Pagina 186 de 212

In this way we satisfy the postulate of the constancy of the

velocity of light in vacuo for rays of light of arbitrary

direction, both for the system K and for the system K′. This may

be shown in the following manner.

We suppose a light-signal sent out from the origin of K at the

time t = 0. It will be propagated according to the equation

image049

or, if we square this equation, according to the equation

x2 + y2 + z2 - c2t2 = 0 . . . . . (10).

It is required by the law of propagation of light, in conjunction

with the postulate of relativity, that the transmission of the

signal in question should take place-as judged from K′-in

accordance with the corresponding formula

r′ = ct′

or,

x′2 + y′2 + z′2 - c2t′2 = 0 . . . . . . (10a).

In order that equation (10a) may be a consequence of equation

(10), we must have

x′2 + y′2 + z′2 - c2t′2 = σ (x2 + y2 + z2 - c2t2) (11).