472 PARTICULAR CASES. 



The work done against electromagnetic forces in this operation 

 is then 



If the current is made to turn about a vertical axis we need only 

 consider the horizontal component H of the field. The work of the 

 rotation of 180 about the axis from the position of equilibrium 

 is then 



W'-alSH. 



If the current turns about a horizontal axis parallel to the 



magnetic meridian, the vertical component Z of the field alone 



comes into play. For a rotation of 180 from the position of 

 equilibrium the work is still 



W" = 2 ISZ. 



The ratio of the works in the two latter cases, 

 W" Z 



is equal to the tangent of the Inclination. Hence, if we could 

 measure these works, we could determine the elements of terrestrial 

 magnetism without having recourse to magnets. 



If the axis of rotation is in the magnetic meridian, the total 

 work is null, when the current, which at first was in this plane, 

 comes back to it after having been turned through 180; the works, 

 which correspond to the two halves of the rotation, are therefore 

 equal and of contrary signs. 



Lastly, the work would be null for any given rotation if the axis 

 of rotation were parallel to the direction of the field. 



489. ASTATIC CIRCUITS. The work of any given displacement 

 is still null when the circuit comprises two closed curves, such that 

 their projections on any plane give two equal surfaces S and S', 

 surrounded by currents moving' in opposite directions. This is the 

 condition which movable currents must satisfy, which are arranged 

 so as not to be under the action of the earth ; what are called astatic 



