198 



LORD RAYLEIGH. 



abolition of the primary current. A third complication arises from the 

 capacity of the secondary coil, in virtue of which the currents need not 

 be equal at ail parts of the length, even at the same moment of time. 

 If we ignore thèse complications, treating the break as instantaneous, 

 the iron as idéal, and the secondary as closed and without capacity, the 

 theory, as formnlated by Maxwell is very simple. In his notation, 

 if x, y dénote the primary and secondary currents, L, M, N the coeffi- 

 cients of self and mutual induction, the energy of the field is 



kf^+M^+k^y. (i) 



If c be the primary current before the break, the secondary current at 

 time t after the break lias the expression 



y = eM e -SIN.t, (2) 



S being the résistance of the secondary circuit. The current begins 

 with a value c. M\N, and gradually disappears. 



The formation of the above initial current is best understood in the 

 light of Kelvin' s theorem, as explained by me in an early paper 2 ). For 

 this purpose it is more convenient to consider the reversée! phenomenon 

 viz., the instantaneous establishment of a primary current c. The theo- 

 rem teaches that subject to the condition x — c the kinetic energy (1) 

 is to be made a minimum; so that 



Jfc+ JV> = 0 



gives the initial secondary current. In the case of the break we have 

 merely to reverse the sign of y. 



Immediately after the break, when x = 0 and^ lias the above value, 

 the kinetic energy is 



\Ny\ or \— . 

 Immediately before the break the kiuetic energy is ^ Le 2 , so that the 



1 ) „Electromagnetic Field," Phil. Trans. 18G4; Scientific Papers, I. p. 546. 



2 ) „On some Electromagnetic Phenomena considered in connexion with. the 

 Dynamical Theory," Phil. Mag. 38, p. 1, 1869; Scientific Papers, I. p. 6. 



