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M CONSTRUCTION OF WAVE-FORM. [I. § 13.
Since the second particle started one-sixteenth of a second after the first, its position in the figure will be below the initial line at a,' making the line a, a,' equal to the line 015 in Fig. 11. The next particle, which is two-sixteenths of a second behind a0 in its path, will be at a/ making a2 a2'' equal to 014 in the same figure. In this way the positions of all the points a,' a! as', &c, in Fig. 12 are determined from Fig. 11. They give us, at once, a general idea of the form of the resulting wave. By laying down more points along the line AB in Fig. 11, we can get as many more points on the wave as we please, and should thus ultimately arrive at a continuous curved line. This is the wave-form resulting from the given vibration-mode with which we started, and, since only one wave-form can be obtained from it, we infer that each different mode of particle-vibration gives rise to a different form of wave.
13. It has now been demonstrated that when a wave is produced by particles vibrating in a plane passing through its line of advance, and in paths perpendicular to that line, the amplitude of the wave is equal to the extent of particle-vibration and the length and form of the wave are determined by the rate and mode of vibration respectively. These relations were also shown to hold conversely.
We will next consider a type of oscillatory