134 KENNELLY-TAYLOR— EXPLORATIONS OVER [April 22, 



and the square of the maximum observed amphtude at the center, or 



M ^Wr^ 



m = 2 — gm. (7) 



^ ^max 



The preceding table sets forth this process for the curve of Fig. 

 iB, drawn theoretically, and checked observationally, with ^ = 50, 

 or the diaphragm divided into 50 annuli of equal mass. The result 

 is that the equivalent mass is 18.3 per cent, of the actual mass of the 

 vibrating area. This result checks that obtained from the mathe- 

 matical integration of the Bessel curve. 



Although 50 annuli of equal area and mass were taken in the 

 case above worked out, so as to attain a fairly high degree of pre- 

 cision in the evaluated equivalent-mass coefficient ; yet, for many 

 purposes, a sufficient degree of precision might be attained by taking 

 only 10 such equal annular areas. 



BIBLIOGRAPHY. 



1. Rayleigh, " Theory of Sound," Vol. i, p. 352, Macmillan Co., 1894. 



2. R. Kempf-Hartmann. Ann. de Physik, 8, pp. 481-538, June, 1902. 



3. W. Wien, Ann. de Physik, 18. S, pp. 1049-1053, December, 1905. 



4. Henri Abraham, Comptes Rendus, Vol. 144, 1907. 



5. Frederick K. Vreeland, Phys. Review, Vol. 27, p. 286, 1908. 



6. Barton, "Text-Book of Sound," p. 211, Sec. 146, Macmillan Co., 1908. 



7. Chas. F. Meyer and J. B. Whitehead, Trans. A. I. E. E., Vol. 31, II., pp. 



1397-1418, 1912. 



8. A. E. Kennelly and G. W. Pierce, " The Impedance of Telephone Re- 



ceivers as Affected by the Motion of Their Diaphragms," Proc. Am. 

 Acad, of Arts and Sci., Vol. 48, No. 6, September, 1912, p. 138; alSo 

 Electrical World, September 14, 1912. 



9. L. Bouthillon and L. Drouet, La Revue Electrique, October 16, 1914 (pub. 



January 15, 1915). 



10. Augustin Guyau, "Le Telephone Instrument de Mesure," Gauthier-Villars, 



Paris, 1914. 



11. E. Jahnke and F. Emde, " Funktionentafeln mit Formeln und Kurven," 



p. 166 (3) and (4). 



12. Paul Schafheitlin, " Die Theorie der Besselschen Funktionen," pp. 68 



and 69. 



13. W. E. Byerly, " Fourier's Series and Spherical Harmonics," p. 233. 



