After experiencing such difficulties, Hakuseki ARAI, who was concerned about the discontinuity of the Imperial line, suggested to the Seii Taishogun (literally, "great general who subdues the barbarians"), Ienobu TOKUGAWA, that there was a need to establish a new subsidiary Miyake to support the Imperial family, after considering the fact that in the Shogun family, there are three branch families of the Tokugawa House.
その苦い経験から皇統の断絶を危惧した新井白石が、徳川将軍家に徳川御三家があるように、皇室にもそれを補完する新たな宮家を必要との建言を征夷大将軍徳川家宣に出した。