We know that the Watanabe letter was written in response to the Mutoh petition because that is how it was described in an 1881 Japanese Ministry Report entitled, "A Study of Historical Evidence of Takeshima" (竹島考証). Here is what was written just before the Watanabe letter in the 1881 report.
"In regard to the two above letters, Watanabe Kouki (渡辺洪基) wrote his opinion in two letters. Items No. 11 and No. 12 are those letters."The Mutoh petition was one of the "two above letters" in the report. It was labeled Item No. 8. This means that the Watanabe letter was written in 1876, sometime after Mutoh's July petition. You can seen Mutoh Heigaku's petiton HERE.
The Watanabe letter explained that there was confusion in the Foreign Ministry in regard to the location of the Matsushima described in Mutoh's petition, but it also said that Liancourt Rocks (Matsushima / Hornet Rocks) were Japanese.
Therefore, if the “Matsushima” being talked about here is Takeshima (Ulleungdo), then it belongs to them. If the Matsushima is not Takeshima, then it must belong to Japan.Mr. Watanabe urged that a survey ship be sent to the area to clear up the mystery, which is what the Japanese government eventually did in 1880. The survey determined that the Matsushima being referred to in the petition was, in fact, Ulleungdo.
The following is a translation of Mr. Watanabe's letter, which can be found as Item No. 11 in the third and last volume of the 1881 text, "A Study of Historical Evidence of Takeshima" (竹島考証):
Opinion on Matsushima - 1
There are several brief descriptions of Takeshima (Ulleungdo) in past records, but there are no discussions of Matsushima. However, these days people are talking a great deal about Matsushima. There are various views. Some say that it is two islands, and some say that it is one island with two names, but I have not heard that it has been decided either way.
The (mentioned) “Takeshima” is considered to be Chosun’s Ulleungdo, which the Shogunate ended up entrusting to them (Koreans) as a convenient quick fix, without considering future implications. Therefore, if the “Matsushima” being talked about here is Takeshima (Ulleungdo), then it belongs to them. If the Matsushima is not Takeshima, then it must belong to Japan. It is still inconclusive.
The location of Matsushima is considered important because it is situated between Joseon and Japan. It is on sea routes between Nagasaki and Vladisvostok and between Shimonseiki and Wonsan, so this is a critical location, where English and Russian warships are frequently seen. So we should be very careful. Even if it is part of Joseon, we still have to protect it. As things stand now, we have no answers to give if other countries ask us about the island. This means the island is ownerless.
Many records say that “Argonaut,” which is the Western name for Takeshima (Ulleungdo), does not exist, and that “Dagelet,” which refers to Matsushima, is actually Takeshima (Ulleungdo). So what we call "Matsushima” (Liancourt Rocks) is called “Hornet Rocks” by Westerners. Foreign maps show Hornet Rocks to be Japanese territory, but there is still no agreement among countries concerning the other two islands.
We do not have the answers either, so the area should be surveyed to determine under whose jurisdiction it belongs. Therefore, we should first contact Shimane Prefecture and investigate their relationship up to now. At the same time, we need to dispatch a ship to do a survey of the area. If Chosun has already started, we need to determine their progress and consider our options. I respectfully urge that this matter be dealt with as soon as possible.
Watanabe Kouki, Director of the Bureau of Documents