Typos or errors by the transcriber. The 15th most assuredly would be the 15th LA Infantry. The 1st and 3rd may in all likelyhood be the 1st and 3rd Companies of the Washington Artillery. Just a guess but check the names with Booth and you may have your answer. Very, very doubtful and unlikely to be members of Louisiana Cav unit troopers in Gordonville, Virginia. That would make no sense and the logistics, no way.