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HANDBOOK OF ACOUSTICS. 

Chapter IV. Thus, to prove the first law, stretch the wire by attaching any sufficient weight, as shown in fig. 23, and observe the pitch of the tone it then gives. Now place the movable bridge in the centre, pluck the half string and again note its pitch. Do the same with of the wire. It will be found that the
tones produced are as follows, calling the tone produced by the whole length, d,
Now we already know, that the ratios of the vibration numbers of these tones are those given in the third column, and we at once see that these latter are the inverse of those in the first column. This experiment may be varied in an infinite number of ways. Thus, by placing the movable bridge so that the lengths of the string successively cut off, are, 







it will be found, that these lengths give the notes of the diatonic scale, and the vibration ratios of the successive intervals of these from the tonic, we already know to be 







which numbers are the former series inverted. Illustrations of this law may be seen in musical instruments with fixed tones, like the piano and harp, in which the strings, as every one knows, become shorter and shorter as the notes rise in pitch. In the guitar, violin, and other instruments with movable tones, variation in pitch is obtained, by varying the length of the vibrating portion of the string.
The second law may be verified, by stretching on the Sonometer, with equal weights, two wires of the same material, the diameter of one of which is, however, twice that of the other. The tones produced will be found to be an octave apart, the smaller wire 
