22O MEASUREMENT OF CURRENTS. 



of the magnet either in the wires of the coil or in masses of metal in 

 the vicinity. 



When the oscillations decrease in geometrical progression, the 

 logarithmic decrement A may be taken as a measure of the damping. 

 The directing couple which is due to the field is equal to RM. If, 

 as above (678), C l is the coefficient of the resistance of the medium, 

 K the moment of inertia of the system, and, disregarding inductive 

 actions (681), 



C? 



-,r2 



4 KMR-C 



844. The damping by the air may be very great as in Joule's 

 galvanometer (837). The needle is sometimes provided with vanes 

 of aluminum or mica, which greatly increase the friction of the air. 

 This means is still more efficacious if the vanes are enclosed within 

 a box, and are very near the sides. In reflecting galvanometers the 

 mirror itself acts as a damper. When it is placed in a very narrow 

 space, we may arrive at an aperiodic motion (Sir W. Thomson's dead 

 beat galvanometer). 



845. The damping by the coil is a much more complicated 

 effect Let a be the angle of the mean plane of the coil with the 

 direction of the external field H, X Q the deflection corresponding to 

 equilibrium of the needle for the constant current I . When the 

 needle in its oscillations makes an angle x with its position of equi- 

 librium, the moment of the action of the coil for unit current is 

 MG cos (a + X Q + X). For a displacement dx, the work of this action 

 on the needle, or the variation of the flow of force from the needle 

 across the circuit, is 



</Q = MG cos (a + X Q + x)dx. 



If R is the resistance and L the coefficient of self-induction 

 of the circuit, the strength I of the current induced by the needle 

 satisfies equation 



(12) L . 



at at 



we have further 



(13) I MG cos 



