One characteristic of masonry structures in general, and stone arch bridges specifically, is the fact that the person(s) who built the bridge inevitably left behind a hallmark. Not just any and all plaques, but the workmanship itself is often telltale. Each builder has his own method, and, in the case of bridge contractors, the contracting company itself had its own method.
Walter Sharp
Walter Sharp, who built many bridges in Kansas, generally used large, chunky blocks of stone, not necessarily all even in size, and tended to build daring-looking spans with relatively thin arch rings. The outer ring of arches he built is usually more or less precision cut, with the arch stones tending to be almost squarish in shape. It is obvious that the rest of the masonry was not precision cut for each place so much as just squared off and mortared in its position.

One other feature of Walter Sharp’s bridges hidden under the roadway is that he tended to make most of the fill solid, loose, mortarless masonry consisting of variable sized stones rather than simply throwing in dirt. This helps to prevent spandrel wall failure during flooding.
Jerry Hammond
Jerry Hammond, who built a few bridges in Cowley County, Kansas, (as well as, apparently, Oklahoma) tended to stick with smaller spans with smaller stones. Jerry Hammond seemed to use liberal doses of mortar. The arch ring on his bridges, while the faces are frequently leveled off, do not use precision cut stones; instead, mortar and stone chips make the angles even on the arch face.

It appears that Jerry Hammond used a heavy amount of stones in the fill of his bridges. Whether or not these stones are thrown in or layed as rough masonry is unclear.
C. C. Jamison
C. C. Jamison built numerous bridges in Butler County, Kansas. He seemed to favor the Roman arch as a general rule, though not always. The masonry on his bridges is inevitably an excellent fit, usually consisting of random-sized stones that are trimmed precisely to fit well against their neighbors.
Curiously, the arch rings on some of his bridges consist of rectangular blocks with the long side used along the arch ring; typically rectangular stones are placed on end in most stone arch bridge construction, which Jamison did in some cases. The choice was likely determined by the nature of the local stones being used.
C. C. Jamison’s workmanship is inevitably outstanding, which may explain why so many of his bridges are still in good shape and still being used.

C. C. Jamison used small stones as infill masonry in his bridges, judging from the ruins of one of his bridges that was replaced. Though hard to tell for sure, the way he laid this interior masonry appears similar to Walter Sharp’s method of doing the same.
Abe Metheny
Abe Metheny built a few bridges in southeastern Kansas. While not many remain, judging from those of his which do still exist, he also favored more rounded arches. It also appears that for both the arch and the bridge he tended to use numerous thin slabs that are laid in the conventional manner in the arch; namely, placed on end.

Judging from the appearances of several replaced bridges by Abe Matheney, Abe Matheney created much of his bridges as one solid mass of masonry as opposed to filling in with dirt or even loose rubble masonry. That said, the stonework of Abe Matheney’s bridges tends to be somewhat loose.
In Summary
These four builders represent just a few of the stone arch bridge builders in Kansas, let alone the country, yet they serve to show how each mason has his own style. After studying many bridges in an area with confirmed, known builders, one can often form a guess as to the person behind other bridges of an unknown origin in the area.