the radar pulse arrives at the target must be, according to the observer, halfway between the transmission and reception times, namely In the particular case where the radar observer is Alice and the target is Bob (momentarily co-located with Dave) as described previously, by k-calculus we have , and so As Alice and Bob were co-located at , the velocity of Bob relative to Alice is given by This equation expresses velocity as a function of the Bondi k-factor. It can be solved for to give as a function of : Velocity composition Consider three inertial observers Alice, Bob and Ed, arranged in that order and moving at different speeds along the same straight line. In this section, the notation will be used to denote the k-factor from Alice to Bob (and similarly between other pairs of observers). As before, Alice sends a blue flash towards Bob and Ed every seconds, by her clock, which Bob receives every seconds, by Bob's clock, and Ed receives every seconds, by Ed's clock. Now suppose that whenever Bob receives a blue flash from Alice he immediately sends his own red flash towards Ed, once every seconds by Bob's clock, so Ed receives a red flash from Bob every seconds, by Ed's clock. Einstein's second postulate, that the speed of light is independent of the motion of its source, implies that Alice's blue flash and Bob's red flash both travel at the same speed, neither overtaking the other, and therefore arrive at Ed at the same time. Therefore, as measured by Ed, the red flash interval and the blue flash interval must be the same. So the rule for combining k-factors is simply multiplication: Finally, substituting gives the velocity composition formula The invariant interval Using the radar method described previously, inertial observer Alice assigns coordinates to an event by transmitting a radar pulse at time and receiving its echo at time , as measured by her clock. Similarly, inertial observer Bob can assign coordinates to the same event by transmitting a radar pulse at time and receiving its echo at time , as measured by his clock. However, as the diagram shows, it is not necessary for Bob to generate his own radar signal, as he can simply take the timings from Alice's signal instead. Now, applying the k-calculus method to the signal that travels from Alice to Bob Similarly, applying the k-calculus method