INDUCED MAGNETISATION 235 



Hydraulic illustration. A hydraulic illustration may 

 help us to realise the meaning of magnetic permeability. 



Imagine that ABCD, Fig. 181, is the cross-section of a slab of 

 spongy or porous material indefinitely extended to right and left, and 

 that a liquid which entirely fills the pores is being forced through 

 it by a pressure across AB in excess of that across CD. Then the 

 liquid will flow with a velocity from AB to CD such that the viscous 

 resistance balances the difference of pressure. On the average the 

 flow will be straight across from AB to CD and the pressure will fall 

 uniformly from one face to the other. This corresponds to a uniform 

 magnetic field. The pressure corresponds to the potential, and its 

 slope, or fall per centimetre, to the intensity. The velocity will be 



O 



FIG. 181. 



proportional to the pressure-slope and will correspond to induction. 

 Evidently, if we draw a tube of flow, velocity x cross-section, or 

 total flow, will be the same throughout its length. 



Now imagine a portion of the slab represented as spherical 

 in the figure made more porous, and therefore less resisting, than 

 the rest. Evidently the liquid will flow more rapidly through 

 this portion. The lines of flow will converge on to the end nearer 

 AB, and diverge from that nearer CD. The surfaces of equal 

 pressure will be deformed just as are the magnetic level surfaces in 

 Fig. 180. The total flow along a tube will be the same whether it is 

 within or without the larger-pored space occupied by the sphere, 

 and the pressure-slope will be less within than without that space. 



We could replace the sphere with its larger pores by one having 

 pores equal to those outside it, if we supposed that where the tubes 

 of flow enter the sphere, there are "sinks" or points at which fluid 

 is removed somehow from the system, the amount removed being 

 the excess of fluid coming up over that which the given pressure- 

 slope will drive through the sphere on the supposition of pores equal 

 in size to those outside. On the surface of the other hemisphere, 

 where the fluid emerges, we must suppose that there are " sources " 

 or points at which fluid is somehow introduced into the system to 

 make up the excess of outward flow over the flow through the sphere. 

 The " sources " must introduce just as much as the " sinks " remove. 

 This mode of representation corresponds to the representation of 

 the magnetic induction by polarity distributed over the surface and 

 it brings to the front the artificial nature of that representation. 



Though we are not here considering permanent magnetism, we 



