1915] SURFACES OF TELEPHONIC DIAPHRAGMS. 119 



when the nodal diameter disappeared and gave place to a single 

 nodal circle. The ratios of the above three frequencies are i : 1.97: 

 3.44; whereas, according to the Bessel-function theory, they should 

 be 1:2.09:3.91. The discrepancies may readily be accounted for 

 by imperfections in boundary support, or by temperature effects. 

 Small changes in clamping were found to exercise a marked in- 

 fluence on these ratios. 



Loading of Diaphragm. 



In the determination of m, r and s, by electrical impedance 

 measurements,*^ only two quantitative relations between these 

 three constants naturally present themselves ; whereas, for the 

 evaluation of these three unknowns, three independent quanti- 

 tative relations must be experimeiltally obtained. It had been 

 hoped to derive the missing third equation, by applying a small 

 known load-mass at the center of the diaphragm, and by repeating 

 the electrical measurements with this load in place. Electrical ex- 

 periments showed, however, that while, occasionally, consistent re- 

 sults were obtained in this way, more often the results were dis- 

 cordant. The reason for the discordance has been shown, from 

 explorations of the diaphragm, to be due to a distortion of the 

 amplitude curves ; whereby the equivalent mass of the loaded 

 diaphragm is no longer the same as when unloaded. 



These conditions are exhibited in the curves of Fig. 15. E 

 shows the zv, r curve, for an unloaded telephonic steel diaphragm, 

 excited acoustically at n^=go4'~', its natural frequency being 7?o = 

 832 — '. The corresponding curve F is for the same diaphragm, 

 after being loaded at the center by a small brass cylinder of 0.536 

 gm. at n = 8i6 '^, its new natural frequency being n^^ = 6g6 ^. 

 After increasing the load to 1.08 gm., the new curve is shown at G 

 (n = 66o^^, 7^0=^616'—^). The shapes of these three curves E, 

 F and G, being so different, it is evident that the equivalent mass 

 of the diaphragm by itself cannot be regarded as constant. 



The authors are indebted to Dr. Geo. A. Campbell for a number 

 of valuable suggestions which he made after having read the MSS. 

 of this paper; also to Professor W. C. Sabine for very useful sug- 

 gestions, during the course of the research. 



6 Bibliography No. 8. 



