i would add that it originated in connection with the 1838 Poinsett (Secretary of War) reforms, which established four companies (much later called "batteries") of mobile field artillery which were "mounted" (only one of which was "fully mounted" horse artillery - more on that at another time). These companies were far more mobile on the battlefield than under prior US systems, which had finally moved from the heavy bracket trail to the single "block" trail, etc. Their increased mobility led to the popular name "flying artillery" which was ingrained during the War with Mexico because the mounted US companies had a significant mobility advantage over their Mexican opponents and exerted an important impact on fights at Palo Alto, Resaca de la Palma, Buena Vista, etc. As noted, three of the four were not true horse artillery/"fully mounted" but all were for the most part mounted. The term "mounted" caused some confusion about this. By the time of the Civil War "flying artillery" apparently became limited to the true horse artillery.