234 MAGNETISM 



draw two level surfaces, or surfaces cutting the lines of induction at 

 right angles, one through Pclose to the point at which the central line 

 enters the iron, and the other through Q close to the point at which 

 it leaves the iron. It is evident that these surfaces must bend, the 

 one downwards, the other upwards, as indicated in the figure, coining 

 nearer together far out at KS, where the field is practically un- 

 affected by the iron, than they are at PQ, close to the iron. Now, 

 we have no way of experimentally measuring the intensity H 

 within the iron. But we make the supposition that it is such that 

 in passing from one level surface to another, intensity x path is 

 constant for all paths whether in air or iron ; or, if H is not uniform, 

 then if ds is an element of path, fHds is the same for all paths 

 from one level surface to another. Since, then, the level surfaces are 

 further apart at PQ than they are in distant parts of the field, H 

 is less within the iron than in those distant parts, i.e. less than it 

 was before the iron was introduced. But just outside the sphere at 

 P or Q the tubes of force or induction have narrowed, in converging 

 on to the iron, and so H is greater there than it was before the iron 

 was introduced. Then H in air at P is greater than H in iron 

 close to P. But B in air at P is equal to B in iron close to P, and 

 since B in air is equal to H in air, B in iron close to P is greater 

 than H in iron at the same point. 

 Let us put in the iron 



ju. is termed the permeability of the iron. 



If we put H = - B and compare with the elasticity relation 



.xtre>s modulus x strain 



we see that 1/yu corresponds to the modulus of elasticity. It 

 represents as it were the dif lie-nit v, while /m represents the ra^e. of 

 magnetisation. 



To sum up. We have in air B = H, where H can be experi- 

 mentally determined, and therefore B can be determined. In iron 

 we can suppose that B is determinate from the continuity of the 

 induction flux along a tube as it passes from air into iron. We 

 can also suppose that H is determinate from the constancy of 

 potential difference as we pass from one level surface to another, 

 whether through air or through iron. We have seen that in iron B 

 must be greater than H, and its ratio to H is termed the permea- 

 bility of the iron. 



We have considered only the case in which the magnetisation 

 is produced by induction, and have disregarded the possibilitv of 

 permanent magnetism in the iron. If there is permanent magnetism 

 we can no longer assume that fHds between two level surfaces is 

 the same through air as through iron. 



