Arthur B. Davies used a few printers for his work including lithographer George C. Miller who printed a series of 25 lithographs, published by Weyhe Galleries in New York. These were Davies' last lithographs, which were mostly done as transfers. Davies would draw on a sheet of transfer paper with litho crayon, these drawings were then transferred to a stone and printed. The resulting image would be in the same direction as the drawing.
"Old Stone Quarry" is next to the last lithograph that Davies did. Much of the composition was done using the side of the litho crayon, the result being broad areas of grays and blacks, only constrained by a few lines of reference. The over-all effect is almost gestural abstraction, until you examine it closer.
One advantage of transfer lithography is that the drawing on the matrix can be done on location and that the composition that is drawn will be the same as the print. Transfer paper is much easier to travel with than litho stones or metal plates. It is likely that Davies did this on site.