STRENGTH OF MATERIALS. 
dric cavities of different diameters, the strengths 
| are directly as the diameters. 
(3.) Large beams are weaker in proportion 
than small ones, for their own weight constitutes 
a part of the force that tends to break them ; 
_ and in similar solid bodies, the stress growing 
_ out of their own weight increases as the cubes of 
_ their homologous dimensions, while the strength 
| only increases with the squares. 
We see from this, that models may be strong, 
| and capable of bearing a stress far beyond any 
_ that can be applied to them ; yet that machines 
constructed exactly similar to them in propor- 
tion and of like materials, but of increased di- 
mensions, may become too weak to bear even 
their own weight ; that there must be a limit to 
the size and extent of any structures that can be 
erected by the hand of man; and that a similar 
limit exists even in the works of nature. Thus, 
in organic bodies, mountains, hills, trees, the 
size they can attain, without risk of disintegra- 
tion, is restricted within certain bounds. In the 
animal creation, the same principle applies, and 
the limit is sooner reached. 
Our theory would show that when a body be- 
comes weak in consequence of an increase of 
length, strength may at first be added by in- 
creasing its breadth, and still more by increasing 
its thickness, the length remaining constant. 
Here, however, the weight is increased in a 
greater ratio than the length, and finally be- 
comes excessive. The same quantity of material 
may assume a stronger form by being fashioned 
into a hollow tube; yet here again a limit is 
reached when the circumference of the tube be- 
comes so thin as to be liable to be crushed by the 
forces that act upon it. 
In animals we find that the smaller classes 
have bones far more slender in proportion than 
those of the larger kinds. Their muscles are far 
less thick in proportion to their length; and 
their masses are diminished in a proportion 
much more rapid than that of the cubes of their 
similar dimensions. We find small animals ca- 
pable of lifting weights greater in proportion to 
those of their own bodies, than larger animals 
can; and in spite of this additional effort, they 
are enabled to continue their exertions for a 
longer period without fatigue. To obtain the 
greatest possible strength with the least possible 
weight, the bones of animals have the form of 
hollow tubes, as have the quills and feathers of 
birds. In the vegetable kingdom, we find trees 
and plants made up of bundles of hollow tubes ; 
and in those where great strength and com- 
parative lightness are necessary, these are again 
arranged so as to form a hollow cylinder ; 
as, for instance, in the whole family of the gra- 
mina. 
(4.) When beams are in an inclined position, 
their strength, which we shall call F, becomes 
K—W cos. 7. This deduction from the hypothe- 
sis is true in practice, so long as the beam does 
361 
not bend under the effort of the weight applied 
to break it. 
(5.) When the pressure, instead of acting upon 
a single point, at the extremity of a beam fixed 
at one end, or in the middle of a beam supported 
or fixed at both ends, is equally distributed 
throughout the whole beam, twice the weight 
will be required to break it. 
As far as we have recited the results of the 
hypothesis, they agree in all useful cases with 
the deductions from experiment. But some of 
the rules, deduced from the hypothesis, do not 
coincide with what occurs in practice. 
Thus it has been shown that there is a differ- 
ence in the strength of triangular beams, accord- 
ing to their position, with an edge or a face up- 
permost ; and that this difference follows differ- 
ent laws, according to the manner in which the 
beam is supported. Experiment absolutely con- 
tradicts this ; for in neither of the three differ- 
ent positions in which beams have been tried, 
has any important difference been found in the 
strength of a triangular beam, when placed with 
an edge, or with a face uppermost. 
So also, hollow cylindric beams have not been 
found stronger, when the cavity has been nearer 
to the side where the fracture terminates, as 
they ought to be in conformity with hypothesis ; 
neither is a square beam stronger when its dia- 
gonal is vertical. 
These remarkable discrepancies, together with 
the less important ones that have been noted in 
the preceding section, arise from an omission in 
the hypothesis ; this does not take into account 
the elasticity and consequent flexure which ma- 
terials undergo before they actually break. 
Table of the respective strength of various substances. 
Metals. 
Wrought iron, Swedish, . 22,000 lbs. 
do. English, 18,000 lbs. 
Cast iron, is 4 16,000 lbs. 
Wood. . 
Teak, : ° : : : 4,900 lbs. 
Ash, rs 3 : : 4 ~ 4,050 
Canada Oak, : 5 3,500 
English Oak, 3,300 
Pitch Pine, 3,250 
Beech, . 5 3,100 
Norway Fir, oe ates 2,950 
American White Pine, 2,200 
Elm, : : 1,013 
We are without any good experiments on the 
respective strength of stone. It would, however, 
appear from some experiments of Gauthey, that, 
in soft freestone, 
s = 68 7 lbs. 
In hard freestone, 
s = 72°75 lbs. 
And from some experiments recorded by Barlow, 
that in brick, 
s = 64 lbs. 
This would make the respective strength of 
stone and brick far beneath that of wood or 
iron. 
