MAGNETIC FIELD. 



A small coil is placed on a support by which it can be rapidly 

 turned through 180 about an axis parallel to 'the plane of the 

 windings, and it is interposed in the circuit of a ballistic galvano- 

 meter. The axis of the coil being, first of all, parallel to the 

 direction of the field, the swing is noted which corresponds to a 

 rotation of 180. For a coil of n windings, the mean surface of 

 which is S, the quantity q of electricity induced in a circuit of 

 resistance R is 



S 



The experiment itself gives the means of verifying that the axis 

 of the coil is parallel to the field, by the condition that the induced 

 discharge is a maximum. 



In order to make the constant of the ballistic galvanometer, care 

 must be taken that the circuit contains a frame of known surface S'. 

 By turning this frame face over, from a horizontal position, or from 

 a vertical position perpendicular to the meridian, the induced dis- 

 charge corresponds to the flow of force 2ZS' or 2HS'; in this way, 

 any measurement of resistance, of galvanometric constant, and of 

 time of oscillation, is avoided. 



When the terrestrial field has a considerable part in the effect 

 produced, the action is eliminated by displacing the coil parallel to 

 itself until it emerges from the limits of the field observed. 



With very powerful fields the surface S may be so small as to 

 permit of an exploration of the distribution of force. 



With comparative experiments, and when the deflections of the 

 galvanometer are small with a feeble damping, the ratio of the fields 

 is equal simply to the ratio of the swings observed. 



We ought in particular to insist on the fact that the method 

 of induction applies to any field, and does not necessitate any 

 of the corrections which we have mentioned in other cases. 



1151. FIELD OF A MAGNET. At a distance which is great 

 compared with the dimensions of a magnet, the magnetic field is 

 the same as that of two infinitely near masses of opposite signs. 



Take as 'the x axis the magnetic axis of a magnet, or the polar 

 line, and for the y axis a right line in the perpendicular plane which 

 passes through the middle of the magnet that is to say, on its mag- 

 netic equator. Let x and y be the co-ordinates of a very distant 

 point P, R the distance \A# 2 +y 2 of this point from the centre of 

 the magnet, w the angle of the right line R with the polar axis, 

 the components X and Y of the field at the point P, and the 



