E.A.W. was E. A. Williams, a Springfield Armory sub-inspector.
While a few early Sharps rifles were made (at government request) for the Maynard tape primer, the priming mechanisms of most Sharps rifles and carbines, including the one seen here, was the Lawrence primer system, which was not a tape primer. It used pellet primers that consisted of two thin copper cups, one fitting into the other, with the priming compound between them. Inside the mechanism there is a plunger or feed arm with one end having a lug that fits into grooves in the inside of the hammer. When the hammer fell, it moved the feed arm forward, shoving a primer pellet out the front and into the path of the hammer. When things worked right, the free-flying pellet was crossing the nipple just as the hammer fell and crushed it.
It seems like something we would later associate with Rube Goldberg, but it did work most of the time. (I have seen one work, using dummy primers.) But the thing was complex and needed to be kept clean, plus the primers were often unavailable, so ordinary musket caps were usually used.
The primers came in tubes containing 20 0r 30 primers, packed in flat sleeves or tin containers holding up to 50 tubes. In spite of problems, there was enough use that the Ordnance Department purchased some 2.5 million of the primer pellets through the war. An original tube of primers will cost well over a hundred dollars today.