MECHANIC S. 
656 
and tliofe of the third kind, where the power is applied. 
The axles of wheels and puUeys, the teeth of wheels, 
ropes, &c. mud: be made ftrong'er or weaker, as they will 
he more or lefs aCted upon. Let the ftrength allowed be 
more than fully competent to the ftrefs to which the part's 
can ever be liable ; but let not the furplus be extravagant ; 
for fuch an excels of ftrength in any part, instead of being 
ferviceable, is injurious by increaling the reft ft a ace the 
machine has to overcome, and thus encumbering, impe¬ 
ding. and often deftroying, the requifite motion ; while, 
on the other hand, a defect of ftrength in any one part 
will canfe a failure there, and either render the whole 
ufelefs, or call for frequent Repairs. 
The propotitions we have given on the ftrength and 
ft refs of materials, however true, according to the princi¬ 
ples afl'umed, are of no ufe in practice till the compara¬ 
tive ftrength of different fubftances is afeertained ; and 
even then they will apply more accurately to fome fub¬ 
ftances than others. Hitherto they have been almoft ex- 
clufively applied to the rc-fifting-forceof beams of timber; 
though it is probable that no materials whatever accord 
lefs with the theory than timber in general. The refill¬ 
ing body is fuppofed in the theory to be perfectly homo¬ 
geneous, or compofed of parallel fibres, equally diftributed 
around the axis, and presenting uniform reft fiance to rup¬ 
ture. But this is not the cafe in a beam' of timber ; for, 
by tracing the procefs of vegetation, it has been found 
that the ligneous coats of a tree, formed by its annual 
growth, are almolf concentric ; and that they are like fo 
many hollow cylinders thru ft into each other, and united 
by a kind of medullary fubftance which offers but little 
refiftance; thefe hollow cylinders, therefore, furnifh the 
chief refiftance to the force which tends to break them. 
Now', when the trunk of a tree is fquared in order that it 
may be converted into a beam, it is evident that all the 
ligneous cylinders greater than the circle inferibed in the 
fquare ofTdCtangle which is the feCtion of the beam, are 
cut off at tire fides; and therefore, as Montucla remarks, 
almoft the whole refiftance arifes from the cylindrical 
trunk inferibed in the folid part of the beam. The por¬ 
tions of the cylindrical coats which are towards the angles 
add a little, it is irue, to the ftrength of that cylinder, as 
they cannot fail to oppofe fome refiftance to the drain¬ 
ing force; but it is far lefs than if the ligneous cylinder 
were entire. Hence we cannot by legitimate cornparifon 
accurately deduce the ftrength of a joilt cut from a fmall 
tree by experiments on another which has been fawn 
from a much larger tree or block ; the latter is generally 
weak, and very liable to break. As to the concentric cy¬ 
linders we have been fpeaking of, they are evidently not 
all of equal ftrength ; which again is contrary to the 
theory, in which they are fuppofed uniform throughout. 
After all, however, it is ftill found that in fome of the 
moft important problems the refults of the theory and 
well-conducted experiments coincide, even with regard to 
timber ; thus, for example, the experiments of Duhamel 
on rectangular beams afford refults deviating but in a flight 
degree from the theorem of Galileo, that the ftrength is 
proportional to the produftof the breadth into the fquare 
of tiie depth. 
The ftrength of materials arifes immediately or ulti¬ 
mately from the cobefion of the parts of bodies. Our 
examination of this property of tangible matter has as yet 
been very partial and imperfect, and by no means enables 
us to apply mathematical calculations with precifion and 
fuccefs. The various modifications of cobefion, in its dif¬ 
ferent appearances of perfect foftnefs, piafticity, duCtility, 
elafticity, hardnefs, have a mighty influence on the ftrength 
of bodies, but are hardly fufceptible of meafurement. 
Their texture alfo, w hether uniform like glafs and duClile 
metals, cryftallized or granulated like other metals and 
freellone, or fibrous like timber, is a circuit)'fiance no lefs 
important; yet even here, although we derive fome ad¬ 
vantage from remarking to which of thefe forms of ag¬ 
gregation a fubftance belongs, the aid is but fmall. All 
we can do in this want of general principles is to make 
experiments on every clafs cf bodies. Accordingly phi¬ 
losophers have endeavoured to inftruCt the public in this 
particular. The Royal Society of London, at its very firft 
inftitution, made many experiments at their meetings, as 
may be Seen in the firft regifters of the Society. (See 
Birch’s Hiftory, and Hooke’s Mathematical Collections.) 
Several individuals have added their experiments. The 
moft numerous collection in detail is by Mufclienbroek, 
pt'ofefl'or of natural philofophy at Leyden. Part of it 
was publiffied by himfelf in his Effais de Phyfique, in 2 
vols. 4to. but the full collection is to be found in his Syf- 
tem of Natural Philofophy, publifhed after his death by 
Lnlofl, in 3 vols. ^to. This was tranflated from the 
Dutch into French by Sigaud de la Fond, and publifhed 
at Paris in 1760 ; and is a prodigious collection of phyfi- 
cal knowledge of all kinds, and may almoft fuffice for a 
library of natural philofophy. But this collection of ex¬ 
periments on the cobefion of bodies is not of that value 
which one expects. We prefume that they were carefully 
made and faithfully narrated ; but they were made on fucli 
fmall fpecimens, that the unavoidable natural inequalities 
of growth or texture produced irregularities in the refults 
which bore too great a proportion to the whole quantities 
obferved. We may make the fame remark on the experi¬ 
ments of Couplet, Pitot, De la Hire, Duhamel,and others 
of the French Academy. In fliort, if we except the ex¬ 
periments of Buffon on the ftrength of timber, made at 
the public expenfe on a large fcale, there is nothing to be 
met with from which we can obtain abfolute meafures 
which may be employed with confidence; and there is 
nothing in the Englifh language except a Simple lift by 
Emerfon, which is merely a fet of affirmations, without 
any narration of circumftances, to enable us to judge of 
the validity of his conclufions; but the character of Mr. 
Emerfon, as a man of knowledge and of integrity, gives 
even to thefe affertions a confiderable value. 
But to make ufe of any experiments, there muft be em¬ 
ployed fome general principle by which we can generalize 
their refults. They will otherwise be only narrations of 
detached fails. We muft have fome notion of that me¬ 
dium, by the intervention of which an external force 
applied to one part of a lever, joilt, or pillar, occafions a 
(train on a diftant part. This can be nothing but the co- 
hefion between the parts. It is this connecting force 
which is brought into aCtion, or, as we more (hortly ex- 
prefs it, excited. This aCtion is modified in every part 
by the laws of mechanics. It is this aCtion which is what 
we call the Jirengtk of that part, and its effeCt is the drain 
on the adjoining parts ; and thus it is the lame force, dif¬ 
ferently viewed, that conftitutes both the (train and the 
ftrength. When we confider it in the light of a refiftance 
to fraCture, we call it Jirengtk. 
Introductory to a detail of the experiments we have al¬ 
luded to, we may premife the following general obferva- 
tions, which are copied Srqom the Encyclopaedia Britannica, 
(art. Strength of Materials.) 
“1. The wood immediately furrounding the pith or 
heart of the tree is the weakelt, and its inferiority is fo 
much more remarkable as the tree is older. In this affer- 
tion, however, we fpeak with fome hefitation. Mufchen- 
broek’s detail of experiments is decidedly in the affirma¬ 
tive. Buffon, on the other hand, fays, that his experience 
has taught him that the heart of a found tree is the ftrongeft ; 
but he gives no inftances. We are certain, from many ob¬ 
servations of our own 011 very large oaks and firs, that the 
heart is much weaker tiian the exterior parts. 
“ 2. The wood next the bark, commonly called the 
white, or blea, is alfo weaker than the reft; and the wood 
gradually increafes in ftrength as we recede from the cen¬ 
tre to the blea. 
“ 3. The wood is ftronger in the middle of the trunk 
than at the fpringing of the branches or at the root; ami 
the wood of the branches is weaker than that of the 
trunk. 
it 
4. 
