Above many old doors sits a small window, sometimes fixed, sometimes hinged to open. That's the transom, and where it opens, transom hardware is what made it work, letting light and air pass over the door even with the door shut. That hardware is specific, ingenious, and exactly the part most likely to be missing now.
The operating transom solved a plain problem: how to open a window set above head height, from below, without a ladder. The answer was the transom operator, a rod-and-arm linkage, a chain, or a geared operator on the wall, that let you swing the transom open from a reachable height and hold it at any angle. It's a neat little machine for a specific job, and when it's gone, the transom becomes a fixed window that can't do the thing it was built for. The rest of the set supports that motion: the hinges the transom pivots on, the catches that hold it closed, the small fittings that connect the operator to the window. The fixed transom, by contrast, is simpler, often a decorative panel of glass, sometimes leaded or numbered with a house address, and its "hardware" is its framing and glazing. An operating transom is worth returning to service, because a house designed to move air is more comfortable than one that can't, and usually the only thing missing is the operator.