In 1876, Mutoh Heigaku (武藤平学), a Japanese businesssman in Vladivostok, proposed to the Japanese Ministry of Foreign Affairs that the government allow him to develop the Japanese territory of Matsushima. See HERE"
Following this, many Japanese who believed there to be a Japanese island called "Matsushima" (松島) in the sea of Japan started sending numerous petitions to Minstry of Foreign Affairs between 1876 and 1878 asking that they be allowed to develop the island. Though Japanese in the Edo era had been clearly aware of the locations of Takeshima (竹島 = today's Ulleungdo) and Matsushima (松島 = today's Takeshima/Liancourt Rocks/Dokdo), the non-existent island on Western maps called "Argonaut" and the turmoil in the Japanese government following the fall of the Edo Shogunate caused confusion and debate on the names and locations of islands in the Sea of Japan between Japan and Korea. See HERE.
In order to resolve these questions, Foreign Minister Terajima Munenori (寺島宗則) finally ordered an on-site survey of Ulleungdo in 1880 (明治十三年) and dispatched the warship Amagi to the Ulleungdo area to clear up the name confusion concerning the islands in the region. The Amagi discovered that "Matsushima" (松島) was actually Ulleungdo and "Takeshima" (竹島) was a small island off the northern shore of Ulleungdo, which Koreans pronounce as Jukdo (竹嶼). The map made during the survey confirms that Takeshima was Ulleungdo's neighboring island of Jukdo (竹島).
Kitazawa Masanari (北澤正誠) wrote an account of this survey in the Takeshima Kosho (竹島考証 - "A Study of Takeshima"). In his account, he concluded that Matsushima was Ulleungdo and confirmed that both Ulleungdo and the island he called Takeshima, which was Ulleungdo's neighboring island of Jukdo, were not Japanese territory. Jukdo is about about two kilometers off Ulleungdo's east shore.
Here is what Kitazawa wrote about the 1880 Amagi survey.
In the above (items) 甲, 乙, 丙, and 丁, there was so much argument about this and that that it was difficult to reach a decision. Even all the talk about conducting a survey had ended. In September 1880, when navy Ensign 三浦重郷 and others of the Warship Amagi returned to port, they said they reached "Matsushima (松島)", where they conducted a survey. The island was the so-called "Ulleungdo(鬱陵島)" of old, where they found a small island off the northern shore that someone said was called "Takeshima(竹島)", though it was not much bigger than a rock. In one morning, long-held suspicions and arguments were cleared up. Now, I present the following picture.
The following is the report and the map of Ulleungdo and Jukdo made during the Amagi survey. It was attached to Kitazawa's "Takeshima Kosho" and labelled as "No.24", which was the last number of the referenced documents in the book.
明治十三年九月十三日 水路局長海軍少將 柳楢悦
No. 24Waterway Report No. 33
This report was submitted by navy Ensign Miura Shigesato (三浦重郷), who is a crewman of the Amagi.
Sea of Japan
At Matsushima, which Koreans call Ulleungdo, we found anchorage. Matsushima (Ulleungdo) is located about 140 ri northwest 3/4 of Oki Prefecture. It was unknown whether or not anchorage was available because no ship had done a precise survey of the area. However, our ship, Amagi, called at this place during our trip to Joseon (Korea) and found a place to anchor off the east shore of the island, as is shown on the map.
September 13, 1880
Navy Rear Admiral Yanagi Narayoshi
Director of the Bureau of Hydrography
After the above report, Kitazawa, the author of this compilation and MOFA official, wrote the final conclusion as follows:
"I finally came to understand the situation when I learned that "Matsushima" (松島) was Ulleungdo, and the other island, which was called Takeshima (竹島), was just a rock(一個の岩石)(竹嶼/Jukdo=Boussole rock). Thus, today's Matsushima is the island that was called "Takeshima" in 1699 (元禄十二年), and (they [= Ulleungdo and Jukdo] are) not historically Japanese territory."
Reference : Lies, Half-truths, & Dokdo Video, Part 5