Let us suppose a body 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.