144 PROCEEDINGS OF THE AMERICAN ACADEMY. 



If L and R are the inductance and resistance of the receiver when 

 damped, the impedance of the damped receiver will be 



Z = R-\- jLco absohms Z (25) 



and if e is the instantaneous value of the impressed e. m. f. of the type 

 Ee^"\ we shall have 



e = iZ abvolts Z (26) 



But owing to the influence of the e. m. f. of motion, the last equation 

 becomes modified to 



e — e^ = iZ abvolts Z (27) 



or 



That is by equation (24) 



e = iZ + c^ abvolts Z (28) 



e = i I Z + — >/3i + /?2 j- = iZ' abvolts Z (29) 



where Z' is the free impedance of the receiver. 



This means that the impedance of the receiver has become increased, 

 through the vibration of the diaphragm, by a motional impedance: 



Z' — Z =— JTTTi absohms Z (30) 



This motional impedance, being the reciprocal of the vector eciuation 

 of a straight line with co as variable, is a circle for variable co, and has a 



diameter — , depressed below the axis of reals by an angle {^i + /?2- 



As to the relative values of /3i and /?2 it seems reasonable that 

 whether the change of flux of a circuit is caused by a small change of 

 current, changing the m. m. f., or by a small change of gap-length, 

 changing the reluctance, the angle of lag of flux behind the cause is 

 the same; that is /52 = /?i = /? (Say). This is borne out by one of our 

 .experiments to be described below (see VI). With this equivalence 

 isubstituted in equations above, we obtain, 



Z' — Z= — 2^ absohms Z (31) 



Consequently, if we vary co from to -|- co , keeping the impressed 

 e. m. f. and all other quantities constant, the motional impedance 

 Z' — Z has a circular graph through the origin, with its principal 



