4 
where F, G, and H are the components of the vector potential and yf the 
electrostatic potential ; thus if the medium is at rest P’, Q’, R/ are the 
components of the electromotive force at the point. 
Professor Poynting interprets this equation to mean that the components 
parallel to the axes of «, y, z of the flow of energy across each element of 
surface are respectively 
ON ELECTRICAL THEORIES. Pak 
i Sy ; 
1 @p-en, 
Ler — Ra), 
[pal f 
a, 62 a — P’p), 
so that according to this view the energy flows in the direction which is 
at right angles both to the magnetic and electromotive forces, and in the 
direction in which a right-handed screw would move if turned round 
from the positive direction of the electric intensity to the positive 
direction of the magnetic intensity; the quantity of energy crossing in 
unit time unit surface at right angles to this direction being 
2 . Electromotive force at the point x magnetic force 
Tr 
x sine of the angle between these forces. 
This interpretation of the expression for the variation in the energy seems 
open to question. In the first place it would seem impossible @ priori to 
determine the way in which the energy flows from one part of the field 
_ to another by merely differentiating a general expression for the energy 
in any region with respect to the time, without having any knowledge of 
the mechanism which produces the phenomena which occur in the 
electromagnetic field: for although we can by means of Hamilton’s or 
_ Lagrange’s equations deduce from the expression for the energy the 
_ forces present in any dynamical system, and therefore the way in which 
the energy will move, yet for this purpose we require the energy to be 
expressed in terms of coordinates fixing the system, and it will not do to 
take any expression which happens to be equal toit. The problem 
of finding the way in which the energy is transmitted in a system whose 
mechanism is unknown seems to be an indeterminate one; thus, for 
example, if the energy inside a closed surface remains constant we cannot 
unless we know the mechanism of the system tell whether this is because 
there is no flow of energy either into or out of the surface, or because as 
much flows in as flows out. The reason for this difference between what 
we should expect and the result obtained in this paper is not far to seek. 
Though the increase in the energy inside a closed surface equals 
|e - Q'y) +... JdS, 
it does not follow that the components of the flow of energy across each 
element of surface are (R/ — Q’y)/4z, &c., for we can find quantities 
u, v,w which are of the dimensions of rate of change of energy per unit 
area, and for which 
{Je + mv +nw)dS= 0. 
