286 PRELIMINARY. 



and to their being placed on the magnetic axis at a distance pro- 

 portional to the magnetic moment of the magnet in question. 



When a system formed of several magnets connected with each 

 other is placed in a uniform field, the action of the magnet is 

 reduced to a couple; accordingly, in order to estimate the total 

 action, we may move all the magnets parallel to themselves, for in- 

 stance, in such a manner that all the negative poles are superposed. 



Consider two magnets represented by the right lines OA and OA' 

 (Fig. 71), and let G be the middle of the line AA' that is to say, 



the centre of gravity of two masses equal to unity, placed at A and A'. 

 The system is equivalent to a single magnet whose length is equal to 

 OG and the masses equal to 2, or to a magnet of double length OB 

 with masses equal to i. The resultant magnet is thus represented 

 by the diagonal of the parallelograms constructed on the right lines 

 OA and OA'. 



Magnetic moments of magnets may therefore be compounded as 

 can forces. For any given system of magnets connected with each 

 other, the resultant moment is represented by the straight line which 

 closes the polygon constructed by adding, end to end, the moments 

 of all the magnets. 



The projection of this line on any given axis being equal to the 

 sum of the projections of all the others, we see that the magnetic 

 axis of any given system, is the right line on which the sum of the 

 projections of the separate moments of the magnets constituting the 

 system is a maximum. 



In like manner, a magnet may be replaced by any given number 

 of magnets, the resultant magnetic moment of which is equal to the 

 moment of the proposed magnet for instance, by the three pro- 

 jections of this magnetic moment on three rectangular axes. 



When two magnetic systems are very distant from each other, 

 their reciprocal action is equal to that of the resultant magnets, for 

 each of the systems may be regarded as being situated in a uniform 

 field produced by the other magnet. 



