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V. § 59.] VIBRATIONFORMS FOR A STOPPED PIPE. 123
"Fig. 39. 



In (A) we have half a segment; in (B) a segment and a half; in (C) two segments and a half; in (D) three segments and a half. The numbers of segments into which the aircolumn is divided in these four cases are, therefore, proportional to
or to the whole numbers 1, 3, 5, 7.
Now by § 53 it appears that the rate of vibration in any form varies as the number of segments which it contains. The vibrationnumbers of the sounds produced in the present instance are, therefore, proportional to 1, 3, 5, 7, respectively, i.e. we get the first four odd partialtones of a sound of which (A) 
