458 MB. 0. HEAVISIDE OH THE FORCES, STRESSES, AND 
and so we come round to the equation of activity again, in the form (146), by using 
(159) in (158). 
Modified Form of Stress-vector, and Application to the Surface separating two Regions. 
§ 23. The electromagnetic stress, P N of (149) and (136) may be put into another 
interesting form. We may write it 
P N = i (E.ND + V.VNE.D) + | (H.NB 4- V.VNH.B).(160) 
Now, ND is the surface equivalent of div D and NB of div B ; whilst YNE and YNH 
are the surface equivalents of curl E and curl K. We may, therefore, write 
P N = i (E// + VDG') + | (Ho-' + VJ'B), .(161) 
and this is the force, reckoned as a pull, on unit area of the surface whose normal is 
N. Here the accented letters are the surface equivalents of the same quantities 
unaccented, which have reference to unit volume. 
Comparing with (122) we see that the type is preserved, except as regards the 
terms in F due to variation of c and g in space. That is, the stress is represented in 
(101) as the translational force, due to E and H, on the fictitious electrification, 
magnetification, electric current, and magnetic current produced by imagining E and 
H to terminate at the surface across which P N is the stress. 
The coefficient which occurs in (161) is understandable by supposing the fictitious 
quantities (“ matter ” and “ current ”) to be distributed uniformly within a very thin 
layer, so that the forces E and H which act upon them do not then terminate quite 
abruptly, but fall off gradually through the layer from their full values on one side to 
zero on the other. The mean values of E and H through the layer, that is, -|E and 
-|H are thus the effective electric and magnetic forces on the layer as a whole, per 
unit volume density of matter or current; or f E and TH per unit surface density 
when the layer is indefinitely reduced in thickness. 
Considering the electric field only, the quantities concerned are electrification and 
magnetic current. In the magnetic field only they are magnetification and electric 
current. Imagine the medium divided into two regions A and B, of which A is 
internal, B external, and let N be the unit normal from the surface into the external 
region. The mechanical action between the two regions is fully represented by the 
stress P N over their interface, and the forcive of B upon A is fully represented by 
the E and H in B acting upon the fictitious matter and current produced on the 
boundary of B, on the assumption that E and H terminate there. If the normal 
and P N be drawn the other way, thus negativing them both, as well as the fictitious 
matter and current on the interface, then it is the forcive of A on B that is repre- 
