440 KENNELLY AND AFFEL. 



resistance of the load in air. Column IX gives the computed stiffness- 

 constant s, as computed from formulas (1) and (4). Theoretically, 

 this stiffness coefficient should remain unchanged throughout. Ac- 

 cording to the Table, it varied between 30.86 and 30.38 megadynes 

 per cm. Column X gives the force-factor a according to formulas (10) 

 and (11). It will be seen that as the load was increased, and the 

 natural frecjuency reduced, this force-factor increased from 6.114 to 

 7.627 megadynes per absampere. This increase may be explained 

 by the change in penetration of the alternating magnetic flux into the 

 substance of the core and poles, as the frequency is changed.^ This 

 change in the force factor a tends to distort the motional-impedance 

 circle to some extent; but since, in the majority of instances, most of 

 the circumference is covered within the range of 100 cycles per second, 

 the actual distortion of the diagram on this account is seldom serious. 

 The method of computing the telephone-receiver characteristic 

 constants by means of mass added to the diaphragm, as outlined above, 

 involves the assumption expressed in (5) that the equivalent mass m 

 of the diaphragm is the same in both the loaded and unloaded states. 

 The theory of the equivalent mass of a diaphragm is outlined in 

 Appendix II. It will be seen that the equivalent mass is always equal 

 to the actual mass of the vibrating area, or area within the clamping 

 boundary of the diaphragm, multiplied by a numerical coefficient, 

 which may be called the "equivalent-mass factor," whose value de- 

 pends upon the distribution of vibration amplitudes over the entire 

 vibrating surface. If the entire acti\e surface of the diaphragm could 

 vibrate with the same amplitude as actually exists at the center, the 

 equivalent-mass factor would be unity. Since the amplitude must 

 diminish towards the boundary, the factor is always less than unity, 

 and may lie, say between the limits 0.15 and 0.50, ordinarily between 

 0.2 and 0.3. When a mass ?»i, is added to the center of a diaphragm, 

 it is apt to disturb the distribution of amplitude over the vil)rating 

 surface, and thus change the equivalent mass m of the diaphragm, 

 considered alone; so that the total equivalent mass of the loaded 

 diaphragm is no longer m + nii. The amount of the disturbance in in 

 created by the load will depend upon various factors, such as the 

 geometry of the diaphragm, the position of the electromagnetic poles, 

 and the magnitude of the load mi; so that a load which might appreci- 

 ably disturb the equivalent mass of one receiver diaphragm, might 

 not appreciably affect the equivalent mass of another. ^° In the case 



9 The theory of this effect has been developed by Dr. R. L. Jones, and is 

 expected to be pubUshed shortly. 



10 Bibliography, No. 17. 



