Magnetic and Electric Energies as a Pressure. 667 

 'Zlu e = v K ==%lu, or agreement of normal components, a 

 condition which also follows from integrating -. -± =^(p !( e) 

 + . . . = as above. The group (16) (17) (18) yields 



X(l-t V 2 /V 2 ) = <7(/+i W /V 2 ), a\l-v*IV 2 j=*(nv e -mw e )/Y. 



. . . (19) 



We have therefore expressions for surface values in 

 terms of a and (u e v e w e ). The formula? for which we have 

 immediate use are : 



Z = x + i y c ~ Weh = *i(i-%u e yv 2 )/(i-v v y\*), . (20) 



2a 2 -2X 2 = - a "{l - W/V 2 )/(l- iV 2 /V 2 ), (21) 



a + (w e Y-v e Z e )/Y=Q, (22) 



2a 2 = %v e (Yc-Zb)IV (23) 



From (20) and (21) we derive 



I 



(2a 2 -:£X 2 ) = -<7f/2 (24) 



According to the well-known method of getting the force 

 due to the transition layer, the right-hand member represents 

 a component of the inward force. The force is therefore a 

 pressure \(%a 2 — £X 2 ) normal to the surface. This pressure 

 is negative, as for the statical problem, with modifying factors 

 due to the motion. 



The relation (22) is quoted as leading immediately to (23), 

 from which 



E + L=$u e (Yc-Zb)/Y (25) 



If the value of L in (21) is differentiated with regard 

 to n e , the result is found to agree with the value of 

 (Yc-Z6)/V as obtained from (19). Thus 



= (Yc—Zb)Y, and E = u eS - + r e - \-w e ~ — L; 



. . . (26) 



and in respect to these surface values per unit volume 

 we have the normal relation connecting energy with 

 kinetic potential. 



2X2 



