So the system of differential equations (A) can be expressed in the concise form
{A} lor f = -s,
and the system (B) can be expressed in the form
{B} log F* = 0.
Referring back to the definition (67) for log [=s], we find that the combinations lor ((lor f)), and lor ((lor F*) vanish identically, when [function] and F* are alternating matrices. Accordingly it follows out of {A}, that
(68) ([part]s_{1}/[part]x_{1}) + ([part]s_{2}/[part]x_{2}) + ([part]s_{3}/[part]x_{3}) + ([part]s_{4}/[part]x_{4}) = 0,
while the relation
(69) lor (lor F*) = 0, signifies that of the four equations in {B}, only three represent independent conditions.
I shall now collect the results.
Let ω denote the space-time vector of the first kind
(u/[sqrt](1 - u^{2}), i/[sqrt](1 - u^{2})) this line and next]
(u = velocity of matter),
F the space-time vector of the second kind (M,-iE)
(M = magnetic induction, E = Electric force,
[function] the space-time vector af the second kind (m,-ie)
(m = magnetic force, e = Electric Induction.
s the space-time vector of the first kind (C, iρ)
(ρ = electrical space-density, C - ρu] = conductivity current,
ε = dielectric constant, μ = magnetic permeability,
σ = conductivity,
