180 SOUND points thus found is drawn the curve having the line c d for its axis. This curve may be regarded as the trace of the composite vibra- tion of a molecule of air, or of a point of the tympanic membrane, on a surface which moves near these points. Hence if we slide this curve along, in the direction of its axis, under a slit in a screen which allows only one point of the curve to appear at once, we shall reproduce in this slit the vibratory motion of the aerial molecule and of the point on the tympanic membrane. The writer has exhibited this mo- tion in a continuous, or rather recurring man- ner, as follows : On a piece of Bristol board he drew a circle, and in one quadrant of this circle he drew 500 equidistant radii. On these radii, as ordinates, he transferred the corre- sponding values of the same ordinates of the resultant curve of fig. 11, diminished to one fourth of their lengths. He thus deflected the axis of the curve of fig. 11 into one fourth of a circle curve ; and this, repeated four times on FIG. 12. the Bristol board, rendered the curve continu- ous and four times recurring, as shown in fig. 12. He now cut this figure out of the board and used it as a template. He placed the lat- ter centred on a glass disk 20 in. in diameter. This disk was coated on one side with opaque black varnish, and with the template and the separated points of a pair of spring dividers he removed from the glass disk a sinuous band, as shown in fig. 12. The glass disk was now mounted on a horizontal axis and placed in front of a lantern, the diameter of whose con- densing lens was somewhat greater than the amplitude of the curve. The image of that port inn of the curve which was in front of the condenser was now projected on a screen, and then a piece of cardboard having a nar- row slit cut in it was placed close to the disk, in the direction of one of its radii. On re- volving the disk he reproduced on the screen the vibratory motion of a molecule of air, or of a point on the tympanic membrane, when these are acted on by the joint impulses of the first six harmonic or pendulum vibra- tions, forming a musical sound. On slowly rotating the disk one can readily follow the compound vibratory motion of the spot of light ; but on a rapid revolution of the disk, persistence of visual impressions causes the vibrating spot to appear elongated into a band. This band is not equally illuminated ; it has six distinct bright spots in it, beautifully re- vealing the six inflections in the curve. By sticking a pin in the centre of fig. 12, as an axis about which revolves a piece of paper having a fine slit, the reader can gain some idea of the complex motion we have described. Of course it is understood that in the above ex- periment the amplitudes of the vibrations are enormously magnified when compared with the wave lengths, and that it is really only when the amplitudes of the elementary pendulum vibrations are infinitely small that the resul- tant curves we have given can be rigorously taken as representing what they purport to ; for the law of " the superposition of displace- ments" depends on the condition that the force with which a molecule returns to its position of equilibrium is directly proportional to the amount of displacement, and this condi- tion only exists in the case of infinitely small displacements ; yet the law holds good for the majority of the phenomena of sound. It is also to be remarked that in order to simplify the FIG. 18. "Resultant Curve formed by combining the curve of a musical note with that of its octave. A : A' : : 1 : J. consideration of the curves, they are all rep- resented with the same phase of initial vibra- tion. Of course the resultants have an infinite FIG. 14. Resultant Curve formed by combining the curve of a musical note with that of its fifth. A : A' : : 1 : |. variety of form, depending on the differences in their initial phases, and on the amplitude of I the harmonic elements. In figs. 13, 14, and
