The law of linear dimensions may be thus stated: The vibration-periods of two similarly circumstanced homologous bodies are to each other as their cubical contents, and therefore the vibration-frequencies of homologous metal plates are to each other as the inverse ratio of their linear dimensions. The octave of a given plate will be a homologous plate having 1/8 of its volume. A circular disk twenty inches in diameter and one inch thick vibrates, e.g., 1024 times per second. The ten octaves from unity successively reducing the size of the disk by 1/8, we get at each reduction the octave of the previous pitch, and at any given octave we have the volume, weight, and vibration-frequency of the vibrating atomic substance.
Ten octave, 1024 vibrations per second; metal disk, twenty inches in diameter, one inch thick. To get the cubical contents of this vibrating aggregate it is necessary to square the diameter; we multiply by 0.7854, which is equal to 314.16 inches in volume. Starting from this point, we progress through successive octaves upward, increasing in pitch and diminishing in size. Keely, Dashed Against the Rock
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