they exist, giving those delicate and ethereal qualities which characterize the various sounds of Nature and of music.

HOW THE EAR ANALYZES A COMPOUND SOUND INTO ITS SIMPLE SOUNDS.

The experiments with the piano serve to explain the wonderful power of the ear in analyzing compound sounds. In the cochlea (snail-shell, C of Fig. 4) of the ear are supposed to exist co-vibrating fibres which are tuned to simple sounds extending over several octaves. To each tuned fibre is fastened a fine filament of the auditory nerve. A simple sound is only given by a pendular vibration. A compound sound is a sensation made by several pendular vibrations of various frequencies entering the ear together. If one pendular vibration enters the ear it vibrates the nerve-filament fastened to the fibre which is tuned to this pendular vibration, and we have the sensation of a simple sound.

But when a compound vibration, made up of several simple pendular vibrations, enters the ear, it acts on several tuned fibres, exactly as our voice, or the sounds of the cornet or trumpet, acted on several piano-strings. Each fibre in the ear enters into vibration with that pendular vibration in the compound sound with which it is in tune. Thus the nerve-filaments are shaken which are fastened to fibres in the ear tuned to the simple sounds in the compound sound, and the sensation of the latter is thus analyzed into its simple sound sensations. What we

have just said suggests at once the question: What sort of motion has a molecule of air when it is acted on at the same time by several pendular vibrations? This is answered by

AN EXPERIMENT WHICH SHOWS THE MOTION OF A MOLECULE OF AIR, OR OF A POINT ON THE DRUM-SKIN OF THE EAR, WHEN THESE ARE ACTED ON BY THE COMBINED PENDULAR VIBRATIONS OF THE FIRST SIX HARMONICS.

We have seen, in Experiment 11, that the pendular motion may be obtained by sliding a card, with a slit in it, over the sinusoidal trace of a vibrating rod. Imagine a similar trace made by a point whose

motion is formed of the combined vibratory motions of the first six harmonics. Such is the trace drawn on the

EXPERIMENT 109.-If we slide, in the direction cd, a card with a slit in it over this trace, you will see in the slit the same vibratory motion, only much slower, that a

point of the drum-skin of the ear has when we hear a compound sound (like that of the piano-wire) which contains the first six harmonics. The student of course remembers that the direction of the length of the slit is in the direction in which the sonorous vibration is traveling through the air.

The curve on cd I obtained as follows: I drew on the line ab the six sinusoids, having their lengths as 1:2 :3 : 4:56. Another line, e d, was drawn below and parallel to a b, and then 500 equidistant lines, perpendicular to a b, were drawn through the curves on a b and extended below the line cd. On each of these vertical lines I got the algebraic sum (calling the distances above ab+ and those below cd-) of the distances of the curves above or below ed, and then transferred this sum to the corresponding vertical line passing through ed. Through the points thus found, above and below cd, I drew the curve which you see on cd.

EXPERIMENT 110.-This curious compound sonorous motion is best exhibited as follows: On a piece of cardboard draw a circle, and in one quadrant of this circle draw 500 equidistant radii. Make the length of these radii vary with the corresponding distances of the curve (Fig. 49) above and below the line e d. Join the ends of these radii with a curve. By repeating this curve four times on the cardboard you will have made the curve continuous, as is shown in Fig. 50. Now cut this curved figure out of the cardboard, and thus form a templet. Place this, centred, on a glass disk of a foot in diameter, covered with opaque black varnish. With the separated points of a pair of spring dividers scribe around the edge. of the templet, and thus remove the varnish in a sinuous band, as shown in Fig. 50.

The glass disk is now mounted on the rotator, and placed between the heliostat and a plano-convex lens, as shown on page 79 in our book on "Light" of this series. A magnified image of that portion of the curve which is in front of the heliostat is thus obtained on a screen.

A

piece of cardboard, having a narrow slit cut in it, is now placed close to the disk and in the direction of its radius. Revolving the disk you will have on the screen a vibratory motion like that which a molecule of air, or a point on the drum-skin of the ear, has when these are acted on

by the combined pendular vibrations of the first six harmonics of a musical note.

screen.

On slowly rotating the disk one can readily follow the compound vibratory motion of the spot of light on the On a rapid revolution of the disk the spot appears lengthened into a luminous band, but this band is not equally illuminated. It has six distinct bright spots in it, beautifully showing the six bends in the curve on the disk.

EXPERIMENT 111.-The student, however, need not go to the expense of buying the glass disk. He is able, no doubt, to copy on a cardboard the curve, about three times as large as Fig. 50, and then, turning it on the rotator before a slit in a card, he may study at his leisure this curious motion. He can even get this motion directly from the figure in his book by sticking a pin in the centre of Fig. 50, and about this revolving a card with a fine slit in it.

EXPERIMENTS BY WHICH COMPOUND SOUNDS ARE ANALYZED BY VIEWING IN A ROTATING MIRROR THE VIBRATIONS OF KÖNIG'S MANOMETRIC FLAMES.

Take a piece of pine board, A, Fig. 51, 1 inch (25 millimetres) thick, 14 inch (38 millimetres) wide, and 9 inches (22.8 centimetres) long. One inch from its top bore with an inch centre-bit a shallow hole inch deep. Bore a like shallow hole in the block B, which is inch thick, 14 inch wide, and 2 inches (51 millimetres) long. Place a 4-inch centre-bit in the centre of the shallow hole in A and bore with it a hole through the wood. Into this fit a glass or metal tube, as shown at E. Bore a 3-inch (5 millimetres) hole obliquely into the shallow hole in B, and into this fit