When a ball, attached to a centre by a flexible cord, is put in motion by any one force, which, in common with all other forces, acts in a right line, the motion will be circular. The tendency which such body has to fly from the centre, is called the centrifugal force; and that exerted by the cord to draw it towards the centre, the centripetal force.

When a body is set in motion by any force, it is enabled, to a certain extent, to act on other bodies, and create motion in them; and, as the velocity it obtained was as the power expended to create that motion, so is the power of transmitting that motion to its velocity. This power of communicating motion, or, in other words, this force possessed by matter in motion, is termed momentum, or the moving force; and the mode of transmitting it, impact: as this force is proportional to the velocity possessed by every particle of matter composing any body, the momentum must be represented by the quantity of matter multiplied by its velocity. For instance, suppose one hundred particles of matter were moving at the rate of one foot per second, the power requisite to overcome their force is exactly the same as that which would be necessary to arrest the motion of one particle moving at the rate of one hundred feet per second: for the velocity of the hundred particles being one foot per second each, their total force would be the force existing in one of them multiplied by one hundred: and again, as the force is in proportion to the velocity, one particle moving at the rate of one foot per second, multipled by one hundred in regard to velocity, will produce a similar result. Also, if a body of one pound weight be moving at the rate of one foot per second, it will possess a certain momentum, and if either its weight or its velocity be doubled, its momentum will be likewise doubled: if both be doubled, the momentum will be quadrupled.

Having now considered the action of one and two forces acting together in opposite and similar directions, we will proceed to examine the action of two forces upon a body, acting neither in the same, nor in contrary directions. Thus, if the line A B, fig. 4, represent a force sufficient to carry the body A to the point B, and AC represent another force sufficient to carry the body A to the point C, then AC and AB being equal to CD and BD, and those two forces act upon the body subsequently to each other, we may conceive that the body would, by passing over the lines A B and B D, or AC and CD, be carried to the point D. Now, if they act upon the body at the same instant,

the result will be the same, and the total expenditure of the forces will place the body, passing by the line AD, at the point D. Likewise, if the forces A B and A C be not at right angles, as in fig. 5, still as CD and BD are equal, and in similar directions to A B and A C, the motion received from them by A will be represented in amount and direction by the line A D. But supposing A B shall be twice or thrice the power of A C, then the effect will be the same as is shown in fig. 6, where the line AB represents thrice the power of A C. The separate actions of A B and AC will be represented as before by BD and CD, which would place the body A at the point D; therefore their combined force will cause it to pass by the diagonal line AD, as in the former instance. This proves that any number of forces acting upon a body in however many lines, not directly opposite to each other, will be compounded into one force: for suppose three forces, A B, AC, and A F, fig. 7, to operate in their several directions at the same instant, on the body A, they will be compounded into the force represented by A I; for if we describe a parallelogram as before by the lines A B and AC, those two forces will be compounded into a force represented by A D; and again, if we do the same with the two forces AC and A F, we shall have the force A H composed of them. We have therefore two forces A D and AH compounded of the three original forces. If we proceed with these two in the same manner, they will be compounded into the force represented by AI; DI and HI completing the parallelogram of which AI is the diagonal: so that any number of forces acting in any number of directions, excepting in opposite ones, may be compounded into one, which is termed their composant, and which is always represented by the diagonal of a parallelogram, like that already shown.

The resolution of forces is exhibited by reversing this problem; for as any number of forces may be combined into one force, so may one force be resolved into any number. If a single force be represented by a ball moving with a certain velocity in the direction of the line A B, fig. 8, when it shall come in contact with and act upon the balls C and D, these two balls will each of them move with one half of the velocity with which B was impelled, and in the direction of the lines C H and DI, drawn from the centre of B through each of their centres so that if the force of B be divided into two equal portions, each of those portions may, by a similar process, be again divided, resolving the original force to infinity.

The next effect of forces upon bodies producing motion, is that in which a body receives motion from one force, whilst it is under the continuous action of another force, not acting upon it in an opposite direction. Suppose the ball A, fig. 9, to be ejected from the mouth of a cannon, the instant it has left it at A, it will be under the influence of the force of gravitation, which will cause it to descend towards the earth in the manner already shown when speaking of accelerated motion, and ultimately will bring it to a state of rest at the point B: for supposing that the ball, by the force of the powder, leaves A, and travels in the first second of time a given number of feet, expressed by the line A C, the gravitating force during such action will cause it to descend sixteen feet, expressed by the line C D; and during the next second, supposing the powder to have impelled it the distance expressed by the line D E, the gravitating force will cause it to fall forty-eight feet, as is shown by E F; and during the next portion of its horizontal motion, expressed by F G, its descent by gravitation will amount to eighty feet, represented by G B. The line, therefore, in which the body would move when acted upon by these two forces only, would be that of a parabolic curve; but as the resistance of the air is to be taken into account in all practical cases, the line of motion changes very considerably, and assumes one that involves a problem of exceeding complexity; which, together with many other results of the effects of combined forces, is of such intricacy as to demand much more room for their solution than the limits of this work will permit us to give.

OF FRICTION.

THE surfaces of bodies, however smooth they may appear to be, will be found, upon a minute inspection, to possess certain irregularities: so that if the body A B, fig. 10, have to move upon the surface of the body CD, and the lower surface of A B possesses prominences which enter into cavities in CD, it is manifest that A B cannot be moved along unless it either rises and falls the height of the several prominences, or breaks them off: in the first, it will have to overcome the attraction of gravitation; in the second, the attraction of cohesion. Again, if the body A B, fig. 11, be placed between CD and E F, which are pressed against its sides by any applied force, and their surfaces be similar to those in the former instance, to effect the movement of A B, the attraction of cohesion must be overcome, as before shown, or the applied force must be conquered. Such is the

almost universal nature of that resistance called friction; for although the irregularities upon the surfaces of bodies are by no means so manifest as those here represented, still, upon minute examination, we are enabled to discover that the smoothest surfaces contain them; and as the amount of resistance increases in direct proportion as the irregularities present themselves, we are warranted in concluding that all resistance arising from friction owes its origin solely to this cause.

OF THE MECHANICAL POWERS.

THE mechanical powers are six in number, the LEVER, the WHEEL and AXLE, the PULLEY, the INCLINED PLANE, the WEDGE, and the SCREW. A perfect knowledge and thorough appreciation of which should be clearly understood by those who purpose to examine into the effects of mechanical combinations; the whole of which, however intricate, originate from, and are reducible to, one or more of the laws which govern these simple machines.

In demonstrating the mechanical powers, that which is not strictly true must be admitted: the force of gravitation, the retardation of friction, the resistance of the atmosphere, and the irregularity arising from the partial elasticity of the substances of which they are formed, must be excluded, and supposed not to exist.

The first-mentioned power is the lever, which is divided into three classes. In fig. 12, A B is a lever, and C the fulcrum, or immovable point on which it rests: now, if a force be applied at B, and the resistance, or the force or weight to be overcome, is at A, then, with the fulcrum so situate between the forces, it is called a lever of the first class; and the operation of the force at B to overcome the resistance at A, will be in proportion as the distance A C is to the distance BC; that is to say, if B C be four times the distance of A C, the force applied at B will be exactly equal to four times the same amount of force at A; or one pound weight at B will counterbalance four pounds weight at A; but to whatever height (suppose one foot) the weight at A be raised, B must descend four times that space, and consequently, to place B in its original position, the force applied must be equal to the raising of four single pounds one foot each, which is the same as the raising of four pounds one foot, as was effected at A.

An actual gain of power does not exist, but the gain in convenience is great; for, by the operation of one pound, four pounds is moved, which, but for the invention of the

lever, could not have been effected. A man whose utmost strength could lift no more than one hundred and fifty pounds is by this means rendered capable of giving motion to four times that weight, although he is obliged to exert his strength through four times the distance. A lever of the second class may be represented by supposing A to be the fulcrum, B the force applied, and C the weight, or resistance to be overcome. The effect of this lever must be estimated by comparing the distances C B to A B; the power will increase or diminish exactly in proportion as A B exceeds C B, and the distance that B moves through will increase exactly in the same proportion.

Suppose, in reference to the same figure, C to be the force applied, A the fulcrum, and B the resistance, it will then represent a lever of the third class. The effect of levers of this class is to lose power for the purpose of gaining either motion or distance. For if, in the last mode, the power applied at B increased as the length of AB became greater than CB, it is plain that in the present case, the resistance at B is placed in a position to gain by the same law: therefore, the nearer the force is placed to B the greater will be the effect; and when applied at B, the greatest; but when the force is at B, it is applied direct to the resistance, and the lever is abandoned; consequently C, in every position between A and B, loses power to a greater or less extent. As the movement of C, in the last case, was one half that of B, so in the present case will the movement of B be twice that of C.

In particular operations, levers of each of these classes have their particular uses. The simplest application of the first sort may be seen in scissors, shears, forceps, &c. the pin in the joint is the fulcrum, the hand is the force applied, and the substance to be cut or pinched is the resistance to be overcome; the second sort of lever is presented to us in the cutting knives used by last-makers, where the band is the power, the ring into which the other end of the knife is hooked is the fulcrum, and the object to be cut is the resistance. Common fire-tongs are levers of the third class, as they possess a capability of being extended at the extremities in using them the motion of the hand produces, perhaps, six times its own motion in the extremities, and a loss of power exists in a similar proportion; but as they have to be used only for a short period, the loss of power is of less importance than the convenience gained. This last class of lever is frequently introduced in machinery,