in the Description of Physical Phenomena. 423 



retentiveness does lead to complications, it is our business to 

 disentangle them; and practically the method of reversals of 

 magnetizing current enables us to do this. But it is not main- 

 tained, at least by me, that magnetic resistance is properly a 

 function of magnetizing force. It is a function of the effect 

 produced, i. e. of the magnetic induction, as is amply proved 

 by the inspection of the numerous curves that have been 

 published in connexion with this question. And it is so just 

 in the same way in which the resistance of matter to com- 

 pression is a function only of the compression, or of the stage 

 which the condensation has reached. 



A word may be usefully said here on the origin of the 

 differential formula used by Lamont to express the so-called 

 magnetic conductivity of a magnet. The ambiguity on which 

 the origin of this formula depends can be well dealt with by 

 the present illustration. 



If we consider the compression of matter which, has at- 

 tained the liquid condition, we may speak of the resistance to 

 any further compression at this point, or under these con- 

 ditions, as being infinite. For the effect produced by the 

 further pressure is nothing. But in the magnetic analogy we 

 always consider a change, the initial condition of which corre- 

 sponds roughly to the gaseous condition, or rather a pre- 

 gaseous condition, in the material analogy. In either case, 

 if, instead of considering the total change, we consider the 

 state of things at a point, then we must suppose the cause to 

 vary by a small quantity, d cause, producing a small effect, 

 d effect ; and the ratio of these may be said to be the re- 

 sistance at the point of the representative curve, or under the 

 given conditions. It is on this mode of statement that 

 Lamontfs differential formula is based. The formula is 

 (Handbach des Magnetismus, p. 41), 



dm = k (M — m) dx ; 



whence by integration, 



M—m=Ge- ix ; 

 x = magnetizing force, 

 m = magnetism, 

 M = maximum of magnetism. 



Here dm/dx is called the magnetic conductivity ; and it is 

 inversely as the magnetic resistance at a point. That mag- 

 netic conductivity, which is inversely as the magnetic re- 

 sistance as I and others use the term, is m/x, i.e. has 

 reference to the total change. I have shown (Electrician, 

 xvi. p. 247) that the assumption m/x=:k (M— m) is that to 

 2F2 



