66 



ADVANCED ELECTRICITY AND MAGNETISM. 



The total work done to establish the two currents i\ and i* 

 is therefore equal to JLiti 2 -f- Mi\i^ -f }L 2 ^2 2 , and the kinetic 

 energy of the two circuits is equal to the total work done. 



Note. Imagine the current iz to be established first and ii 

 afterwards, then another expression for the kinetic energy would 

 be obtained. The only difference being that in one case the 

 expression for W contains the M in equation (4) of Art. 41 

 whereas in the other case the expression for W contains the M 

 in equation (3) of Art. 41. But the two expressions for W must 

 be the same, therefore the two M's are identical. 



43. Mechanical analog of the transformer again considered. 

 The mass of the lever AB in Fig. 49 was neglected in the dis- 

 cussion of Art. 40, but Fig. 50 shows a lever with heavy balls at 

 its two ends and an attached mass C at its center, the two lever 

 arms / and / being assumed to be equal for the sake of sim- 

 plicity. The velocity of A is i it the velocity of B is i Zl and 



the velocitv of C is 



and 



the kinetic energy of the system is : 



where, as may be easily shown: 



^ L A - 



4 



C 

 4 



Fig. 50. 



Equation (i) is identical to equation (i) of Art. 42, and the 

 mechanism of Fig. 50 is completely analogous to two inductively 

 related or "coupled" circuits. 



44. Coupled circuits containing capacity. A common arrange- 

 ment of apparatus at the sending station for wireless telegraphy 



