The 3rd courthouse was quickly built in 1873, a grand French Renaissance-style building, with a clock and bell tower rising 113 feet into the sky. It had a mansard roof, and was constructed of brick with iron cornices. Its size was a disadvantage when fire broke out in 1901; ladders and water could not reach the upper floors where the fire began. Documents were however safe in fireproof vaults built to protect them.

The fourth courthouse is the one you see and was completed in 1905. It is the grandest of all Kentucky courthouses.  http://www.hopewellmuseum.org/markers-courthouse.html

Twain and Cable were there either on December 31, 1884 [ http://twain.lib.virginia.edu/huckfinn/tourschd.html ] or January 1, 1885 [ http://www.twainquotes.com/SpeechIndex.html ] 

Image from:  http://www.hopewellmuseum.org/markers-courthouse.html