APPENDIX. 



Note to 199, 200. According to the equations (6) 199, 

 the force on an element of medium in an electric or magnetic field 

 becomes infinite at the surface between two media of different 

 inductivities, for there JJL is discontinuous. The layer in which 

 this takes place is however infinitely thin, so that the total force 

 on the surface is finite. We may find the force, as stated in 199, 

 by integrating throughout the space included in an infinitely thin 

 layer containing the surface of discontinuity, as in 85. We may 

 also use the results of 200, finding the components of the stress 

 in both media by equations (8). The six components X x , Y y , 

 Z z , Y Z) Z x , X y , will in general have discontinuities at the surfaces 

 of discontinuity of //., and the forces on the unit of surface are 

 equal to these discontinuities. For instance let us consider a 

 surface bounding a medium of inductivity fa, surrounded by a 

 medium of inductivity fjL l} the surface being such that the lines of 

 force are normal to it in both media. Then taking the direction 

 of the normal to a certain element for that of the X-axis, we have 

 in the medium 1, 



the force being a tension. In the medium 2 we have 

 (2) X X = 



The two tensions being in opposite directions on the two sides 

 of the surface, the resultant force acting on unit of surface is the 

 difference, 



(3) T^^QBJFt-MJ, 



w. E. 36 



