diagonal of the parallelogram. The same law holds good, whatever be the inclination of the forces; and hence we have the general principle, that a body, acted upon by two forces, describes the diagonal of a parallelogram, the sides and angles of which represent the intensity and direction of those two forces; and will do this in the same time in which, by the action of one of the forces, it would have described a side, and with a uniform velocity.

From this principle we see how, in machinery, we may substitute two forces, acting at angles, instead of a single force; or, on the other hand, how we may substitute one force instead of two, three, four, or more, forces. Suppose we have three forces, and wish to find one which will produce the same effect. We must determine its direction and intensity. To do this, we take the lines representing two of the forces, and construct a parallelogram from them; and, in the diagonal, we have a single force equivalent to the two. Taking this diagonal, with the third force, we construct another parallelogram; and the diagonal of this last parallelogram will give us the equivalent of all the three forces, and will represent its intensity and direction.

CENTRE OF GRAVITY.

One of the most interesting applications of this principle is, in investigating the properties and determining the place of that point in a body, which is called its centre of gravity. The several particles of matter in a body being solicited by gravity, we may consider it as acted upon by a great many different forces, which, if reduced to one, will always pass (whatever be the position of the body) through a certain point in it, around which its parts seem to balance each other, and which, if supported, will give support to the whole fore, the body, at the end of a second, must be both in the vertical line, C E, and in the horizontal one, D E, that is, at E, their point of intersection; and must have described, during this instant of time, the diagonal line, B E.

mass.

The stability of edifices and other masses of matter depends, therefore, on the position of their centre of gravity. If a line, drawn from this centre, perpendicular to the horizon, falls within the base, the body will evidently stand; and its stability will be greater, the further that line falls from the side of the base; so that the stability is greater, in proportion to the size of the base, as compared with the perpendicular height of the centre of gravity. If it falls without the base, the body will fall instantly; if upon the side of the base, the body will stand with what is termed unstable equilibrium, and be overthrown by the application of the slightest force.

Fig. 2.

Where bodies, like carriages, are to be moved, and are subject to inclinations, towards one side and another, it is necessary to place the centre of gravity low; otherwise, a slight inclination will throw the perpendicular line without the base, and cause the body to be overthrown. In Fig. 2, A B represents a wagon, on the slope of a hill; C D represents the level of the ground; E F the base of the wagon and the slope of the hill. If the wagon be so laden, that the centre of gravity be at B, the perpendicular, B E, will fall within the base, and the wagon will stand. But if the load be so altered, that the centre of gravity be raised to A, the perpendicular, A C, will fall outside of the base, and the wagon be overset. The difficulty which the young child finds, in walking, arises principally from his inability to keep the centre of gravity of his body over the base. Quadrupeds have, in this respect, an advantage over the young of other animals.

C

E

D

To determine the position of the centre of gravity in a body is important, on many accounts; but especially, because, when a force is to be applied to a body to move it, it should be made generally to pass through the centre; otherwise, a rotary as well as progressive motion would be communicated to the body.

There is a third law of motion, which is generally called the principle of action and reaction. It consists in the fact, that, to every action of one body on another, there is an equal and contrary reaction. That is, in other words, if I strike a blow with my fist, the fist receives just as severe a blow as it inflicts. If one vessel, under full sail, strike against another, at rest, it receives a shock just as great as that which it communicates. It is on this principle that a bird is able to support itself in the air, by beating with its wings against the air below. This air, being struck, reacts against the body of the bird, with a power sufficient to keep it in its place, or to enable it to rise and fall, at pleasure.

CHAPTER III.

MECHANICAL AGENTS CONTINUED.

HAVING Considered the three fundamental laws of motion, we now proceed to the forces, which may be employed to produce motion. They are of two kinds, animate and inanimate.

ANIMATE FORCES.

The animate forces consist of the strength of men and animals. As this depends upon the principle of life, respecting which we are entirely ignoránt, and as the strength of an animal is influenced by his constitution, state of health, the climate in which he lives, and various other causes, it is impossible to ascertain the laws which regulate it, as accurately as we can ascertain those which regulate inanimate forces. Still, many experiments and calculations have been made, and principally to ascertain the most advantageous modes in which an animal can be worked; the velocity and load with which he can work most effectively or permanently; the relative strength of different

animals; and the comparative economy of using them. It has been ascertained,

1. That the most advantageous method of employing the strength of a horse is in the act of drawing a load; and the least advantageous, in carrying a load, especially up hill: while, as one might infer from the perpendicular position and structure of his body, the reverse is the case with man, and that rowing is, perhaps of all ways of applying human strength, the most effective.

2. That an animal will work most effectively, from day to day, if his velocity be small and his load large; that the working rate ought never to be more than one half, nor generally more than one third, of the greatest velocity with which the animal can travel without load; and that, with this velocity, his load should never be more than four ninths of the greatest which he can bear. Thus, if the greatest speed with which a horse can travel, without a load, be twelve miles per hour, and the greatest load which he can carry, without moving, be four hundred pounds, he will work, permanently, with most advantage, when his rate of going is four miles an hour, and his load about one hundred and eighty pounds.

3. That a horse can exert an effective force, from day to day, equal to that of six men; and an elephant, a force equal to six horses: and,

4. That, considering the expense of keeping a horse, which is not greater than that of keeping a man, nor more than one sixth of that of keeping an elephant, his fitness for different kinds of service and any kind of road, and his uniting fleetness with strength, he possesses a great advantage, in regard to economy and convenience, over every other animal,* for general use. In regard to employing human force, or, in other words, the strength of men, it is obvious,

* Exception must be made, in particular climates, in favor of the camel, mule, &c.; and, in our own country, the ox is to be preferred, for farm-labor.

1. That it is of all forces the most expensive,—since it costs as much to feed a man as a horse, while he can perform only one sixth part of the service.

2. It is the least convenient, since the power of the individual is confined within very narrow limits, both of speed and strength; and, in many kinds of work, it is impossible to employ a large number of men together. It is obvious, for example, that no number of men would be able to drag a stage-coach, at the rate of twelve miles an hour; and, to show the comparative inefficiency of human labor, in another way, we may mention the statement of Homer, that twelve women had to be constantly employed at the hand-mills, in the house of Ulysses, in order to grind corn enough for his family, a work which might have been performed by a very small stream of water, or by a single horse.

3. Human force, when exercised without intelligence, has a degrading influence on the mind and heart. Hence, wherever we can substitute animal or other brute force for that of men, we are bound to do it, that the power of the latter may be reserved for cases, in which they can exert intelligence and skill, and have scope for the exercise of their moral affections. Freemen revolt at the idea of being chained to the cars of the wealthy or powerful; or at taking the place of brutes, in the plough or at the mill. Should they not be equally anxious to avoid other occupations, which exert no healthful influence on the character, and which could be performed with as much effect, and with greater economy, by animals, or even by inanimate forces? Examples of such occupations may be found in churning, threshing, hayraking, spinning, weaving, &c. &c.

INANIMATE FORCES.

Under this head are included, gravity, water, wind, steam, &c., which may all be referred, indirectly, to three sources; to wit, gravity, elasticity, and heat.