glass and dućtile metals, crystallized or granulated like other metals and freestone, or fibrous like timber, is a circumstance no less important; yet even here, although we derive some advantage from remarking to which of these forms of aggregation a substance belongs, the aid is 3 but small. All we can do in this want of general principles Experiis to make experiments on every class of bodies. Accord- o o ingly philosophers have endeavoured to instruct the public. * in this particular. The Royal Society of London at its very first institution made many experiments at their meetings, as may be seen in the first registers of the Society +...+ See Several individuals have added their experiments. The most ; : numerous colle&tion in detail is by Muschenbroek, professor of o natural philosophy at Leyden. Part of it was published by so.himself in his Essais de Physique, in 2 vols 4to ; but the fulltio 1 Coite:colle&tion is to be found in his System of Natural Philoso-tiers. phy, published after his death by Lulofs, in 3 vols 4to. This was translated from the Low Dutch into French by Sigaud de la Fond, and published at Paris in 1760, and is a prodigious colle&tion of physical knowledge of all kinds, and may al- * most suffice for a library of natural philosophy. But this collečtion of experiments on the cohesion of bodies is not of that value which one expects. We presume that they were carefully made and faithfully narrated; but they were made on such small specimens that the unavoidable natural inequa. lities of growth or texture produced irregularities in the refults which bore too great a proportion to the whole quantities observed. We may make the same remark on the experiments of Couplet, Pitot, De la Hire, Du Hamel, and others of the French academy. . In short, if we except the experiments of Buffon on the strength of timber, made at the public expence on a large scale, there is nothing to be met with from which we can obtain absolute measures which may be employed with confidence; and there is nothing in the English language except a fimple list by Emerson, which is merely a set of affirmations, without any narration of circumstances, to enable us to judge of the validity of his conclusions : but the charaćter of Mr Emerson, as a man of knowledge and of integrity, gives even to these assertions a confiderable value. - -- 4. . But to make use of any experiments, there must be employed Renored some general principle by which we can generalize their re-of ful ox sults. They will otherwise be only narrations of detacheao.” faëts. We must have some notion of that intermedium, by ion. the intervention of which an external force applied to one Part of a lever, joist, or pillar, occasions a strain on a distant Part. This can be nothing but the cohesion between the

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Strength of parts. Materials.

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5 tion is modified in every part by the laws of mechanics. It strength is this ačtion which is what we call the strength of that part, *fined, and its effect is the strain on the adjoining parts; and thus it is the same force, differently viewed, that constitutes both the strain and the strength. When we consider it in the light of a refistance to fraćture, we call it sirength. We call every thing a force which we observe to be ever

accompanied by a change of motion ; or, more strićtly

speaking, we infer the presence and agency of a force where. ver we observe the state of things in respect of motion different from what we know to be the result of the aëtion of all the forces which we know to act on the body. Thus when we observe a rope prevent a body from falling, we infer a moving force inherent in the rope with as much confi. dence as when we observe it drag the body along the ground. The immediate ačtion of this force is undoubtedly exerted between the immediately adjoining parts of the rope, 'i'he

immediate effect is the keeping the particles of the rope to.

gether. They ought to separate by any external force drawing the ends of the rope contrarywise; and we ascribe

6 their not doing so to a mechanical force really opposing this Causes external force. When desired to give it a name, we name known on it from what we conceive to be its effect, and therefore its ly from . . . o.- : * : - - - , , , .* ------ ... • , s , , ... charaćteristic, and we call it coh Eston. This is merely a fedts, name for the fact; but it is the same thing in all our deno

minations. We know nothing of the causes but in the ef

fects; and our name for the cause is in fact the name of the

effect, which is co HE ston. We mean nothing else by gravitation or magnetism. What do we mean when we say that Newton understood thoroughly the nature of gravitation, of the force of gravitation; or that Franklin understood the nature of the electric force? Nothing but this: Newton confidered with patient sagacity the general facts of gravitation, and has described and classed them with the utmost - precision. . In like manner, we 'shall understan the nattli e - of cohesion when we have discovered with equal generality the laws of cohesion, or general facts which are observed in the appearances, and when we have described and classed them with equal accuracy. as therefore attend to the more simple and obvious phenomena of cohesion, and mark with cate every circumitance of resemblance by which they may be classed. is receive these as the laws of cohesion, charaćteristic of its supposed cause, the force of cohesion. We cannot pretend to cnter on this vast research. A he modifications are inhumerable; and it would require the penetration of more than Newton to dete& the circumstance of fimilarity amidst raillions of discriminating circumstances. Yet this is the on!y way of discovering which are the primary fačts characteristic of the force, and which are the modifications. The study is immense, but is by no means desperate; and we entertain great hopes that it will ere long be successfully profecuted : but, in our particular predicament, we must content ourselves with selecting such general laws as seem to give us the most immediate information of the circumstances that must be attended to by the mechanician in his constructions, that he may unite strength with simplicity, economy,

, , and energy. * * * * a As bodies is, Then, it is a matter of fact that all bodies are in a cerclattic, tain degree perfeółly elastic ; that is, when their form or

bulk is changed by certain moderate compressions or distrac. tions, it requires the continuance of the changing force to continue the body in this new state ; and when the force is removed, the body recovers its original form. We limit the assertion to certain moderate changes: For instance, take a lead wire of oth of an inch in diameter and ten feet

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It is this connecting force which is brought into , long; fix one-end firmly to the ceiling, and let the wire Strength of


hang perpendicular; affix to the lower end an index like the Materials.

hand of a watch ; on some stand immediately below let there be a circle divided into degrees, with its centre corresponding to the lower point of the wire: now turn this index twice round, and thus twist the wife. When the index is let go, it will turn backwards again, by the wire's untwisting itself, and make almost four revolutions before it stops; after which it twists and untwits many times, the index going backwards and forwards round the circle, diminishing however its arch of twist each time, till at last it settles precisely in its original position. This may be repeated for ever, Now, in this motion, every part of the wire partakes equally of the twist. The particles are stretched, require force

to keep them in their state of extension, and recover com

pletely their original relative positions. These are all the characters of what the mechanician calls persed elasticity,

'l'his is a quality quite familiar in many cases; as in glass,

tempered steel, &c. but was thought incompetent to lead, which is generally confidered as having little or no elasticity. But we make the assertion in the most general terms, with the limitation to moderate derangement of form. We have made the same experiment on a thread of pipe-clay, made by forcing soft clay through the small hole of a syringe by means of a screw ; and we found it more elastic than the lead wire : for a thread of oth of an inch diameter and 7 feet long allowed the index to make two turns, and yet completely recovered its first position. - 2d/y, But if we turn the index of the lead wire four times


round, and let it go again, it untwists again in the same

männer, but it makes little more than four turns back again ; and after many oscillations, it finally stops in a position almost two revolutions removed from its original position. It has now acquired a new arrangement of parts, and this new arrangement is permanent like the former; and,

what is of particular moment, it is perfeółly elastic. This what is change is familiarly known by the denomination of a ser. meant by The wire is said to have TAKEN A set. When we attend */*

minutely to the procedure of nature in this phenomenon, we find that the particles have as it were slid on each other, still cohering, and have taken a new position, in which their conne&ting forces are in equilibrio : and in this change of relative fituation, it appears that the conne&ting forces which maintained the particles in their first fituations were not in equilibrio in some position intermediate between that of the first and that of the last form. The force required for changing this first form augmented with the change, but only to a certain degree ; and during this process the conme&ting forces always tended to the recovery of this first form. But after the change of mutual position has passed a certain magnitude, the union has been partly destroyed, and the particles have been brought into new fituations; such, that the forces which now connect each with its neighbour tend, not to the recovery of the first arrangement, but to push them farther from if, into a new fitua

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This is not reasoning from any theory. It is narrating faćts, on which a theory is to be founded. What we have been just now saying is evidently a description of that senfible form of tangible matter which we calf dušility. It has every gradation of variety, from the softness of butter to the firmness of gold. All these bodies have some elasticity ; but we say they are not perfe&ly elastic, because they do not completely recover their original foim when it has been

- - greatly

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$trength of greatly detanged. The whole gradation may be most di- by any external cause, to recede from this situation of mutu. of *iak flinétly observed in a piece of glass or hard sealing wax. In al inactivity; for since force is requisite to produce either *

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*TY” the ordinary form glass is perhaps the most completely elas. tic body that we know, and may be bent till just ready to snap, and yet completely recovers its first form, and takes no set whatever ; but when heated to such a degree as just to be visible in the dark, it loses its brittleness, and becomes so tough that it cannot be broken by any blow ; but it is no longer elastic, takes any set, and keeps it. When more heated, it becomes as plastic as clay but in this state is 1eto markably distinguished from clay by a quality which we may viscidity call viscs DITY, which is formething like elasticity, of which clay and other bodies purely plastic exhibit no appearance, This is the joint operation of strong adhesion and softness. When a rod of perfeótly soft glass is suddenly stretched a little, it does not at once take the shape which it acquires after some little time. It is owing to this, that in taking

the dilatation or the compression, and to maintain it, we '.

are obliged, by the constitution of our minds, to infer that
it is opposed by a force accompanying or inherent in every
particle of dilatable or compressible matter ; and as this
necessity of employing force to produce a change indicates
the agency of these corpuscular forces, and marks their kind,
according as the tendencies of the particles appear to be
toward each other in dilatation, or from each other in com-
pression; so it also measures the degrees of their intensity.
Should it require three times the force to produce a double
compresfion, we must reckon the mutual repultions triple
when the compression is doubled ; and so in other instances.
We fee from all this that the phenomena of cohesion indicate
some relation between the intensity of the force of cohesion

Particles ačted on by actrecti-in- ai.d. repulious.

- - * 13 and the dislande between the centres of the particles. To The great

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immediately. Each part drawing its neighbour, and each mechanism. part yielding, the prominent parts are pulled down and blunted, and the sharp hollows are pulled upwards and aiso blunted. The scal must be kept on till all has become not I F only stifs but hard.

Observed This viscidity is to be observed in all plastic bodies which
***" h9. are homogeneous. It is not observed in clay, because it is
too." not homogeneous, but consists of hard particles of the ar-
. gillaceous earth sticking together by their attraction for
water. Something like it might be made of finely pow-
dered glass and a clammy fluid such as turpentine. Visci-
dity has all degrees of softness till it degenerates to ropy
fluidity like that of olive oil. Perhaps something of it may
be found even in the most perfeót fluid that we are acquaint-
ed with, as we observed in the experiments for ascertaining

fpecific gravity.
There is in a late volume ef the Philosophical Transac-
tions à narration of experiments, by which it appears that
the thread of the spider is an exception to our first general
ław, and that it is perfectly dućtile. It is there asserted,
that a long thread of goslamer, furnished with an index,
takes any position whatever; and that though the index be
turned round any number of times (even many hundreds),
it has no tendency to recover its first form. The thread

force of gravitation. Could we discover this law of a&tion
between the corpuscles with the same certainty and distinét-
ness, we might with equal confidence say what will be the
result of any position which we give to the particles of
bodies; but this is beyond our hopes. The law of gra-
vitation is so simple that the discovery or detection of it
amid the variety of celestial phenomena required but one step
and in its own nature its possible combinations full do not
greatly exceed the powers. of human research. One is al-
most disposed to say that the Supreme i3eing has exhibited
it to our reasoning powers as sufficient to employ with suc-
cess our- utmost #. but not so abstruse as to discourage
us from the noble attempt. It seems to be otherwise with
respect to cohesion. Mathematics informs us, that if it de-
viates sensibly from the law of gravitation, the fimplest com.
binations will make the joint action of several particles an al-
most impenetrable mystery. We must therefore content our-
selves, for a long while to come, with a careful observation
of the simplest cases that we can propose, and with the dis-
covery of secondary laws of action, in which many parti-
cles combine their influence. In pusuance of this plan, we

& $o • . •. T 3. 3dy, That whatever is the situation of the particles of a Particles body with respect to each other, when in a quiescent state, kept in

takes completely any set whatever. We have not had an they are kept in these situations by the balance of opposite. so plawo o * & - * --- - of - e- * opportunity of repeating this experiment, but we have di. forces. This cannot be refused, nor can we form to our. to:

olinétly observed a phenomenon totally inconsistent with it.
If a fibre of gossamer about an inch long be held by the
end horizontally, it bends downward in a curve like a slen-
der slip of whalebone or a hair. If totally devoid of elasti-
city, and perfectly indifferent to any set, it would hang
down perpendicularly without any curvature.
When duétility and elasticity are combined in different
proportions, an immense variety of sensible modes of aggre-
gation may be produced. Some degree of both are pro-
bably to be observed in all bodies of complex constitution ;
that is, which consist of particles made up of many different
kinds of atoms. Such a constitution of a body must afford
many situations permanent, but easily deranged.

the particles of a dućtile body, the particles are at such
distance that they still cohere. The body may be stretched
a little; and on removing the extending force, the body
shrinks into its first form. It also refifts, moderate com-
pressions; and when the compressing force is removed, the
body swells out again. Now the corpuscular fati here is,
that the particles are ačted on by attractions and repulsions,
which balance each other when no external force is acting
on the body, and which augment as the particles are made,

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selves any other notion of the state of the particles of a cf forces.

body. Whether we suppose the ultimate particles to be of
certain magnitudes and shapes, touching each other in fingle
points of cohesion ; or whether we (with Boscovich) con-
fider them as at a distance from each other, and aćting on
cach other by attractions and repulsions—we must acknow-
ledge, in the first place, that the centres of the particles
(by whose mutual distances we must estimate the distance of
the particles) may and do vary their distances from each
other. , What else can we say when we observe a body in-
crease in length, in breadth, and in thickness, by heating it,
ror when we see it diminish in all these dimensions by an ex-

termal compression 3 A particle, therefore, fituated in the

midst of many others, and remaining in that fituation, must
be conceived as maintained in it by the mutual balancing of
all the forces which connect it with its neighbours. It is

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like a ball kept in its place by the opposite action of two tien of fprings. This illustration merits a more particular applica-oo: pro

tion. Suppose a number of balls ranged on the table in the
angles of equilateral triangles, and that each ball is connected
with the fix which lie around it by means of an elastic
wire curled like a cork-screw ; suppose such another stratum
of balls above this, and parallel to it, and so placed that


2. ' each

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