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



allow induced currents to circulate which might interfere with 

 the result. 



In this form of the experiment there was no sensible mutual 

 induction between the coils A and B. Should there be such, 

 the result may be considerably modified. For instance, let the 

 wire A 2 be thrown at the break into the circuit of A 2 and the bat- 

 tery. This may happen in two ways. If the connexions are so 

 made that the currents are parallel in A l A 2 , there "will be no 

 sensible spark ; but if the directions of the currents are opposed, 

 the spark appears equal to the full spark |L<r 2 . 



And this is in accordance with theory. The current X is 



given by the same condition as before, which leads to the 



equation 



La?+M#=(LH-2M + N)X, 



M being the coefficient of mutual induction between the two 

 circuits . The spark is therefore 



iLtf 2 -i (L + 2M + N) X 2 =y ^— , as N = L. 



Now in the first-mentioned connexion M = L very nearly, and in 

 the second M = — L; so that the observed sparks are just what 

 theory requires. 



With regard to those electrical phenomena whicli depend on 

 the mutual induction of two circuits, it may be remarked that it 

 is not easy to find exact analogues in ordinary mechanics which 

 are sufficiently familiar to be of much use as aids to conception. 

 A rough idea of the reaction of neighbouring currents may be 

 had from the consideration of the motion of a heavy bar to 

 whose ends forces may be applied. If when the bar is at rest 

 one end is suddenly pushed forwards in a transverse direction, 

 the inertia of the material gives the centre of gravity in some 

 degree the properties of a fulcrum, and so the other end begins 

 to move backwards. This corresponds to the inverse wave in- 

 duced by the rise of a current in a neighbouring wire. If the 

 motion be supposed infinitely small, so that the body never turns 

 through a sensible angle, the kinetic energy is proportional to 



4 (« 2 + W)x? + i (b* + k*)y* + (ab — k*)xy 9 

 where a and b are the distances of the driving-points (whose velo- 

 cities are x and y) from the centre of gravity, Jc 2 the radius of gyra- 

 tion about the latter point. This corresponds to the expression 

 for the energy of the electromagnetic field due to two currents, 



JL^ + M^y + JNy 1 - 

 and if we imagine the motion of the driving-points to be re- 

 sisted by a frictional force proportional to the velocity, we get a 

 very tolerable representation of the electrical conditions. 



