224 MEASUREMENT OF CURRENTS. 



L 



and, neglecting the square of the ratio , we have 



JX 



('9) 



We deduce from the first of these equations 



I 2KR 2H 7* I / 2L \ 



To the same degree of approximations equations (18) and (19) 

 give, putting ^=i+ 



Unless the damping is considerable, the times of oscillation r and T O 

 differ but little from each other. 



If the ratio -J be neglected, we deduce from equation (20) 



JN. 



AX M 2 G 2 



The damping X increases then with the constant G of the coil, 

 with the ratio of the square of the magnetic moment of the needle 

 to its moment of inertia, and inversely as the resistance of the 

 circuit. It is a maximum when the coil is closed. 



If we add to the circuit a resistance R', the approximate values 

 of the elements X' and T of the new oscillations satisfy the equation 



