176 MAGNETISM 



W = awi', 



where m is the weight of the magnet W, the weight just sufficient 

 to detach the armature, and a a constant for a given quality of 

 steel, the magnet in each case being in the state of normal 

 saturation. 



Inasmuch as a differs very widely with the quality of steel 

 employed, the formula has little general value, but it may be 

 pointed out that for magnets of similar form and of the same 

 quality it is equivalent to 



W oc Z 3X * oc / 2 , 



where / is a linear dimension, say the breadth ; in other words. \V is 

 proportional to the cross-section. 



Nickel and cobalt magnets. While iron is pre-eminent 

 in its magnetic properties, all bodies, as we .shall sec in Chapter 1'i, 

 give signs of polarity under magnetic induction, though in general 

 so slight that the polarity can only be observed easily in 

 exceedingly strong fields such as are produced by powerful 

 electro-magnets. There are, however, two other metals, nickel and 

 cobalt, which, though far less magnetic than iron, still show very 

 appreciable polarity under induction. Pieces of tln^e metals will 

 fly to, and be held on by, a strong pole. 



They may be very appreciably magnetised by insertion within 

 a magnetising coil and they exhibit some retentivity, nickel, 

 especially when hardened, more than cobalt. It has been found 

 possible to make a compass needle of hardened nickel. 



The magnetic field. When we consider the space round a 

 magnet in connection with the magnetic actions which may be 

 manifested in it, we term the space the " field **" of the magnet. 



If we place a magnet on a table, a small compass needle also 

 placed on the table tends to set in a definite direction in the field. 

 Its NSP is acted on by a force which we may regard as the resultant 

 of the repulsion of the NSP and the attraction of the SSP of the 

 magnet. We shall suppose that the needle is very small, M 

 small that its poles may be taken as equidistant from the magnet 

 poles ; then its SSP is acted on by the resultant of the attraction 

 of the NSP and the repulsion of the SSP of the magnet, and these 

 two forces are respectively equal and opposite to those on the NSP. 

 Then the two resultants are equal and opposite, and a couple acts 

 on the needle. It therefore sets with its axis in the direction of 

 the resultant forces on the poles. If it is disturbed from this 

 equilibrium position the couple tends to restore it, and if left 

 to itself it will vibrate more or less rapidly according to the 

 magnitude of the force on either pole. In fact, the needle 

 is a kind of double magnetic pendulum with opposite pulls 

 on the two ends, and just as the time of vibration of a given 

 gravity pendulum is inversely as the square root of the force of 



