Integrals of the equations of propagation of electrical disturbances have been given by the present writer which express the electric and magnetic forces at any point outside a surface enclosing all the sources in terms of an electric current distribution and a magnetic current distribution over the surface. The result for a source at a point can be obtained by taking as the surface a sphere of very small radius with its centre at the point. This suggests that the equations representing Faraday’s laws can be written 1/V
2
∂X/∂
t
+4π
i
x
= ∂ϒ/∂
y
– ∂β/∂
z
, 1/V
2
∂X/∂
t
+ 4π
i
v
=∂∝/∂
z
– ∂ϒ/∂
x
, 1/V
2
∂z/∂
t
– 4π
i
z
= ∂β/∂
x
– ∂∝/∂
y
(1) – ∂∝/∂
t
+ 4π
m
x
= ∂z/∂
y
– ∂Y/∂y, – ∂β/∂t + 4π
my
= ∂X/∂
z
– ∂Z/∂
x
, – ∂ϒ/∂
t
+ 4π
mz
∂Y/∂
x
– ∂X/∂
y
, (2) where X, Y, Z are the components of the electric force, α, β, γ are the components of the magnetic force,
i
x
,
i
y
,
i
z
are the components of an electric current distribution, and
m
x
,
m
y
,
m
z
are the components of a magnetic current distribution throughout the space. The object of the present communication is to express X, Y, Z, α, β, γ in terms of the electric current and magnetic current distributions and to apply the result to the discussion of the electric constants of a transparent medium. It is convenient to take instead of equations (1) and (2) the following equations, which include (1) and (2) as a particular case
Integrals of the equations of electrodynamics with to the electric constants of a transparent medium
