But we must deal with space-like intervals before we can decide whether the above theory of time-like intervals will do. It is to be observed that space-like intervals are obtained by calculation from time-like intervals. Let us imagine the following ideal experiment: An astronomer on the sun sends a message to an earthly mirror, and an astronomer on the earth sends one to a solar mirror. Each observes the time of departure and return of his own message, and the time of arrival of the other's message. Each finds that the other's message is received at a time half-way between the arrival and departure of his own message. They compare notes, and discover this fact about each other's observations. They will conclude that, according to the reckonings of both, the two messages were despatched simultaneously, and that the measure of the space-like interval between the despatch of the two messages is half the time between the despatch and return of either, i.e. about eight minutes. We may re-state the general method involved as follows: Let us have two transactions and connected by a number of causal routes, all going straight from to ; and let the longest of these consist of events. Suppose that there is another transaction such that its later event extends to , and that there is no longer causal route from to , nor any causal route at all from to . Here corresponds to the sending of the signal from the earth, to the sending of the signal from the sun, and to the arrival of the solar signal at the terrestrial observatory. The question is: What is to be the interval between and ? There cannot be a causal route from to , because if there were it could be prolonged to , and would be longer than the single event which extends from to , contra hyp. Thus no causal series connects and ; there is a causal series connecting and ; and is a transaction that begins an event which ends in the transaction . In these circumstances, we say that the interval between and [Pg 371] is of a different kind from that between and , but has the same numerical measure. The fact that this definition works is what appears as the constant velocity of light.