3f)8 BELL SYSTEM TECHNICAL JOURNAL 



ultimately of the same frcniuency as tiie impressed e.m.f., whereas 

 in the former they are ultimately of an infinite series of frequencies. 



In the preceding example, the variable impedance element is a 

 resistance r{t). If the variable element is taken as an inductance 

 \{t) the voltage, corresponding to equation (290) is 



The case of a variable capacity element is handled as follows: 

 Let \/C=S and assume that 5 is variable: thus, S = So-\-(jit). The 

 drop across the variable condenser element is then 



v{t)=a{t) I'liOdL 

 Jo 



Similarly a variable mutual inductance ju(0 between branches m and 

 n produces the voltages 



in branch m, and 



in branch n. This case may be illustrated by: 



The Induction Generator Problem 



In a sufficiently general form, this problem, which includes the 

 fundamental theory of the dynamo, may be stated as follows : 



Given an invariable primary and secondary circuit with a variable 

 mutual inductance Mj\t) which is an arbitrary but specified time 

 function, and let the primary be energized by an e.m.f. E{t) im- 

 pressed in the circuit at the reference time / = 0: required the primary 

 and secondary currents. 



In operational notation the problem may be formulated by the 

 equations : 



Z,J,-pMf{t)I,=E{t), 



-pMf{t)h^Z.nl2=0, 



in which Zu and Z22 are the self impedances of the primary and sec- 

 ondary respectively; MJ\t) is the \'ariable mutual inductance; E{t) 

 is the applied e.m.f. in the primary; and p denotes the differential 



