302 
PROFESSOR J. H. POYNTING ON ELECTRIC CURRENT AND THE 
which have cut dx, dy, dz drawn from a point in such a way as to create magnetic 
intensities in the positive direction along dx, dy, dz. 
The excess of the number of tubes which have passed in over those which have 
passed out through the boundary of any area will be equal to the time integral of the 
total current through the area. 
The components of the total current are 
, (if dg dh 
u =p+jt v=( i+it w=r+ it 
p, q, and r being the components of the conduction current or the number of tubes 
dissipated per second, and f g, h the components of the induction actually existing. 
As in the last case, if we put f— \ udt, &c., we at once obtain the equations 
. „ dC dB^ 
^ ~ dy dz 
, dA dC , 
,, dB dA 
4,rA =^“*7. 
Corresponding to the current equations (2) we have three equations obtained from the 
condition that the rate of increase of magnetic induction through an area is equal to 
the integral of the electric intensity round it in the negative direction. These are 
da _ dQ 
dt dz 
db _dR 
dt dx 
dc dB 
dt dy 
dip 
dy 
dP 
dz 
> 
dQ 
dx 
If C, is the specific conductivity we may by Ohm’s law put the current equations 
after integrating in the form 
/'=cpp p 
✓=c,{q*+|3 
v=c,p+f 
whence in media where K is constant 
|7dQ_dR\ K /dQ_dR\ 
dz dy 'Jlp dy/ '4:7r\dz dy) 
