262 MAGNETISM 



dielectrics in the electric field. In the electric field, for 

 instance, between two parallel metal plates charged with cr 

 the tension along the lines of force must be ^Trcr 2 in order 

 to account for the work done in separating the plates. But 

 there is no exactly corresponding magnetic system, nothing like 

 a charged conductor. Since the magnetic induction tubes are 

 continuous, there are magnetic stresses on each side of the surface 

 separating two media, and energy is distributed throughout the 

 tube. We cannot make a real magnetic experiment like that with 

 an attracted disc electrometer, where we weigh the pull by the 

 dielectric on the surface. Even the electric system is indeterminate, 

 for we can hardly argue conclusively from the pulls in a uniform 

 field to those in a field in which the level surfaces are curved. 

 The tensions and the pressures keeping an element in equilibrium 

 might depend on the curvature of the lines of force. But we can 

 at least show that the electric stress sytem devised by Maxwell holds 

 with a uniform field, and can further show that it gives force -s which 

 agree with the actual forces on bodies. We have no satisfactory 

 starting-point for a magnetic system ofstres8e8,aodit is probably In M 

 to be guided by analogy with the electric field, remembering again 

 that the problem is really indeterminate and that the >y*trm assumed 

 is only one of an infinite number of possible solutions. Maxwell* 

 proposed a magnetic stress system which in a medium of perme- 



H 2 



ability 1 gives a tension along the lines of force and an e<jiial 



H 2 



pressure perpendicular to them. In a medium of permeability 



O7T 



yu, homogeneous and isotropic, so that induction and intensity are in 

 the same direction, his system consists of a tension H 2 /8-7r along, 

 and a pressure H 2 /8?r perpendicular to, the lines of force, and in 



H 2 



addition a tension (/z 1) = /cH 2 along the lines of force. 



a*Yr 



This stress system is not satisfactory. The >\ >tem of tension and 

 pressure, each equal to H 2 /8-7r, would keep each element of a 

 homogeneous medium in equilibrium, and it can be shown that it 

 would account for the surface forces on a magnetised bodv in air, 

 that is, for the forces on the surfaces of discontinuity. But the 

 additional tension /cH 2 within the body would only form a system 

 in equilibrium in a uniform field. We shall consider in place of 

 Maxwell's system one analogous to the electric system, and shall 

 therefore assume that there is in a homogeneous isotropic body a 



TT2 TJ2 



tension ^ along the lines of force and an equal pressure ^1 

 perpendicular to them. 



* Electricity and Magnetism, ii. Sect. 642. The stresses in the medium are 

 discussed at length in Walker's Aberration and the Electro-magnetic Field, and in 

 Heaviside's Electrical Papers, vol. ii. 



