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seen to pass undisturbed through the other series. Let the tracing AaBeC, fig. 44 represent a wave of the first series, and AdBbG one of the second series, and let the dotted straight line, AgBhC,
Fig. 44.
represent the surface of still water. In the first place consider the motion of a particle of water at g. The first wave would cause the drop to rise to a, and the second if acting alone would raise it to d. According to the fundamental laws of mechanics, each force will have its due effect and the drop will rise to the height k such that ag -\- dg = gk. Again, the drop at h, if under the influence of the first wave alone, would rise to e, but the second wave would depress it to b. Under these two antagonistic forces it falls to I, such that hi = lib he. By ascertaining in this way, the motion of each point along the wave, we can, by joining all these points, determine the form of the compound wave made up of these two elementary ones.
The same mechanical laws apply to sound waves as to water waves. Thus if the two tracings A and B, in fig. 45, be the asso­ciated wave forms of two simple tones at the interval of an octave, then C, constructed from these, in the way just explained, will be the associated wave form produced by their union; that is, C is the associated wave form of a compound tone consisting of the first two partials. We have here supposed that A and B commence together, that is, in the same phase. If we suppose the curve B to be moved to the right until the point (1) falls under the point (2), and then compound these waves, we obtain a different resultant wave form, D. If B were displaced a little more to the right, another wave form would result. Helmholtz has shown experi­mentally that, when two sound waves are compounded in different phases, although waves of different forms are obtained, yet no difference can be detected in the resulting sounds; that is, the sounds corresponding to the forms 0 and D would be exactly alike.