Statistics for occurrence #1 of “Gaines' Mill” in chapter 10 of The Photographic History of The Civil War: in ten volumes, Thousands of Scenes Photographed 1861-65, with Text by many Special Authorities, Volume 5: Forts and Artillery.:

..., fitted over a vent communicating with the powder in the breech of the gun, served the An essential factor in the winning of pitched, open battles was a plentiful supply of ammunition. At Gaines' Mill , in June, 1862, the Union soldiers found it difficult to cheer convincingly when they had shot away all their cartridges, and found themselves separated from their ammunition wagons by the fast-swell...
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