THEORY OF VIBRATIONS 33 



in the notation of 12 (3). The second factor has its maximum 

 value 1/fi when p = n, and evidently diminishes more rapidly, 

 as p/n deviates from unity, the smaller the value of 0. The 

 question may be conveniently illustrated graphically by con- 

 structing a curve which shall shew the dissipation corresponding 

 to different frequencies. As regards the abscissa, it would in 

 strictness be most proper to take, not the ratio p/n, but its 

 logarithm, since equal intervals (in the musical sense) then 

 correspond to equal lengths of the axis of x. We might 

 therefore write 



,(3) 



but when, as usually happens, the sensible resonance is confined 

 to a small range of p/n, we may use the simpler formulae 



ft 



Hr* 



1 



.(4) 



The curve represented by the latter equation is symmetrical 

 about the axis of y, and approaches the axis of x asymptotically 

 as x increases. It is evident that if $ be increased in any 



ratio, the new curve is obtained by increasing all the abscissae in 



that ratio, and diminishing the ordinates in the inverse ratio, 



the area (TT) included between the curve and the axis of x being 



L. 3 



