The Last Quarter
Half lit again, and shrinking — the opposite half from first quarter, lit from the other side.
Where to look: Rises around midnight, is highest at sunrise, and sets around noon. This is the quarter almost nobody sees, for scheduling reasons rather than astronomical ones.
The terminator is back in the middle and the shadows are long again, so the craters are as good as at first quarter — better, if anything, because the pre-dawn air is usually steadier than the evening air. The catch is that you have to be up at four in the morning to find out.
Commonly muddled: Also called third quarter. Same phase, same moment, two names, both in current use.