Here are three hits from a Goggle search:

The grounds of the State House are home to several famous landmarks. The three-tiered fountain with cranes is a recast of the original fountain that sat in front of the Arkansas Building during the 1876 Philadelphia Centennial Exposition. The fountain traveled by train to Arkansas after the exposition ended and was installed in front of the State House in 1877, one year before the first city water system began to operate. The Lady Baxter Cannon is a Civil War–era cannon used as part of Little Rock’s defense against Union forces. Later, Elisha Baxter’s supporters moved the cannon to the grounds during the Brooks-Baxter War.
http://www.encyclopediaofarkansas.net/encyclopedia/entry-detail.aspx?entryID=2111

…..

The cannons stayed in the Arkansas River until April of 1874. At that time an argument between Elisha Baxter and Joseph Brooks over who won the 1872 governor's election erupted in violence. Baxter was declared the winner but Brooks believed he should have been elected and tried to have the election results changed.

Finally both sides put together armies to take control of the State House. Baxter's army found the cannons in the river and repaired both guns. They were placed on Markham Street to frighten Brooks's men. Eventually President Ulysses S. Grant settled this dispute by recognizing Baxter as the governor of Arkansas
http://www.oldstatehouse.com/collections/classroom/arkansas_news.aspx?issue=11&page=6&detail=482

……

During the Brooks-Baxter "war" of 1874, partisans of Governor Elisha Baxter repaired the gun and mounted on the riverbank. The piece was never fired, however, until a blank charge was set off at the close of the "war" to celebrate Baxter's victory.For more information on the Brooks-Baxter Wars visit this link.
http://www.waymarking.com/waymarks/WM94WM_Lady_Baxter_Cannon_Little_Rock_Arkansas