In 1855, the French army took a pair of prototype artillery pieces to a range near the seaside city of Calais. There they fired the new weapons at targets set at distances that ranged from one thousand meters (three-fifths of a mile) to five thousand meters (three miles).
Soon thereafter, Guillaume Piobert, compared the results of these trials with figures pulled from similar tests of cannon (bronze sixteen-pounder guns of the Valée system of 1827) that differed from the experimental equipment in one, and only one, respect. Where the cannon balls shot by the older pieces began their journeys by rolling along smooth passageways, the studded, pointy-nosed cylinders shot by their remodeled counterparts spun their way through rifled barrels before taking to the air.
General Piobert measured the accuracy of the two types of artillery pieces by comparing the ‘mean deviation’ (écart moyen) of each projectile fired. (The closer a place on the target struck to the point of aim, the lower the deviation, and thus the greater the precision of the shot.)
At a range of thousand meters, the rifled version of the sixteen-pounder proved twice as accurate (or nearly so) as its smoothbore sibling. At two thousand meters, this advantage quadrupled. That is, at a distance of one-and-a-quarter miles, the rifled piece achieved a degree of precision eight times greater than that of its competitor.
At 2,500 meters, the impressive advantage of the rifled piece diminished slightly. However, it managed to redeem itself by striking targets that had been well beyond the reach of the cannonballs fired by its smoothbore counterpart.
Source
Unfortunately, I could not find a copy of Piobert’s original study. I therefore relied upon a précis included in an article from a desk-top encyclopedia. Charles Laboulaye ‘Boulets’ (‘Artillery Projectiles’) Complement du Dictionaire des Arts et Manufactures (Supplement to the Dictionary of Arts and Manufactures) (Paris: LaCroix, 1861), page 73.
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Fascinating statistics. And what really would have been impressive is if the fire control devices of the day had been as accurate and durable as the rifled cannon tubes. I do believe that was one reason why the US Army elected to standardize field batteries on the 12 Pounder Gun-Howitzer M1857 (Napoleon) versus the 3 Inch Ordnance Rifle or any of the Parrott rifles (that and cost perhaps?).