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    The question has been raised as to whether the iiis were open at both ends or not.Those acquainted with the theory of the vibration of tubes will readily admit that they were

    stopped at one end, for the following reasons.

    Sound in a tube, open or not, is produced by the vibrating movement of the air, andthe sound will vary in pitch accordmg to the degi-ee of pressure of the air. The different

    notes so produced are called harmonics. The longer and narrower the tube, the more harmonicsit will give.

    A long tube open at both ends will give the following harmonics, which are markedI, 2, 3, etc, according to their place in the succession of sounds.



    -.i 456789 etc.A tube closed at one end \vill give only the harmonics marked with odd numbers, with

    this important peculiarity, that to produce the same note this tube requires only half the lengthof an open tube.

    m ^ ^e-


    1 1 etc.

    The Hrst Inumg-chang tube measured only i foot. An open tube of that size wouldscarcely give any sound, whereas a corked tube i foot long gives the same note as an opentube 2 feet long. Moreover, the tubes of the Pandean pipe, which was a collection of bamboosmade on the principle of the lus, were closed at the lower end.

    To their series of 12 lils the Chinese added two new series, one lower and one higher.The lils were used merely to regulate the instruments and give a uniform pitch to themusic. The diameter of all the las must be the same.' Meng K'ang (^ ^) says that the