Posted this on Clash of Empires, but for the benefit of those on this forum, here it is again (Barry, correct me if I'm wrong)...
Ok, John, the quarter move is basically a mechanic to see where the attack ends up! If the chargers are infantry and more than the minimum distance of three inces, you probably don't even have to worry about it. For example, a charger that starts ten inches away will not catch a unit that routs even the minimum distance of eleven inches!
Here's a pic...
Blue starts 3 inches away from red, successfully completes the charge sequence and causes red to rout! Red rolls a D6 and gets a "2", meaning red will rout 12 inches (rout moves are 10+1D6 inches). Movement now comences in quarter moves... red moves 3 inches (1/4 of 12")... blue moves 3.5" (1/4 of 14", the charge move in Column of Attack)... they continue to alternate... you will see that blue catches red on the last quarter move. Red will be dispersed and removed from the table. Blue will be jubiliant, but disordered, as after any melee. If Red had rolled a three on it's rout move, blur could not have caught them... thus my note that you can probably ignore the quarter move in infantry vs infantry unless the ideal condition I illustrated above exists.
However, lets say a shiny new unit of Perry Dragoons (I can't wait to get these model) charges an infantry unit that is in the Duke of Orange's command, has failed to form square, and routs, again rolling a "2" for the sake of easy math! The dragoons have a chrage move of 36 inches and were twelve inches away when they charged. The infantry moves 1/4 speed or 3 inches. The dragoons move 1/4 speed of 9 inches and are now only 6 inches behind (12+3-9=6). The infantry moves their second 1/4 move, but the dragoons will catch them at the end of the second 'quarter' (6+3-9=0... end of the infantry). The cavalry are disordered and end up six inches behind the original position of the infantry. Had the infantry rolled higher on their rout die, they would have lived to totter on another quarter move, but still would likely have been caught. However, depending on the situation, the cavalry may try to pull up and let the infantry go rather than ending up disordered in a bad tactical position (i.e. in charge range of the enemy heavy cavalry loitering in reserve).
Again, the quarter move is primarily a mechanic to determine where chargers end their move. You can always simply the process with an abstraction - infantry that will contact routing infantry end their move where the router did (likewise cavalry vs cavalry) and cavalry running down infantry end their move at 50% of the infantry's rout move... or something like that!
Hope this helps!