The general six-vector [function] is composed from the vectors φ, φ^* in the following way:—
[function] = ρφ + ρ^* φ^*,
rho and rho^* denoting the contents of the pieces of mutually perpendicular planes composing [function]. The "conjugate Vector" [function]^* (or it may be called the complement of [function]) is obtained by interchanging ρ and ρ^*
We have,
[function]^* = ρ^*φ + ρφ^*
We can verify that
[function]_{y z}^* = [function]_{x l} etc.
and [function]^2 = ρ^2 + ρ^*^2, ([function][function]^*) = 2ρρ^*. | [function] |^2 and ([function][function]^*) may be said to be invariants of the six vectors, for their values are independent of the choice of the system of co-ordinates.
[M. N. S.]
Note 12. Light-velocity as a maximum.
Page 23, and Electro-dynamics of Moving Bodies, p. 17.
Putting v = c - x, and w = c - λ, we get
V = (2c - (x + λ))/(1 + (c - x)(c - λ)/c^2) = (2c - (x + λ))/(c^2 + c^2 - (x + λ)c + xλ/c^2)
= c (2c - (x + λ))/(2c - (x + λ) + xλ/c)
Thus v < c, so long as | xλ | > 0.
Thus the velocity of light is the absolute maximum velocity. We shall now see the consequences of admitting a velocity W > c.
Let A and B be separated by distance l, and let velocity of a "signal" in the system S be W > c. Let the
