But _A B_ is always the same, whatever the side deflection or displacement of the pendulum may be. Whence then we see that when a pendulum is pulled aside a distance _E B_ (which is always equal to _A D_), then the force tending to bring it back to _E_ is always proportional to _E B_. But if the pendulum be fairly long, say 39-1/7 inches, and the displacement _E B_ be small,—in other words, if we do not drag it much out of the vertical,—then we may say that the force tending to bring it back to _F_, its position of rest, is not very different from the force tending to bring it back to _E_. But _F B_ is the “displacement” of the pendulum, and, therefore, we find that when a pendulum is displaced, or deflected, or pulled aside a little, the amount of the deflection is always very nearly proportional to the force which was used to produce the deflection. This important law can be verified by experiment. If _C_ is a small pulley, and _B C_ a string attached to a pendulum _A B_ whose bob is _B_. Then if a weight _D_ be tied to the string and passed over a pulley _C_, the amount _F B_ by which the weight _D_ will deflect the bob _B_ is almost exactly proportional to _D_, so long as we only make the deflection _E B_ small, that is two or three inches, where say 39-1/7 inches is the length _A B_ of the pendulum. If _F B_ is made too big, then the line _B F_ can no longer be considered nearly equal to the arc of deflection _E B_, and the proposition is no longer true. Hence then, both by experiment and on theory, we find that for small distances the displacement of a pendulum bob is approximately equal to the force by which that displacement is produced. But if so, then from what has gone before, we have an example of harmonic motion. The weight of the bob, tending to pull the bob back to _E_, acts just as an elastic band would act, that is to say pulls more strongly in proportion as the distance _F B_ is bigger. In fact, if we could remove the force of gravity still leaving the mass _B_ of the pendulum bob, the force of an elastic band acting so as to tend to pull the bob back to rest might be used to replace it. It would be all one whether the bob were brought back to rest by the downward force of its own gravity, or by the horizontal force of a properly arranged elastic band of suitable length. [Illustration: FIG. 37.]