Repairing dry stone walls, like building them, is an ancient craft. The common name for it is gapping, and a lot of farmers in Britain who have walls around their fields usually know how to do it themselves.
Gapping takes place between portions of dry stone wall that are still in good condition. You have to find enough stone to gap properly. Hopefully it is all still there lying in the field beside the wall or down in the ditch after a car ran into it.
Yesterday we did more artistic gapping. We built between some of the huge cored beams of travertine that we added to the top of our Canadian wall this February. Royce Kelly from Arkansas helped us for a while, just for a break from sawing roof tiles all day, to be used on the Gualala watchtower.
The holes left after coring the travertine beams are the remaining negative shapes after they've cut out the 24 inch high 'column' sections. They are 'throw aways' and yet they can be used quite effectively, as we have done here, to a create modern looking architectural cope detail along the top of the wall. All we had to do was gap them together.