378 Intelligence and Miscellaneous Articles. 



In the following the case shall be treated of the fluctuations of re- 

 sistance being indefinitely small in comparison with the total resist- 

 ance ; and the reaction of the vibrating plate upon the conduction, 

 by which at all events only current-waves of inconsiderable strength 

 compared with the original ones are produced, shall be neglected. 

 The equation representing what takes place then becomes 



at 



Hei'3 E signifies the electromotive force of the battery employed, 

 "W the resistance, J the intensity of the current, and Q the electro- 

 dynamic potential of the circuit upon itself. 



We now put "W=W -f w, J=J o -fi. W and J denote resist- 

 ance and current-intensity in the state of repose, w and i their 

 variations during the vibrations ; w and i are, according to our hy- 

 pothesis, small quantities. After this substitution our equation 

 becomes 



(J„+0(W o +*,)=E-Q^A±il 



If we take into account that J W = E, that iw is a small quantity 

 of the second order, which in comparison with those of the first 



order we will neglect, and that — ^-9- — ' = — , our equation as- 

 sumes the form 



3>+W i+Qf|=0 (1) 



To this equation we can attach the following remark. If iv } and 

 i v as well as w 2 and i 2 , are two systems of waves which satisfy the 

 equation, then tv l -\-iu 2 and \ + i 2 also satisfy it ; that is, the differ- 

 ent wave-systems are superposed without mutual disturbance. The 

 microphone must necessarily possess this property if most of the 

 influences operating upon it are not to express themselves entirely 

 or for the most part as noises ; and not only so, but it follows from 

 the assumption of very small changes of resistance in proportion to 

 the total resistance, because thereby the equation became linear ; 

 consequently we see that the fulfilment of this condition is also ne- 

 cessary in practice for the good rendering of a sound. 



If we now analyze each vibration into summands according to 

 Fourier's series, we need only treat the summands singly. Accord- 

 ingly let tu=A sinpp 27r, let the current-wave belonging to it be 



Bsmf^ 



(f*r+*) 



so that we assume the phase-change 3; this, introduced into equa- 

 tion (1), yields 



