STRENGTH

, vis, force, power.

Some authors make the Strength of animals, of the same kind, to depend on the quantity of blood; but most on the size of the bones, joints, and muscles; though we find by daily experience, that the animal spirits contribute greatly to Strength at different times.

Emerson has most particularly treated of the Strength of bodies depending on their dimensions and weight. In the General Scholium after his propositions on this subject, he adds; If a certain beam of timber be able to support a given weight; another beam, of the same timber, similar to the former, may be taken so great, as to be able but just to bear its own weight: while any larger beam cannot support itself, but must break by its own weight; but any less beam will bear something more. For the Strength being as the cube of the depth; and the stress, being as the length and quantity of matter, is as the 4th power of the depth; it is plain therefore, that the stress increases in a greater ratio than the Strength. Whence it follows, that a beam may be taken so large, that the stress may far exceed the Strength: and that, of all similar beams, there is but one that will just support itself, and nothing more. And the like holds true in all machines, and in all animal bodies. And hence there is a certain limit, in regard to magnitude, not only in all machines and artificial structures, but also in natural ones, which neither art nor nature can go beyond; supposing them made of the same matter, and in the same proportion of parts.

Hence it is impossible that mechanic engines can be increased to any magnitude at pleasure. For when they arrive at a particular size, their several parts will break and fall asunder by their weight. Neither can any buildings of vast magnitudes be made to stand, but must fall to pieces by their great weight, and go to ruin. |

It is likewise impossible for nature to produce animals of any vast size at pleasure: except some sort of matter can be found, to make the bones of, which may be so much harder and stronger than any hitherto known: or else that the proportion of the parts be so much altered, and the bones and muscles made thicker in proportion; which will make the animal distorted, and of a monstrous figure, and not capable of performing any proper actions. And being made similar and of common matter, they will not be able to stand or move; but, being burthened with their own weight, must fall down. Thus, it is impossible that there can be any animal so large as to carry a castle upon his back; or any man so strong as to remove a mountain, or pull up a large oak by the roots: nature will not admit of these things; and it is impossible that there can be animals of any sort beyond a determinate size.

Fish may indeed be produced to a larger size than land animals; because their weight is supported by the water. But yet even these cannot be increased to immensity, because the internal parts will press upon one another by their weight, and destroy their fabric.

On the contrary, when the size of animals is diminished, their Strength is not diminished in the same proportion as the weight. For which reason a small auimal will carry far more than a weight equal to its own, whilst a great one cannot carry so much as its weight. And hence it is that small animals are more active, will run faster, jump farther, or perform any motion quicker, for their weight, than large animals: for the less the animal, the greater the proportion of the Strength to the stress. And nature seems to know no bounds as to the smallness of animals, at least in regard to their weight.

Neither can any two unequal and similar machines resist any violence alike, or in the same proportion; but the greater will be more hurt than the less. And the same is true of animals; for large animals by falling break their bones, while lesser ones, falling higher, receive no damage. Thus a cat may fall two or three yards high, and be no worse, and an ant from the top of a tower.

It is likewise impossible in the nature of things, that there can be any trees of immense size; if there were any such, their limbs, boughs, and branches, must break off and fall down by their own weight. Thus it is impossible there can be an oak a quarter of a mile high; such a tree cannot grow or stand, but its limbs will drop off by their weight. And hence also smaller plants can better sustain themselves than large ones.

As to the due proportion of Strength in several bodies, according to their particular positions, and the weights they are to bear; he farther observes that, If a piece of timber is to be pierced with a mortise-hole, the beam will be stronger when it is taken out of the middle, than when taken out of either side. And in a beam supported at both ends, it is stronger when the hole is made in the upper side than when made in the under, provided a piece of wood is driven hard in to fill up the hole.

If a piece is to be spliced upon the end of a beam, to be supported at both ends; it will be the stronger when spliced on the under side of a beam: but if the piece is supported only at one end, to bear a weight on the other; it is stronger when spliced on the upper side.

When a small lever, &c, is nailed to a body, to move it or suspend it by; the strain is greater upon the nail nearest the hand, or point where the power is applied.

If a beam be supported at both ends; and the two ends reach over the props, and be sixed down immoveable; it will bear twice as much weight, as when the ends only lie loose or free upon the supporters.

When a slender cylinder is to be supported by two pieces; the distance of the pins ought to be nearly 3/5 of the length of the cylinder, and the pins equidistant from its ends; and then the cylinder will endure the least bending or strain by its weight.

A beam sixed at one end, and bearing a weight at the other; if it be cut in the form of a wedge, and placed with its parallel sides parallel to the horizon; it will be equally strong every where; and no sooner break in one place than another.

When a beam has all its sides cut in form of a concave parabola, having the vertex at the end, and its absciss perpendicular to the axis of the solid, and the base a square, or a circle, or any regular polygon; such a beam sixed horizontally, at one end, is equally strong throughout for supporting its own weight.

Also when a wall faces the wind, and if the vertical section of it be a right-angled triangle; or if the fore part next the wind &c be perpendicular to the horizon, and the back part a sloping plane; such a wall will be equally strong in all its parts to resist the wind, if the parts of the wall cohere strongly together; but when it is built of loose materials, it is better to be convex on the back part in form of a parabola.

When a wall is to support a bank of earth or any fluid body, it ought to be built concave in form of a semicubical parabola, whose vertex is at the top of the wall, provided the parts of the wall adhere firmly together. But if the parts be loose, then a right line or sloping plane ought to be its figure. Such walls will be equally strong throughout

All spires of churches in the form of cones or pyramids, are equally strong in all parts to resist the wind. But when the parts do not cohere together, then they ought to be parabolic conoids, to be equally strong throughout.

Likewise if there be a pillar erected in form of the logarithmic curve, the asymptote being the axis; it cannot be crushed to pieces in one part sooner than in another, by its own weight. And if such a pillar be turned upside down, and suspended by the thick end, it will not be more liable to separate in one part than another, by its own weight. |

Moreover, if AE be a beam in form of a triangular prism; and if AD = (1/9)AB, and AI = (1/9) AC, and the edge or small similar prism ADIF be cut away parallel to the base; the remaining beam DIBEF will bear a greater weight P, than the whole ABCEG, or the part will be stronger than the whole; which is a paradox in Mechanics.

As to the Strength of several sorts of wood, drawn from experiments, he says, On a medium, a piece of good oak, an inch square, and a yard long, supported at both ends, will bear in the middle, for a very short time, about 330lb averdupois, but will break with more than that weight. But such a piece of wood should not, in practice, be trusted for any length of time, with more than a third or a fourth part of that weight. And the proportion of the Strength of several sorts of wood, he found to be as follows:

As to the Strength of bodies in direction of the fibres, he observes, A cylindric rod of good clean fir, of an inch circumference, drawn in length, will bear at extremity 400lb; and a spear of fir 2 inches diameter, will bear about 7 ton.—A rod of good iron, of an inch circumference, will bear near 3 ton weight. And a good hempen rope of an inch circumference, will bear 1000lb. at extremity.

All this supposes these bodies to be sound and good throughout; but none of them should be put to bear more than a third or a fourth part of that weight, especially for any length of time. From what has been said; if a spear of fir, or a rope, or a spear of iron, of d inches diameter, were to lift 1/4 the extreme weight; then

The fir would bear 8 (4/5)dd hundred weight.

The rope would bear 22dd hundred weight.

The iron would bear 6 (3/4)dd ton weight.

As to Animals; Men may apply their Strength several ways, in working a machine. A man of ordinary Strength turning a roller by the handle, can act for a whole day against a resistance equal to 30lb. weight; and if he works 10 hours a day, he will raise a weight of 30lb. through 3 1/2 feet in a second of time; or if the weight be greater, he will raise it so much less in proportion. But a man may act, for a small time, against a resistance of 50lb. or more.

If two men work at a windlass, or roller, they can more easily draw up 70lb, than one man can 30lb, provided the elbow of one of the handles be at right angles to that of the other. And with a fly, or heavy wheel, applied to it, a man may do 1/3 part more work; and for a little while he can act with a force, or overcome a continual resistance, of 80l; and work a whole day when the resistance is but 40lb.

Men used to bear loads, such as porters, will carry, some 150lb, others 200 or 250lb. according to their Strength.

A man can draw but about 70 or 80lb. horizontally; for he can but apply about half his weight.

If the weight of a man be 140lb, he can act with no greater a force in thrusting horizontally, at the height of his shoulders, than 27lb.

As to Horses: A horse is, generally speaking, as strong as 5 men. A horse will carry 240 or 270lb. A horse draws to greatest advantage, when the line of direction is a little elevated above the horizon, and the power acts against his breast: and he can draw 200lb. for 8 hours a day, at 2 1/2 miles an hour. If he draw 240lb, he can work but 6 hours, and not go quite so fast. And in both cases, if he carries some weight, he will draw the better for it. And this is the weight a horse is supposed to be able to draw over a pulley out of a well. But in a cart, a horse may draw 1000lb, or even double that weight, or a ton weight, or more.

As the most force a horse can exert, is when he draws a little above the horizontal position: so the worst way of applying the strength of a horse, is to make him carry or draw uphill: And three men in a steep hill, carrying each 100lb, will climb up faster than a horse with 300l. Also, though a horse may draw in a round walk of 18 feet diameter; yet such a walk should not be less than 25 or 30 feet diameter. Emerson's Mechan. pa. 111 and 177.