THE ELECTRIC AND LU:\[INIFEROU>S MEDIUM, 
253 
towards the two sidos of the interface. As there cannot be free magnetic surface- 
density or purely superficial current-sheets, the traction on the interface is represented, 
under the most g’eneral circumstances, whatever extraneous magnetic field may theie 
exist, by purely normal pull of intensity towards each side, where v is the normal 
component of the magnetization at that side. When the medium is non-magnetic, 
there is no such superficial traction, but only the bodily electromagnetic forcive on 
the true electric currents of the material medium, which is represented by the above 
stress system. 
39, The form of the mechanical forcive is identical whether the polarization is 
electric or magnetic, provided there are no electric currents; in the first case it is 
the material reaction to the static strain in tlie sether, in the other case it is the 
reaction to the motional mthereal forcive arising from the revolving electrons in the 
molecule. Omitting for simplicity the slight effect of the convection current in cases 
where any exists, the forcive arising from the electric polarization of the medium 
consists of a bodily force (X', Y', Z') and torque (L', M', N ), Avhere 
X' =/^ + ?' g + r f + /’P + ,</' I - ‘I . T'' = » 
/<'Q, 
together with an interfacial traction between media 1 and 2 which is along the 
normal and equal to — 27 ru'/ -f 27rn7 towards the medium 2, n' representing the 
component of the polarity (7 » normal; the motional foicive aiising 
from the magnetic polarity and the electric currents, consists of a bodily force 
(X, Y, Z) and torque (L, M, N) where 
C 7 + VC - ivh - ^ 
(lx 
L = Be - Qh, 
together Avlth a normal interfacial traction — -f 2771 ^ 1 ^ toxvaids the medium 2, 
V representing the normal component of the magnetization (A, B, C). When the 
mthereal displacement current is neglected, the latter forcive is the same as would 
arise from Maxwell's magnetic stress specification. It may be shown that 
X' = djclx {fT - \ (/P + i/Q + APv)} + djcly {g"?) + d/dz {h'T) -f Jidb/dt - gdcjdt, 
so that the former forcive is Avhat avouIcI arise from an analogous electric stress 
specification in which (P, Q, R), (/', g\ h'), Att {/", g", h"), correspond to (a, ^8, y), 
(A, B, C), («, h, c) respectively, with the exception hoAvever in this case also of 
an outstanding bodily forcive {hdhjdt — gdcjdt, which is not included in 
the stress. A theory Avhlch assumes that there is but one medium in which 
everything is transmitted by contact action, not two interacting media matter and 
rether as here, is compelled to get rid of any outstanding forcive like this, Avhich is 
not expressible explicitly in terms of stress : for this reason supporters of that view 
have found it necessary to introduce into the electric field a purely hypothetical 
mechanical forcive arising from the electric field acting on the so-called magnetic 
