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74 ACCUMULATED IMPULSES. [III. §
cause the pendulum to oscillate through a larger angle [§ 19] than before, and, the effects of many impulses being in this way added together, an extensive swing of the pendulum is the result.
When the distance through which the weight travels to and fro, though in itself considerable, is small compared to the length of the supporting string the time of oscillation is the same for any extent of swing within this limit, and depends only on the length of the string. My readers will find this important principle illustrated in any manual of Elementary Mechanics, and I must ask them to take it for granted here. For the sake of simplicity, let us suppose that we are dealing with a pendulum of such a length as to perform one complete oscillation in each second, and therefore to make a single forward or backward swing in each half second. It will be clear, from what has been said above, that the maximum effect will be produced on the motion of the pendulum by applying a forward and a backward impulse respectively during each alternate half second, or which is the same thing, administering a pair of to-and-fro impulses during each complete oscillation of the pendulum. We have a simple instance of such a proceeding in the way in which two boys set a heavily-laden swing in violent motion. They stand facing each other, and each boy, when the swing is