to be moving in a circular path, around a center to which it is firmly held; and let us, moreover, suppose the impelling force, by which the body was put in motion, to have ceased; and, also, that the body encounters no resistance to its motion. It is then, by our supposition, moving in its circular path with a uniform velocity, neither accelerated nor retarded. Under these conditions, what is the force which is being exerted on this body? Clearly, there is only one such force, and that is, the force which holds it to the center, and compels it, in its uniform motion, to maintain a fixed distance from this center. This is what is termed centripetal force. It is obvious, that the centripetal force, which holds this revolving body to the center, is the only force which is being exerted upon it.

Where, then, is the centrifugal force? Why, the fact is, there is not any such thing. In the dynamical sense of the term "force," the sense in which this term is always understood in ordinary speech, as something tending to produce motion, and the direction of which determines the direction in which motion of a body must take place, there is, I repeat, no such thing as centrifugal force.

There is, however, another sense in which the term "force" is employed, which, in distinction from the above, is termed a statical sense. This "statical force" is the force by the exertion of which a body keeps still. It is the force of inertia--the resistance which all matter opposes to a dynamical force exerted to put it in motion. This is the sense in which the term "force" is employed in the expression "centrifugal force." Is that all? you ask. Yes; that is all.

I must explain to you how it is that a revolving body exerts this resistance to being put in motion, when all the while it is in motion, with, according to our above supposition, a uniform velocity. The first law of motion, so far as we now have occasion to employ it, is that a body, when put in motion, moves in a straight line. This a moving body always does, unless it is acted on by some force, other than its impelling force, which deflects it, or turns it aside, from its direct line of motion. A familiar example of this deflecting force is afforded by the force of gravity, as it acts on a projectile. The projectile, discharged at any angle of elevation, would move on in a straight line forever, but, first, it is constantly retarded by the resistance of the atmosphere, and, second, it is constantly drawn downward, or made to fall, by the attraction of the earth; and so instead of a straight line it describes a curve, known as the trajectory.

Now a revolving body, also, has the same tendency to move in a straight line. It would do so, if it were not continually deflected from this line. Another force is constantly exerted upon it, compelling it, at every successive point of its path, to leave the direct line of motion, and move on a line which is everywhere equally distant from the center to which it is held. If at any point the revolving body could get free, and sometimes it does get free, it would move straight on, in a line tangent to the circle at the point of its liberation. But if it cannot get free, it is compelled to leave each new tangential direction, as soon as it has taken it.

This is illustrated in the above figure. The body, A, is supposed to be revolving in the direction indicated by the arrow, in the circle, A B F G, around the center, O, to which it is held by the cord, O A. At the point, A, it is moving in the tangential direction, A D. It would continue to move in this direction, did not the cord, O A, compel it to move in the arc, A C. Should this cord break at the point, A, the body would move; straight on toward D, with whatever velocity it had.

You perceive now what centrifugal force is. This body is moving in the direction, A D. The centripetal force, exerted through the cord, O A, pulls it aside from this direction of motion. The body resists this deflection, and this resistance is its centrifugal force.

Fig. 1

Centrifugal force is, then, properly defined to be the disposition of a revolving body to move in a straight line, and the resistance which such a body opposes to being drawn aside from a straight line of motion. The force which draws the revolving body continually to the center, or the deflecting force, is called the centripetal force, and, aside from the impelling and retarding forces which act in the direction of its motion, the centripetal force is, dynamically speaking, the only force which is exerted on the body.

It is true, the resistance of the body furnishes the measure of the centripetal force. That is, the centripetal force must be exerted in a degree sufficient to overcome this resistance, if the body is to move in the circular path. In this respect, however, this case does not differ from every other case of the exertion of force. Force is always exerted to overcome resistance: otherwise it could not be exerted. And the resistance always furnishes the exact measure of the force. I wish to make it entirely clear, that in the dynamical sense of the term "force," there is no such thing as centrifugal force. The dynamical force, that which produces motion, is the centripetal force, drawing the body continually from the tangential direction, toward the center; and what is termed centrifugal force is merely the resistance which the body opposes to this deflection, precisely like any other resistance to a force.

The centripetal force is exerted on the radial line, as on the line, A O, Fig. 1, at right angles with the direction in which the body is moving; and draws it directly toward the center. It is, therefore, necessary that the resistance to this force shall also be exerted on the same line, in the opposite direction, or directly from the center. But this resistance has not the least power or tendency to produce motion in the direction in which it is exerted, any more than any other resistance has.

We have been supposing a body to be firmly held to the center, so as to be compelled to revolve about it in a fixed path. But the bond which holds it to the center may be elastic, and in that case, if the centrifugal force is sufficient, the body will be drawn from the center, stretching the elastic bond. It may be asked if this does not show centrifugal force to be a force tending to produce motion from the center. This question is answered by describing the action which really takes place. The revolving body is now imperfectly deflected. The bond is not strong enough to compel it to leave its direct line of motion, and so it advances a certain distance along this tangential line. This advance brings the body into a larger circle, and by this enlargement of the circle, assuming the rate of revolution to be maintained, its centrifugal force is proportionately increased. The deflecting power exerted by the elastic bond is also increased by its elongation. If this increase of deflecting force is no greater than the increase of centrifugal force, then the body will continue on in its direct path; and when the limit of its elasticity is reached, the deflecting bond will be broken. If, however, the strength of the deflecting bond is increased by its elongation in a more rapid ratio than the centrifugal force is increased by the enlargement of the circle, then a point will be reached in which the centripetal force will be sufficient to compel the body to move again in the circular path.

Sometimes the centripetal force is weak, and opportunity is afforded to observe this action, and see its character exhibited. A common example of weak centripetal force is the adhesion of water to the face of a revolving grindstone. Here we see the deflecting force to become insufficient to compel the drops of water longer to leave their direct paths, and so these do not longer leave their direct paths, but move on in