﻿TJieory of the Telephone. 299 



was still just visible. We may conclude that a force of 

 1 gram weight corresponds to a current of about ^Jj^ of an 

 ampere. Now, 1 gram weight is equal to 981 dynes, so that 

 for comparison with (10) 



force = '6xl0 6 r (11) 



The force observed is thus about the third part of that which 

 had been estimated, and the agreement is sufficient. 



Although not needed for the above comparison, we shall 

 presently require to know the linear displacement of the 

 centre of the telephone-plate due to a given force. Observa- 

 tions with the aid of a micrometer-eyepiece showed that a 

 force of 5 grams weight gave a displacement of 10~ 4 x 6*62 

 centim., or 10~ 4 x 1*32 for each gram, viz. 10" 7 x 1*34 centim. 

 per dyne. Thus by (11) the displacement x due to a current 

 r expressed in amperes is 



#=-080r (12) 



We have now to estimate what motion of the telephone- 

 plate may be expected to result from a given periodic force 

 operating at its centre. The effect depends largely upon the 

 relation between the frequency of the imposed vibration and 

 those natural to the plate regarded as a freely vibrating body. 

 If we attempt to calculate the natural frequencies a priori, 

 we are met by uncertainty as to the precise mechanical con- 

 ditions. From the manner in which a telephone-plate is 

 supported we should naturally regard the ideal condition as 

 one in which the whole of the circular boundary is clamped. 

 On this basis a calculation may be made, and it appears * that 

 the frequency of the gravest symmetrical mode should be 

 about 991 in the case of the telephone in question. But it 

 may well be doubted whether we are justified in assuming 

 that the clamping is complete, and any relaxation tells in the 

 direction of a lowered frequency. A more trustworthy con- 

 clusion may perhaps be founded upon the observed connexion 

 between displacement and force of restitution, coupled with 

 an estimate of the inertia of the moving parts. The total 

 weight of the plate is 3*4 grams ; the outside diameter is 

 5*7 centim., and the inside diameter, corresponding to the 

 free portion of the plate, is 4*5. The effective mass, supposed 

 to be situated at the centre, I estimate to be that correspond- 

 ing to a diameter of 2'5 centim., viz. '65 gram. A force of 

 restitution per unit displacement equal to (10~ 7 x 1*34) -1 , or 

 10 G x 7*5, is supposed to urge the above mass to its position 



* ' Theory of Sound/ 2nd ed. § 221 a. 

 X2 



