232 Lord Bayleigh on the Behaviour of Iron and Steel 



large deflection occurs. If the force be now removed, the 

 recovery is incomplete, indicating that the iron retains residual 

 magnetism. Subsequent applications and removals of the 

 force produce a nearly regular effect, and always of such a 

 character as to prove that the magnetic changes in the iron 

 exceed those demanded by the law of proportionality. As 

 might be expected, the excess varies as the square of the 

 force ; and thus, when the force is small enough, it becomes 

 insignificant, and the law of proportionality expresses the 

 facts of the case with sufficient accuracy. But the precise 

 limit to be fixed to the operation of the law depends neces- 

 sarily upon the degree of accuracy demanded. 



The readings with and without the force being tolerably 

 definite, it would of course be possible, by pushing in the 

 compensating-coil, to bring about an adjustment in which the 

 application or removal of the force causes no deflection. But 

 this state of things must be carefully distinguished from the 

 compensation obtainable with ver} T small forces, in that it is 

 limited to one particular step in the magnitude of force. If 

 we try a force of half the magnitude, we find the compensation 

 fail. Not only so, but the reading will be different under the 

 same force according as we come to it from the one side or 

 from the other. The curve representing the relation between 

 force and magnetization is a loop of finite area. 



Except for the purpose of examining whether the whole 

 magnetization is assumed instantaneously (absence of drift), 

 there is little advantage in the compensation being adjusted 

 for the extreme range under trial. It is usually better to 

 retain the adjustment proper to very small forces. Even 

 though it fails to give a complete compensation, the coil offers 

 an important advantage, which will presently appear; and its 

 use diminishes the displacement to be read upon the scale. 



We have seen that when the forces are very small there is 

 a definite relation between force and magnetization, of such a 

 character that one is proportional to the other : the ratio k 

 (the susceptibility) is a definite constant. When, however, 

 certain limits are exceeded there is no fixed relation between 

 the quantities ; and if h is still to be retained, it requires a 

 fresh definition. It is not merely that k, as at first defined, 

 ceases to be constant, but rather that it ceases to exist. Upon 

 this point the verdict of experiment is perfectly clear. There 

 is no curved line by which the relation between force and 

 magnetization can be unambiguously expressed, and which 

 can be traversed in both directions. As soon as the line 

 ceases to be straight, it ceases also to be single. I have 

 thought it desirable to emphasize this point, because the term 



