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S TR Strength of TRENGTH. OF Materials, in mechanics, is a sub- tion of this property of tangible matter has as yet been very strength of Materials. SI

ject of so much importance, that in a nation so emic partial and imperfect, and by no means enables us to apply

vent as this for invention and ingenuity in all species mathematical calculations with precision and success. The Importance of manufa&ures, and in particular so distinguished for various modifications of cohesion, in its different appearof the tub. its improvements in machinery of every kind, it is fome. ances of perfe& softness, plasticity, ductility, elafticity, hardject.

what fingular that no writer has treated it in the detail ness, have a mighty influence on the strength of bodies, but
which its importance and difficulty demands.

are hardly susceptible of measurement. Their texture also,
of science who visits our great manufactures is delighted whether uniform like glass and ductile metals, crystallized or
with the ingenuity which he observes in every part, the in. granulated like other metals and freestone, or fibrous like
numerable inventions which come even from individual arti- timber, is a circumstance no less important; yet even here,
fans, and the determined purpose of improvement and re- although we derive some advantage from remarking to which
finement which he sees in every workshop. Every cotton of these forms of aggregation a substance belongs, the aid is
mill appears an academy of mechanical science; and mecha- but small

. All we can do in this want of general principles Esperinical invention is spreading from these fountains over the is to make experiments on every class of bodies.

Accord, meets to whole kingdom: But the philosopher is mortified to fee ingly philosophers have endeavoured to instruct the public this ardent spirit so cramped by ignorance of principle, and in this particular. The Royal Society of London at its many of thele original and brilliant thoughts obscured and very first institution made many experiments at their meetclogged with needless and even hurtful additions, and a com- ings, as may be seen in the first registers of the Society .+ Sce plication of machinery which checks improvement even by Several indiriduals have added their experiments. The molt Birche' its appearance of ingenuity. There is nothing in which . numerous collection in detail is by Muschenbroek, profesor of Hier, and this want of scientific education, this ignorance of principle, natural philosophy at Leyden. Part of it was published by Malbena is so frequently observed as in the injudicious proportion of himself in his Efais de Physique, in 2 vols 4to ; but the full tie il Colleza the parts of machines and other mechanical structures; pro- collection is to be found in his System of Natural Philofo- tiers. portions and forms of parts in which the strength and pofi- phy, published after his death by Lulofs, in 3 vols 4to. This tion are nowise regulated by the strains to which they are was translated from the Low Dutch into French by Sigaud exposed, and where repeated failures have been the only de la Fond, and published at Paris in 1760, and is a prodigious lessons.

collection of phyfical knowledge of all kinds, and may alIt cannot be otherwise. We have no means of instruc- most suffice for a library of natural philosophy. But this tion, except two very short and abstracted treatises of the collection of experiments on the coheson of bodies is not of late Mr Emerson on the trength of materials. We do not that value which one expects. We presume that they were recollect a performance in our language from which our ar- carefully made and faithfully narrated; but they were made tists can get information. Treatises written expressly on on such finall specimens that the unavoidable natural inequa. different branches of mechanical arts are totally filent on lities of growth or texture produced irregularities in the rethis, which is the basis and only principle of their perform- fults which bore too great a proportion to the whole quan

Who would imagine that Price's British CAR« tities observed. We may make the same remark on the ex. PENTER, the work of the first reputation in this country, periments of Couplet, Pitot, De la Hire, Du Hamel, and and of which the sole aim is to teach the carpenter to erect others of the French academy. In short, if we except the Solid and durable structures, does not contain one propofio experiments of Buffon on the strength of timber, made at tion or one reason by which one form of a thing can be the public expence on a large scale, there is nothing to be thown to be stronger or weaker than another? We doubt met with from which we can obtain absolute measures which very much if one carpenter in an hundred can give a reason may be employed with confidence ; and there is nothing in to convince his own mind that a joist is stronger when laid the English language except a simple lift by Emerson, which on its edge than when laid on its broad fide. We speak in is merely a set of affirmations, without any narration of cirthis strong manner in hopes of exciting some man of science cumstances, to enable us to judge of the validity of his conto publish a syftem of instruction on this subject. The li- clulions : but the character of Mr Emerson, as a man of mits of our Work will not admit of a detail : but we think knowledge and of integrity, gives even to these affertions a it necessary to point out the leading principles, and to give considerable value. the traces of that systematic connection by which all the But to niake use of any experiments, there must be employed Rendered knowledge alrcady poffeffed of this subject may be brought some general principle by which we can generalize their retul together and properly arranged. This we shall now attempt sults. They will otherwise be only narrations of detached gees skats in as brief a manner as we are able.


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facts. We must have some notion of that intermedium, by Strength of

the intervention of which an external force applied to one materials The strength of materials arises immediately or ultimate part of a lever, joist, or pillar, occasions a itrain on a ditant arises from ly from the cohesion of the parts of bodies. Our examina- part. This can be nothing but the cohesion between the cuhelion, Vol. XVIII. Part I.





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

action, or, as we more shortly express it, excited. This ac- hang perpendicular; affix to the lower end an index like the Materials,

tion is modified in every part by the laws of mechanics. It hand of a watch; on some stand immediately below let there Strength is this action which is what we call the strength of that part, be a circle divided into degrees, with its centre corresponda dcfined.

and its effect is the strain on the adjoining parts; and thus ing to the lower point of the wire : now turn this index
it is the same force, differently viewed, that constitutes both twice round, and thus twist the wire. When the index is
the strain and the strength. When we consider it in the let go, it will turn backwards again, by the wire's untwift-
light of a resistance to fracture, we call it frength.

ing itself, and make almost four revolutions before it stops ;
We call every thing a force which we observe to be ever after which it twilts and untwiiis many times, the index go-
accompanied by a change of motion; or, more strictly ing backwards and forwards round the circle, diminishing
speaking, we infer the presence and agency of a force where. however irs arch of twist each time, till at lalt it settles pre-
ver we observe the state of things in respect of motion dif- cisely in its original position. This may be repeated for ever,
ferent from what we know to be the result of the action of Now, in this motion, every part of the wire partakes equal-
all the forces which we know to act on the body. Thus ly of the twist. The particles are stretched, require force
when we observe a rope prevent a body from falling, we in to keep them in their state of extenfion, and recover com.
fer a moving force inherent in the rope with as much confi. pletely their original relative positions. These are all the
dence as when we observe it drag the body along the ground. characters of what the mechanician calls perfe&t elasticity,
The immediate action of this force is undoubtedly exerted This is a quality quite familiar in many cases ;'as in glass,
between the immediately adjoining parts of the rope. The tempered feel, &c. but was thought incompetent to lead,
immediate effect is the keeping the particles of the rope to- which is generally considered as having little or no elasticity.
gether. They ought to separate by any external force But we make the affertion in the most general terms, with
drawing the ends of the rope contrarywise; and we ascribe the limitation to moderate derangement of form. We have

their not doing so to a mechanical force really oppoling this made the fame experiment on a thread of pipe-clay, made Causes external force. When delired to give it a name, we name by forcing soft clay through the small hole of a syringe by known on it from what we conceive to be its effect, and therefore it's means of a screw; and we found it more elallic than the ly from

characteristic; and we call it COHESION. This is merely a lead wire : for a thread of oth of an inch diameter and
fects, name for the fact ; but it is the same thing in all our deno- feet long allowed the index to make two turns, and yet com-

minations. We know nothing of the causes but in the efo pletely recovered its first position.
fects; and our name for the cause is in fact the name of the 2dly, But if we turn the index of the lead wire four times
effect, which is COHESION: We mean nothing else by gra- round, and let it go again, it untwists again in the same
vitation or magnetism. What do we mean when we say manner, but it makes little more than four turns back
that Newton understood thoroughly the nature of gravita. again ; and after many oscillations it finally stops in a pofi-
tion, of the force of gravitation, or that Franklin understood tion almost two revolutions removed from its original posi.
the nature of the electric force? Nothing but this: Newton tion. It has now acquired a new arrangement of parts, and
confidered with patient sagacity the general facts of gravi. this

, riew arrangement is permanent like the former; and,
tation, and has described and claffed them with the utinolt what is of particular moment, it is perfectly elastic.

This What is precition. In like manner, we shall understand the nature change is familiarly known by the denomination of a ser. nieant by of cohesion when we have discovered with equal generalitỹ The wire is faid to have TAKEN A SET. When we attend a fit. the laws of cohelion, or general facts which are observed in

which are observed iri minutely to the procedure of nature in this phenomenon, we the appearances, and when we have described and claffe'd find that the particles have as it were slid on each other, them with equal accuracy.

still cohering, and have taken a new position, in which their Let us therefore attend to the more simple and obvious connecting forces are in equilibrio : and in this change of phenomena of cohelion, and mark with care every circum relative situation, it appears that the connecting forces which Itañce of relemblarice by which' they may be classed. Let maintained the particles in their firit fituations were not in üs receive there as the laws of coheron, chara&teristic of its equilibrio in some position intermediate between that of the fuppofed caufe, the force of cohesion.

We cannot pretend first and that of the latt form. The force required for to cnter on this valt research. The modifications are in. changing this first form augmented with the change, but numerable; and it would require the penetration of more only to a certain degree ; and during this process the conthan Newton to detect the circumstance of similarity amidit pecting forces always tended to the recovery of this first millions of difcriminating circumstances. Yet this is the on- form. But after the change of mutual position has paffed ly way of discovering which are the primary facts charac- a certain rňagnitude, the union has been partly destroyed, beristic of the force, and which are the modifications. The and the particles have been brought into new situations ; Kudy is immense, but is by no means desperate; and we en: luch, that the forces which now connect each with its tertain great hopes that it will ere long be successfully pro- neighbour tend, not to the recovery of the first arrangefecuted : but, in our particular predicament, we must con- ment, but to pash them farther from it, into a new fituatent ourselves with fele&ring such general laws as seem to tion, to which they now verge, and require force to prevent give us the most iminediátė information of the circumstances them froni acquiring. The wire is now in fact again perthat must be attended to by the mechanician in his construc- fectly elastics that is, the forces which now connect the tions, that he may unite frength with fimplicity; economy, particles with their new neighbours augment to a certain and energy

degree as the derangement from this new position augments. I/, Then, it is a matter of fact that all bodies are in a cer. This is not reasoning from any theory. It is narrating Clattic. tain degree perfectly elallic ; that is, when their form or facts, on which a theory is to be founded. What we have

hulk is changed by certain moderate compressions or distrac: been just now saying is evidently a description of that fen-
zioné, it requires the continuance of the changing force to lible form of tangible matter which we call ductility. It has Dudility,
continue the body in this new state į and when the force is every gradation of variety; from the foftness of butter to the
removed, the body recovers its original forn, We limit the firmness- of gold. All these bodies have fome elasticity;
allertion to certain moderate changes : For instance, take a but we say they are not perfectly elastic, because they do
bad wire of all of an inch in diameter and ten feet not completely recover their original fuíni when it has been


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8 TR Strength of greatly deranged. The whole gradation may be molt di. by any external cause, to recede from this fituation of mutu. Strength of Materials,

finctly observed in a piece of glass or hard fealing wax. In al inactivity ; for fince force is requisite to produce either Alaterias
the ordinary form glass is perhaps the most completely elaf- the dilatation or the compreffion, and to maintain it, we
tic body that we know, and may be bent till just ready to are obliged, by the contitution of our minde, ço inser that Particles
snap, and yet completely recovers its first form, and takes it is opposed by a force accompanying or inherent in every adalon
no set whatever ; but when heated to such a degree as just particle of-dilatable or compressible matter : and as this by aierec-
to be visible in the dark, it loses its brittleness, and becomes neccffity of employing force to produce a change indicates repulivuse
so tough that it cannot be broken by any blow; but it is the agency of these corpuscular forces, and marks their kind,
no longer elastic, takes any set, and keeps it. When more according as the tendencies of the particles appear to be
heated, it becomes as plastic as claybut in this state is ie- toward each other in dilatation, or from each other in com-

markably distinguished from clay by a quality which we may preffion; so it also measures the degrees of their intensity. Viscidity call viscIDITY, which is fomething like elasticity, of which Should it require three times the force to produce a double

clay and other bodies purely plastic exhibit no appearance, compreffion, we must reckon the mutual repultions triple
This is the joint operation of strong adhesion and softness. when the compression is doubled ; and so in other inilances.
When a rod ol pertectly Soft glass is suddenly stretched a We fee from all this that the phenomena of colchon indicate
little, it does not at once take the shape which it acquires, some relation between the intenfity of the force of cohesion
after some little time. It is owing to this, that in taking and the dillance between the centres of the particles. To The great
the impression of a scal, if we take off the seal while the wax discover this relation is the great problen in corpuscular problem in
is yet very hot, the sharpness of the impression is destroyed mechanism, as it was in the Newtonian inveftigation of the corpufcilie

immediately. Each part drawing its neighbour, and each force of gravitation. Could ive discover this law of action
part yielding, the prominent parts are pulled down and becween the corpuscles with the same certainty and distinct- .
blunted, and the sharp hollows are pulled upwards and also nels, we might with equal confidence say what will be the
blunted. The scal must be kept on till all has become not result of any position which we give to the particles of
only ftiff but hard.

bodies ; but this is beyond our hopes. The law of gra This vilcidity is to be observed in all plastic bodies which vitation is fo simple that the discovery or detection of it

are homogeneous. It is not observed in clay, because it is amid the variety of celestial phenomena required but one step ; plan:c bol pot homogeneous, but consists of hard particles of the ar- and in its own nature its posible combinations Aill do not

gillaceous carçlı sticking together by their attraction for greatly exceed the powers of human research. One is al.

Something like it might be made of finely pou- most disposed to say that the Supreme Being has exhibited dered glass and a clammy fluid such as turpentine. Visci- it to our reasoning powers as sufficient to employ with sucdity has all degrees of softness till it degenerates to ropy cess our utmost efforts, but not so abitruse as to discourage fluidity like that of olive oil. Perhaps something of it may tis from the noble attempt. It seems to be otherwise with be found even in the most perfect fluid that we are acquaint. repect to coletion. Mathematics informs us, that if it de. ed with, as we oblerved in the experiments for ascertaining viates sendibly from the law of gravitation, the simplest comspecific gravity.

binations will make the joint action of several particles an alThere is in a late volume of the Philosophical Transac- most impenetrable mystery. We muft therefore content ourtions á narration of experiments, by which it appears that selves, fer a long while to come, with a careful observation the thread of the spider is an exception to our first general of the simplest cases that we can propose, and with the difa law, and that it is perfectly ductile. It is there asserted, covery of fecondary laws of action, in which many partithat a long thread of goflamer, furnished with an index, cles combine their influence. Iu pusuance of this plan, we takes any position whatever ; and that though the index be observe, turned round any number of times (even many hundreds), zdis, That whatever is the situation of the particles of a Particies it has no tendency to recover its first form. The thread 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 fituations by the balance of opposite

ce by a opportunity of repeating this experiment, but we have di.

This cannot be refused, nor can we form to our-balance flinctly observed a phenomenon totally inconsistent with it. felves any other notion of the state of the particles of a cf forcese If a fibre of gossamer about an inch long be held by the body. Whether we fuppose the ultimate particles to be of end horizontally, it bends downward in a curre like a fen- certain magnitudes and thapes, touching each other in fingle der Nip of whalebone or a hair. If totally devori of elasti- points of cohesion; or whether we (with Bolcovich) concity, and perfectly indifferent to any set, it would hang lider them as at a distance from each other, and acting on down perpendicularly without any curvaturc.

cach other by attractions and repullions—we must acknowWhen ductility and elasticity are combined in different ledge, in the first place, that the centres of the particles proportions, an immense variety of fenable modes of aggre- (by whose mutual distances we must estimate the distance of gation may be produced. Some degree of both are pro- the particles) may and do vary their distances from each bably to be observed in all bodies of complex constitution ; other. What elle can we say when we observe a body inthat is, which confift of particles made up of many different crease in length, in breadth, and in thickness, by heating it, kinds of atoms. Such a conftitution of a body muft afford ror when we lee it diminish in all these dimensions by an exmany situations permanent, but easily deranged.

ternal compression? A particle, therefore, situated in the In all these changes of difpofition which take place among midst of many others, and remaining in that hatuation, must the particles of a ductile body, the particles are at such be conceived as maintained in it by the mutual balancing of distance that they still cohere. The body may be stretched all the forces which connect it with its neighbours. It is illustra. a little ; and on removing the extending torce, the body like a ball kept in its place by the opposite action of two tion of thrinks into its firit foin. It also refifts, moderate com- springs. This illustration merits a more particular applica-this pressions ; and when the compresling force is removed, the tion. Suppose a number of balls ranged on the table in the position body swells out again. Now the corpuscular jadi here is, angles of equilateral triangles, and that each ball is connected that the particles are acted on by attractions and repullions, with the fix which lię around it by means of an clastic which balance each other when no external force is acting wire curled like a cork-screw ; fuppose such another stratum on the body, and which augment as the particles are made of balls above this, and parallel to it, and so placed that



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