524 PARTICULAR CASES OF INDUCTION. 



All the other quantities being constant, it may happen that 

 the resistance R varies periodically ; the current will still be 

 periodical, and the amplitude of the variations will be proportional 

 to the strength of the current which is produced with a constant 

 resistance that is to say proportional to the electromotive force. 



Such a current will produce periodical induced currents in an 

 adjacent circuit. This is what takes place in the microphone when 

 the variations in resistance are produced by the vibrations of two 

 bodies in contact, such as pieces of carbon; it is also the case 

 with the selenium photophone, in which the variations in resistance 

 produced by the intermittent action of light are utilised. 



The same result would be attained if the coefficient of self- 

 induction L was variable, which might be attained either by 

 periodically altering the configuration of the circuit, or by oscillating 

 the iron armature of an electromagnet. 



546. INDUCTION IN AN OPEN CIRCUIT. We have hitherto only 

 considered closed circuits. If the wire submitted to induction is 

 not closed, we may assume that the effect of the electromotive forces 

 of induction is to tend to move the electrical masses towards the 

 end of the wire, and to set up for a moment a definite difference 

 of potential between these ends. On Maxwell's theory of displace- 

 ment this problem does not present any fresh difficulties, for the 

 circuits are always closed by the dielectric. It seems natural, 

 moreover, to extend the theory to the case of open circuits, 

 especially if the circuit contains a great number of turns (as in 

 the case of coils), and if the conditions are such that the current 

 could at each instant be regarded as identical throughout the whole 

 length of the wire. 



Let us consider, for instance, the induction of two adjacent 

 circuits (540), and suppose that the ends of the induced wire 

 communicate separately with the armatures of a condenser of 

 capacity C. If we open the inducing circuit, and call V the 

 difference of potential of the armatures of the condenser at the 

 period / after this break, the intensity I' of the induced current 

 will be defined by the equations 



L' + RT + V = 0, 



'<** 



We may further suppose that the insulation of the condenser 



