INDUCED MAGNETISATION 231 



that if the intensity at a point in the non-magnetic medium is H 

 and the induction at the same point is B, then B = H. 



Since the induction and the intensity are thus made to coincide 

 in air, the only medium in which we directly measure H, the 

 employment of the two terms appears at first sight needless. 

 But we shall see directly that we are led to assign to them 

 different values in magnetic media, and in permanent magnets and 

 in crystalline media they may even have different directions. 

 They imply, too, even in air, different modes of viewing the action. 

 "Intensity" is the result of experiment. We suppose that we 

 place a unit test pole at the point considered and measure the 

 mechanical force upon it. It is the measure of the action of the 

 medium on something, as it were, outside itself, viz. the test pole. 

 It corresponds in fact to stress in ordinary elasticity. " Induction " 

 implies that there is an alteration in the medium and corresponds 

 to strain in elasticity. In elasticity we have 



stress = modulus x strain, 



and when we know the modulus we can determine the strain by 

 measuring the stress. The magnetic equation B H implies 

 units so arranged that the magnetic quantity corresponding to 

 the modulus is unity in air. 



We may here follow the analogy with elasticity one step 

 further. The energy per unit volume in a strained body is 

 proportional to stress x strain. In the magnetic field, then, we 

 might expect it to be proportional to the product HB, or, since we 

 make B = H, proportional to H 2 . We shall see later in the chapter 

 that there is some reason to suppose that it is H 2 /8?r. 



Lines and tubes of induction in air. Lines and tubes 

 of force in air may now be described as lines and tubes of 

 induction, and along a given tube 



induction x cross-section = constant. 



The total flux of induction through any closed surface, the 

 surface being entirely in air, will be zero whether it encloses 

 magnetised matter or not. For if it does enclose it the two 

 polarities are equal and opposite, and the total polarity within the 

 surface is zero. 



Induction within a magnetised body. Let us suppose 

 that an iron sphere without permanent magnetism is placed in a 

 field in air which before its introduction was uniform, i.e. was such 

 that the lines of induction were straight and parallel. We take 

 the case of a sphere, since on a certain supposition, as we shall see 

 later (p. 242), the course of the lines of force within the sphere can 

 be determined, but the general ideas we gain from the sphere will 

 apply for any form. The course of the lines of induction in the 

 air will be altered by the introduction of the iron as indicated in 



