## B

3. The total wristwatch time x from event #1 to event #3 is the sum of the wristwatch time T^ between events #1 and #2 plus the wristwatch time tg between events #2 and #3:

4. Now ask: When—at what frame time t—will the stone, following its natural path, pass the intermediate point and emit the second flash #2? Answer with the Principle of Extremal Aging: Time t will be such that the aging (t in equation ) is an extremum. To find this extremum set the derivative of x with respect to t equal to zero. Take the derivative of both sides of  and substitute from equations  and :

Use Principle of Extremal Aging to find the time for the middle flash

Quantity whose value is the same for adjacent segments

5. The last equality in equation  leads to the equation

6. In expression  the frame time t is the time for the particle to traverse segment A. Call this time fA. The time (T -1) is the frame time for the particle to traverse segment B. Call this time iB Then equation  can be rewritten in the simple form 