The Jackson County Courthouse is a former county courthouse in Jacksonville, Oregon, United States, built in 1883. The courthouse is a contributing property of the Jacksonville Historic District, which is listed on the National Register of Historic Places (NRHP). It was formerly the Jacksonville Museum owned by Jackson County and operated by the Southern Oregon Historical Society (SOHS), which also managed several other historic properties in Jacksonville. The museum in the courthouse closed in 2006 because of lack of funding. Ownership of the historic courthouse was transferred to the City of Jacksonville in 2012. The SOHS still operates Hanley Farm in Central Point and a research library in Medford.
Widows Bar Lock and Dam was a dam once located along the Tennessee River in Jackson County, Alabama, USA. It was situated above the mouth of the Tennessee River, near the river's confluence with Widows Creek. The dam was completed 8 September 1924, and was designed and operated by the U.S. Army Corps of Engineers. It was serviced by a by navigation lock. When the Tennessee Valley Authority took control of flood control and navigation improvement operations in the Tennessee Valley in the 1930s, Widows Bar was considered too high maintenance, and it was dismantled as part of the construction of Guntersville Dam.
Jacksonville is the largest city by population in the U.S. state of Florida, and the largest city by area in the contiguous United States. It is the county seat of Duval County, with which the city government consolidated in 1968. Consolidation gave Jacksonville its great size and placed most of its metropolitan population within the city limits; with an estimated population of 853,382 in 2014, it is the most populous city proper in Florida and the Southeast, and the 12th most populous in the United States. Jacksonville is the principal city in the Jacksonville metropolitan area, with a population of 1,345,596 in 2010.
The United States Congress declared war on Mexico on May 13, 1846 after only having a few hours to debate. Although President José Mariano Paredes's issuance of a manifesto on May 23 is sometimes considered the declaration of war, Mexico officially declared war by Congress on July 7. After the American invasion of New Mexico, Chihuahua sent 12,000 men led by Colonel Vidal to the border to stop the American military advance into the state. The Mexican forces being impatient to confront the American forces passed beyond El Paso del Norte about 20 miles (32 km) north along the Rio Grande. The first battle that Chihuahua fought was the battle of El Bracito; the Mexican forces consisting of 500 cavalry and 70 infantry confronted a force of 1,100–1,200 Americans on December 25, 1846. The battle ended badly by the Mexican forces that were then forced to retreat back into the state of Chihuahua. By December 27, 1846, the American forces occupied El Paso Del Norte. General Doniphan maintained camp in El Paso Del Norte awaiting supplies and artillery which he received in February 1847.

Question: What is the population ranking of the city that houses the courthouse that is in the same administrative territorial entity as Widows Bar Dam, in the country who won the battle?
Answer: 12th