622 CONSTANTS OF MAGNETISATION. 



With a cylindrical magnet the value of Q for' different points 

 will enable us to construct what Gaugain has called the curve of 

 demagnetisation (417). When the circuit is displaced between 

 two positions x l and x z , the induced discharge measures the 

 variation Q 1 - Q 2 of the internal flow of induction from one section 

 to another that is to say, the flow of force which emerges from 

 the bar (324) by the lateral surface between the two corresponding 

 sections. 



1195. Let us suppose now that the circuit S forms part of a 

 cylindrical coil which has n l spires for unit length. The flow of 

 induction across the spires comprised within a length dx is 



</Q = - n^dx dydz + t^n^dx Adydz. 



The ends of the coil being in the planes x l and x 2 , the total 

 flow of induction which traverses it, is the integral of this expression 

 between the limits x l and x 2 . If V x and V 2 are the potentials in 

 the bounding planes and dv an element of volume of the magnet, 

 we may write 



Q-**! j (v^ydz-n I fVi^fr + 4**, | Adv. 



If the extremities of the coil are so distant on either side of the 

 magnet that the potential is sensibly null, we get simply 



M x denoting the projection on the x axis of the magnetic moment 

 of the body. 



If the magnet is removed, the discharge induced in the circuit 

 of the coil will enable us to determine the moment M x . 



More generally, we know (338) that the potential energy of a 

 magnet M in a uniform field F with which it makes the angle 6 

 is - MF cos 6. If a frame of any shape whatever, traversed by 

 a current I, produces a uniform field GI, the potential energy 

 of the magnet placed in this field will be - MGI cos 9\ and the 

 work WI necessary to bring the magnet in another direction & 

 will be 



WI = MGI(cos0-cos0'). 



