4 The Hon. J. W. Strutt on some Electromagnetic Phenomena 



they become equal, will depend on its magnitude as compared 

 with the other data of the problem. 



There is for every conducting circuit a certain time-constant 

 which determines the rapidity of the rise or fall of currents, and 

 which is proportional to the self-induction and conductivity of 

 the circuit. Thus, to use Maxwell's notation, if L and R be re- 

 spectively the coefficient of self-induction and the resistance, the 



time-constant is ^ =r. If the current c exist at any moment 



in the circuit and fall undisturbed by external electromotive 



_t_ 

 force, the value at any time t afterwards is given by % = c. e T . 

 Any action which takes place in a time much smaller than t will 

 be sensibly unaffected by resistance. 



We see, then, that we may neglect the effects of resistance 

 during the time of equalization of the currents, provided that 

 the operation is completed in a time much smaller than the time- 

 constants of either circuit. And this I shall suppose to be the 

 case. The value of the common current or velocity at the mo- 

 ment the impact is over will of course be given by the condition 

 that the momentum, electromagnetic or ordinary, is unchanged. 

 If L and N be the coefficients of self-induction for the main and 

 branch circuits respectively, x and X the original and required 

 currents, the analytical expression of the above condition is 



(L + N)X=L#, 

 or 



It is here supposed that there is no sensible mutual induction 

 between the two circuits. 



The spark is the result of the excess of the one current over 

 the other, and lasts until its cause is removed. Its mechanical 

 value is the difference between that of the original current in 

 the main circuit and that of the initial current in the combined 

 circuit, and is expressed by 



l L ^-i(L + N)X 2 ; 



or if the value of X be substituted, 



2 °° L + N 



Exactly the same expression holds good for the heat produced 

 during the collision of the inelastic bodies, which is necessarily 

 equal to the loss of ordinary actual energy, at least if the per- 



