562 APPENDIX. 



acting towards the medium 1. But since the induction is con- 

 tinuous, we have & = $2 and the force becomes, 



T 8 tv v\ 8 



(4) T -&<A- r ** 



We may also obtain the formula (4) in a simple manner by 

 considering the energy-density in the two media. This is in the 

 media 1 and 2 



S 2 S 2 



and g respectively. 



If now we consider the surface displaced normally a distance 

 dn toward the medium 1 the prism standing on the element dS 

 exchanges its energy 



dSdn, 

 for the amount 



dSdn, 

 8777*2 



so that there is a loss of energy 



during the motion through the distance dn. Accordingly the 

 force on the element dS is that given by (4) towards the medium 

 1*. If there is a real charge on the surface, so that the induction is 

 discontinuous, we have 



(5) r-^. 



and if /^ = /*. 2 this becomes 

 (6) T=^(f\ + F 2 ). 



This is exemplified in 147. 



As a second particular case, let us consider a surface of discon- 

 tinuity at which the induction is tangential. Then we have in the 

 medium 1 the pressure 



* The deduction given by Maxwell, art. 440, is only approximate, lacking the 

 factor /tg in the denominator. 



