Below is a map of Japan published by Joseph Hutchin Colton of New York in 1855. An explanation at the bottom of the map says that it was "compiled from the maps of Siebold with additions from the surveys and reconnaisances of the U.S., Japan Ex." The map is stored in the US Library of Congess.
Since Colton's map of Japan was compiled from the maps of Siebold, it included Siebold's non-existent island of "Argonante," which was also labeled on this map as "Taka sima." (The non-existent island of "Argonante" was the result of a mismapping of Ulleungdo by the British ship Argonaut in 1789.) The map also shows Korea's real Ulleungdo labeled as both "Matsu sima" and "Dagelet Island."
At the time, the Japanese believed Takeshima (竹島) to be the Korean island of Ulleungdo (鬱陵島) and Matsushima (松島) to be a Japanese Island (Liancourt Rocks); however, the mismapping of the islands on Western maps, such as this one, caused confusion for Japanese mapmakers (See 1875 Map , 1882 Map, & 1894 Map) and government officials. Finally, the Japanese government sent the Japanese warship Amagi to the area in 1880 to conduct a survey and clear up the confusion (1880 survey). The Amagi reported that Matsushima (松島) was actually the Korean island of Ulleungdo, which also had a neighboring island named "Takeshima" (竹嶼), which is pronounced as "Jukseo" or "Jukdo" in Korean. (1880 Survey Map)
As a result of the 1880 survey, Japan changed the Japanese name for the Korean island of Ulleungdo from "Takeshima" (竹島) to "Matsushima" (松島), and the name of Japan's old Matsushima (Liancourt Rocks) to "Liancourt Rocks." When Japan incorporated Liancourt Rocks in 1905, they renamed it "Takeshima" (竹島), which was the old Japanese name for Korea's Ulleungdo.