Yamaguchi (original family name was Narisawa, changed as he was adopted) was born to a vassal of the shogun in 1856, growing up in Numadu because his brother-in-law On WATANABE, English scholar and translator, was a professor at Numadu Hei School (Numazu officer academy) (Yamaguchi was too young to enter).
山口（旧姓成澤、養子のため改姓）は安政3年に幕臣の子として生まれ、義兄の英学者・翻訳家の渡部温（『イソップ寓話』の翻訳等で名高い）が沼津兵学校教授を務めていたため、幼時を沼津で過ごす（年少のため入学はせず）。