We now pass on to notice another very important matter. If we have any pendulum, or mass suspended by a spring, having therefore a certain natural period of vibration, we can set it in motion by administering to it small repeated blows or pushes. If the interval between these impulses corresponds with the natural time-period of oscillation, it will be found that quickly a very large swing is accumulated or produced. If, on the other hand, the interval between the blows does not correspond with the natural time of vibration, then their effect in producing vibration is comparatively small. This may be illustrated with great ease by means of the ball suspended by a spring. Suppose that by means of an indiarubber puff-ball I make a little puff of air against the suspended ball. The small impulse produces hardly any visible effect. Let this puff be repeated at intervals of time equal to that of the natural free period of vibration of the suspended ball. Then we find that, in the course of a very few puffs, we have caused a very considerable vibration or swing to take place in the heavy ball. If, however, the puffs of air come irregularly, they produce very little effect in setting the ball in motion. In the same manner a pendulum, consisting of a heavy block of wood, may be set swinging over a considerable range by a very few properly timed taps of the finger. We may notice another instance of the effect of accumulated impulses when walking over a plank laid across a ditch. If we tread in time with the natural vibration-period of the flexible plank, we shall find that very soon we produce oscillations of a dangerously large extent. Whereas, if we are careful to make the time of our steps or movement disagree with that of the plank, this will not be the case. It is for this reason that soldiers crossing a suspension bridge are often made to break step, lest the steady tramp of armed men should happen to set up a perilous state of vibration in the bridge. It is not untruthful to say that a boy with a pea-shooter could in time break down Charing Cross Railway Bridge over the Thames. If we suppose a pea shot against one of the sections of this iron bridge, there is no doubt that it would produce an infinitesimal displacement of the bridge. Also there is no question that the bridge, being an elastic and heavy structure, has a natural free time of vibration. Hence, if pea after pea were shot at the same place at intervals of time exactly agreeing with the free time-period of vibration of the bridge, the effects would be cumulative, and would in time increase to an amount which would endanger the structure. Impracticable and undesirable as it might be to carry out the experiment, it is nevertheless certainly true, that a boy with a pea-shooter, given sufficient patience and sufficient peas, could in time break down an iron girder bridge by the accumulation of properly timed but infinitely small blows.