132 KENNELLY-TAYLOR— EXPLORATIONS OVER [April 22, 



where 



jQ^{kr) stands for {/^{kr))^. 



But M = Trp'a^ is the total mass of the vibrating diaphragm area. 





+ ^ {Jo{'ika)Ji{ka) — iJo(ka)Ji{ika)} . 



ak 

 Applying the ratios of (6) Appendix I., this reduces to: 



w I , , 



M (i+X)2 

 I 



2/0^(3.196) 



(1-05571)' 

 _ 0.20378 

 ~ 1.1145 

 = 0.18285 



or, to three significant digits, 0.183. 



The "equivalent mass coefficient," 0.183, for this diaphragm, 

 had also been obtained by quadrature methods applied to the heavy 

 curve in Fig. iB^ before the integration was performed as above. 



In the case of steel telephone diaphragms excited by bipolar 

 electromagnets, the curves of w,-, r are likely to depart from simple 

 Bessel-function curves, see Fig. 14. In such cases, the coefficient 

 of equivalent mass must be deduced from the exploration curve. In 

 cases examined, this coefficient varied between 0.2 and 0.5. 



A quadrature method employed to find the equivalent mass 

 coefficient from curves of any shape is as follows : 



Draw the w,- curve as in Fig. iB. Divide the line of abscissas 

 into an integral number n of annular rings of equal area; so that 

 each ring will have a mass of M/n, where M is the total mass of the 

 circular vibrating area of the diaphragm, in grams. We then 

 multiply this annular mass into the square of the observed ampli- 

 tudes at the middle points of the successive annuli. The sum of 

 these terms will be equal to the product of the equivalent mass m, 



