426 The Magnetic Field produced by Electric Currents [OH. xm 



wire, wound as closely as possible round the space in which the needle 

 moves, and the needle is suspended as delicately as possible by a fine 

 torsion-thread. To make the instrument still more sensitive, permanent 

 magnets can be arranged so as to neutralize part of the intensity of the 

 earth's field. The instrument is read by observing the motion of a ray of 

 light reflected from a small mirror which moves with the needle : it is from 

 this that the instrument takes its name. 



III. The Ballistic Galvanometer. This instrument does not measure 

 the current passing at a given instant, but the total flow of electricity 

 which passes during an infinitesimal interval. If the needle is at rest in 

 the plane of the coil, a current sent through the coil will establish a 

 magnetic field tending to turn the needle out of this plane. So long as 

 the needle is approximately in the plane of the coil, the couple acting on 

 the needle will be proportional to the current in the coil : let it be denoted 

 by ci, where i is the current. 



Then if co is the angular velocity of the needle at any instant, we shall 

 have an equation of the form 



j.dco 



mk* -=- = ci, 

 at 



where mk* is the moment of inertia of the needle. Integrating through the 

 small interval of time during which the current may be supposed to flow, 

 we obtain 



m& 2 H = c I idt. 



Here O is the angular velocity with which the needle starts into 

 motion, and I idt is the total current which passes through the coil. 



Thus the total flow I idt can be obtained by measuring H, and this 



again can be obtained by observing the angle through which the needle 

 swings before coming to rest at the end of its oscillation. 



MECHANICAL FORCES IN THE FIELD. 



Intensity due to any closed circuit. 



496. It has been seen, in 423, that the mutual potential energy of 

 a magnetic particle of moment unity at any point x', y r , z', and a shell 

 of strength < is equal to minus </> times the number of tubes of induction 

 of the field set up by the particle that are enclosed by the shell, and this 

 again is equal, by 445, to 



