1046 THE BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1954 



Since the value of r is very much less than one, the series in (24) con- 

 verges quite rapidly at low domain wall velocities, and we only keep 

 the first two terms. 



Until now, we have been concerned with a small volume of the mag- 

 netic lattice fixed in space. As in deriving (11), if we wish to calculate the 

 rate of loss of energy for unit area of the domain wall moving with con- 

 stant velocity, we must integrate dgi/dt over a cyhnder of unit cross- 

 section normal to the wall, gi^ is now a function of it — z/v) where v is 

 the velocity of the domain wall, and z is a coordinate normal to the wall. 

 If we form this integral, and use (16) and (24), we find: 



de(i-^ rf, (25) 



dt 



(26) 



dt dz 



For the first term in (25) we find, using (26) : 



«2 



(27) 



r oLit - z/v) dJ^L^M dz= -V r g[M - z/v) dd = 0, 

 J-« dt Jbi 



since gi^ is the same on both sides of the domain wall. Now if we use (26) 

 in the second term of (25), and remember the result in (27), we have: 



r ^ ,1, = _,,^ r d oLit- z/v) deit - z/v) ^^ ^^^^ 



J-oo dt J-oo dz dz 



We may, without loss of generality, evaluate the intergral in (28) 

 at ^ = 0. It is therefore the integral of a function of z over z. In order to 

 evaluate it, we wish to express gi„ as a function of 6. We have: 



where we have replaced gi^ by dgi^/dd. We note now, from the relation 

 between g and gi , that dgi/dt = —dg/dt. We therefore set the right hand 



