30 BRIJ. SYSTI'.M TECIIXIC.IL JOURNAL 



current flowing through it both expressed in root mean scjuare \alues^, 



then 



e={T+R)i (1) 



It is con\eiiii'nl to defme a ciuantity Af wlilch I shall call the uni- 

 lateral mutual imiiedance In' the qeuation 



e, = ][lH (2) 



where ei is the electromotive force created in the transmitter when 

 a current ii flows in the receiver circuit. It is a quantity which is 

 closely related to the eff"ectiveness of the mechanical coupling and 

 the efificiencies of the transmitter and receiver. 



If the electrical coupler be considered part of the receiver, and 

 the transmitter and receiver circuits are connected together as in 

 Fig. 1, then e = ei, and i = ii_. Consequently 



M=T+R (3) 



is the condition for sustained oscillation. This condition is in efTect 

 a pair of conditions, as the two sides of the equation must be equal 

 both in amplitude and in phase. These two conditions are sufficient 

 to determine the frequency and intensity of howling. 



In order to express M and R in more fundamental physical constants, 

 it is necessary to examine more closely the mechanical and electrical 

 connections. Before doing this for some important special cases, 

 it will be necessary to discuss some of the electro-dynamical properties 

 of transmitters and receivers. 



Electrodynamical Properties of Transmitters 

 AND Receivers 



For the sake of clarity the discussion will be confined to permanent 

 magnet receivers and carbon transmitters. The modifications neces- 

 sary for other types of instruments will, I think, be evident from the 

 discussion. Representing by Fr and Ft the forces acting on the 

 diaphragms of the receiver and transmitter respectively, and by y 

 and 2 their displacements, we ha\'e the following equations defining 

 the "stiffness factors" Sr and Sr 



Sr = ^'- (4) 



y 



St = ^ (5) 



z 



^ In what follows all ()uanlitics involving periodic variations will he expressed 

 as root mean square values unless otherwise specified, and the vector notation 

 will be used for denoting phases. 



