Law of Vibratory Motions in Water and Air—Superposition of Vibrations—Interference of Sonorous Waves—Destruction of Sound by Sound—Combined Action of Two Sounds nearly in Unison with each other—Theory of Beats—Optical Illustration of the Principle of Interference—Augmentation of Intensity by Partial Extinction of Vibrations—Resultant Tones—Conditions of their Production—Experimental Illustrations—Difference-Tones and Summation-Tones—Theories of Young and Helmholtz § 1. _Interference of Water-Waves_ From a boat in Cowes Harbor, in moderate weather, I have often watched the masts and ropes of the ships, as mirrored in the water. The images of the ropes revealed the condition of the surface, indicating by long and wide protuberances the passage of the larger rollers, and, by smaller indentations, the ripples which crept like parasites over the sides of the larger waves. The sea was able to accommodate itself to the requirements of all its undulations, great and small. When the surface was touched with an oar, or when drops were permitted to fall from the oar into the water, there was also room for the tiny wavelets thus generated. This carving of the surface by waves and ripples had its limit only in my powers of observation; every wave and every ripple asserted its right of place, and retained its individual existence, amid the crowd of other motions which agitated the water. The law that rules this chasing of the sea, this crossing and intermingling of innumerable small waves, is _that the resultant motion of every particle of water is the sum of the individual motions imparted to it_. If a particle be acted on at the same moment by two impulses, both of which tend to raise it, it will be lifted by a force equal to the sum of both. If acted upon by two impulses, one of which tends to raise it, and the other to depress it, it will be acted upon by a force equal to the difference of both. When, therefore, the sum of the motions is spoken of, the _algebraic sum_ is meant—the motions which tend to raise the particle being regarded as positive, and those which tend to depress it as negative.