I have attached some of the information regarding the bullet I found. I didn't know a one inch gun had been manufactured during this time period either.
Models 1862-1871
Model 1862. In 1862, at the age of 44, Richard Gatling had demonstrated his first working model of the Gatling gun in Indianapolis, Indiana. He patented the Gatling gun on November 4, 1862. Its key elements were a lock cylinder containing six strikers which revolved with six gun barrels, powered by a hand crank. The gun used separate .58 cal. paper cartridges and percussion caps, which resulted in gas leakage. The model 1862 Gatling gun attained a very high rate of fire of 200 spm (shots per minute) for that time.
Model 1865. By changing to a unitary cartridge, Gatling overcame the problem with gas leakage only to encounter problems in the ammunition feed mechanism. Gatling designed a new breech mechanism which fixed the feed problem, leading to the development of the much improved model 1865 six-barrel 1 inch Gatling gun, the forerunner of all later model Gatling guns.
Model 1865 1 inch caliber Gatling gun on artillery carriage (Copyright Arco Publishing)
Model 1866. After successful trials at Frankford Arsenal and Fort Monroe, the U.S. Army ordered 50 1 inch cal. and 50 .50 cal. model 1866 six-barrel Gatling guns. All but five of the .50 cal. guns were converted to .45 cal. beginning in August 1866. The gun used a simple tin box to hold cartridges. These guns were all fixed-mounted on an artillery carriage.
Model 1871 had improved breech bolts that could be easily removed for maintenance in the field used a new curved cartridge magazine. In 1872 a new hopper design permitted use of a 400 round Broadwell drum. The Broadwell drum was a circular cluster of 20 vertical feed magazines containing 20 cartridges each. When a magazine emptied, the gunner manually turned the drum to align the next full magazine. The U.S. Army purchased one 1 inch cal. and nine .50 cal model 1871 ten-barrel weapons. Models 1862-1871
