OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
359 
tion from some fixed plane by z, the line integral of the M.I. is —while the current, 
being an alteration of displacement, is ~ 
Therefore 
_d^ =K M .( 2 ) 
dz dt ' ' 
But since the displacement is propagated on unchanged with velocity v, the displace ¬ 
ment now at a given point will alter in time dt to the displacement, now a distance dz 
behind, where dz—vdt. 
Therefore 
d(§ d% /o v 
1t=- v di . ( 3 > 
Substituting in ( 2 ) 
dQ t z dQt 
-£= Kv t* 
whence 
.( 4 ) 
the function of the time being zero, since <§ and (S are zero together in the parts which 
the wave has not yet reached. 
If we take the line integral of the E.M.I. round a face perpendicular to the M.I. 
and equate this to the decrease of magnetic induction through the face, we obtain 
similarly 
®=liv§ .(5) 
It may be noticed that the product of (4) and (5) at once gives the value of v, for 
dividing out ® we obtain 
l=/xK'y 3 
or 
v= VM 
But using one of these equations alone, say (4), and substituting in (l) K for and 
dividing by (§ 3 , we have 
K _ K aKV 
47r 87 t 87 r 
or 
1 =(jlKv‘ 2 
whence 
