[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)/c²) = (2c - (x + λ))/(c² + c² - (x + λ)c + xλ/c²)
= c (2c - (x + λ))/(2c - (x + λ) + xλ/c)
Thus v lt; 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 (observing) system S′ have velocity +v with respect to the system S.
Then velocity of signal with respect to system S′ is given by W′ = (W - v)/(1 - Wv/c²)