"Cold gun correction" refers to a condition that was once thought to be the result of a gun being cold — the firing of the first round through a cold gun resulted in a slightly shorter range and a slight increase in bearing deviation.
It was later found that if the gunner's mates had swabbed the gun, then the first round fired through it — the gun being cold — would be slightly short in range and have a slight increase in bearing deviation. If the gunner's mates had not swabbed the gun, there would be no decrease in range and no increase in bearing deviation.
It was found that the rotating band wipes the oil from the bore of the gun, but the oil builds up on the rotating band and increases the friction retarding it. This causes a slight decrease in the velocity of the projectile, causing it to fall slightly short of the intended range. The reduced velocity also causes a slight increase in bearing deviation.
Tables were then produced for each size of gun giving the amount of range reduction to be entered as a spot for the first round fired if the gun had been swabbed. After firing the first round, the spot is removed. No spot is required if the gun has not been swabbed. The bearing deviation is so slight that no correction is made.
The term "cold gun correction" was thereafter deemed to be in error, but as the term had been used for so long, it was — and continues to be — used.
A description of the old cold gun correction error may be found in Exterior Ballistics 1935, § 1315.