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18 TRANSVERSE VIBRATIONS. [I. §9.
Let the 17 spots lying equidistantly along the dotted straight line at the head of Fig. 7 represent as many particles of an elastic string stretched between fixed points of attachment not shown in the figure. These particles are about to vibrate in straight lines perpendicular to the direction of the string. (0) shows the state of things when the particles plot out two complete waves A and B. The distinction between 'crest' and 'trough' has now disappeared. All that can be said is that each wave is formed of two protuberances lying on opposite sides of the undisturbed position of the string, which replaces the 'level-line' of the water-waves and is, like it, represented by a dotted line in the figure.
By looking along 0 from left to right the reader will notice that each particle occupies in its own path a position one-eighth of a period of vibration behind that of the particle next to the left of it. (Compare p. 15). (1), (2), (3)...8how the positions of the particles after one-eighth, two-eighths, three-eighths... of a complete period of particle-vibration. By following any one of the vertical lines of spots it will be seen that in the instance selected for this figure, each particle moves more rapidly in the neighbourhood of its undisturbed position than it does near the extremities of its swing. In (8) the particles have