those of the grave sounds; for they all have the same velocity of progress, and reach us in the same time. The melody and harmony are heard simultaneously, whatever the distance of the orchestra. The exact sensation of the piece played is felt on every side—a thing which could not take place if the high tones of the violins and flutes were transmitted more rapidly than the grave sounds of the violoncellos and contrabasses. It being thus possible to assimilate simple sounds with simple colors, we have to suppose that the number of vibrations determines the color. A luminous point produces, to emit the various colors: red, 497; orange, 528; yellow, 529; green, 601; blue, 648; indigo, 686; and violet, 728 trillion vibrations per second. Each color corresponds with a luminous film of variable thickness. The thicknesses of the several films representing the simple colors—or, what are the same, the wave-lengths of these colors—are: red, 620; orange, 583; yellow, 551; green, 512; blue, 475; indigo, 449; violet, 423 millionths of a millimetre. Red, we thus see, corresponds to the grave notes and violet to the acute notes of the musical scale. To obtain an idea of the thickness of the films corresponding to the different colors, we might take as a standard for comparison a sheet of common paper, which is about a tenth of a millimetre thick. Two hundred and fifty thicknesses of the violet film would have to be laid upon one another to produce this thickness, and one hundred and sixty of the red.
In order to explain the cause of the complex colors of natural objects we may again have recourse to the properties of vibrating motions, which, like those of the phenomena of sound, can be placed one upon another. Thus, when a cord is stretched over a sonorous box, like the string of a violoncello, we can make it all vibrate; its ends will be motionless, while the middle will vibrate with the maximum amplitude. The motionless extremities are called nodes, and the middle is a belly. We can also draw the bow across this cord in such a manner that, while vibrating as a whole, the two halves of the cord will each vibrate on its own account, following a law of individual vibration. Under these conditions a superposition of two vibratory movements is realized—that of the whole cord and that of the two halves vibrating separately. There results a complex sound formed of the fundamental sound and the superposed harmonic. It is this superposition that gives to the ear the sensation of the timbre of different sounds; the phonograph, with which everybody is acquainted, is based on this principle. The vibrations of a single membrane can reproduce several superposed vibratory movements, and thus register human speech.
Most of the complex colors, such as rose, maroon, or the various tints of green, can be formed in the same manner. They
