444 
MR, 0. HEAVISIDE OH THE FORCES, STRESSES, AND 
It is important to recognize that this flux of energy is not dependent upon the 
translational motion of the medium, for it is assumed explicitly to be at rest. The 
vector W cannot, therefore, be a flux of the kind Q q q before discussed, unless possibly 
it be merely a rotating stress that is concerned. 
The only dynamical analogy with which I am acquainted which seems at all 
satisfactory is that furnished by Sir W. Thomson’s theory of a rotational ether. 
Take the case of e 0 = 0, h 0 = 0, k = 0, g — 0, and c and g, constants, that is, pure 
ether uncontaminated by ordinary matter. Then 
curl H = cE,.(98) 
- carl E = ,/<H.(99) 
Now, let H be velocity, [x density; then, by (99), — curl E is the translational 
force due to the stress, which is, therefore, a rotating stress; thus, 
P N = YEN, a, = VNE; 
( 100 ) 
and 2E is the torque. The coefficient c represents the compliancy or reciprocal of 
the quasi-rigidity. The kinetic energy H 3 represents the magnetic energy, and the 
potential energy of the rotation represents the electric energy ; whilst the flux of 
energy is VEH. For the activity of the torque is 
and the translational activity is 
Their sum is 
__ curl H 
2E. - v> 
E curl H, 
- H curl E. 
may, perhaps, be appropriately termed the Duplex method, since its characteristics are the exhibition of 
the electric, magnetic, and electromagnetic relations in a duplex form, symmetrical with respect to the 
electric and magnetic sides. But it is not merely a method of exhibiting the relations in a manner 
suitable to the subject, bringing to light useful relations which were formerly hidden from view by the 
intervention of the vector-potential and its parasites, but constitutes a method of working as well. 
There are considerable difficulties in the way of the practical employment of Maxwell’s equations of 
propagation, even as they stand in his treatise. These difficulties are greatly magnified when we pro¬ 
ceed to more general cases, involving heterogeneity and eolotropy and motion of the medium supporting 
the fluxes. The duplex method supplies what is wanted. Potentials do not appear, at least initially. 
They are regarded strictly as auxiliary functions which do not represent any physical state of the 
medium. In special problems they may be. of great service for calculating purposes; but in general 
investigations their avoidance simplifies matters, greatly. The state of the field is settled by E and H, 
and these are the primary objects of attention in the duplex system. 
As the papers to which I have referred are not readily accessible, I may take this opportunity of 
mentioning that a Reprint of my ‘ Electrical Papers’ is in the press (Macmillan and Co.), and that the 
first volume is nearly ready. 
