<正> Let p be an odd prime with p≡1 (mod 4) and Q(p1/2) be the real quadratic field. Alsolet ε and h denote the fundamental unit and the the class number of Q(p1/2), respectively.The main pur-pose of this paper is to study the "explicit" expressions of εh and ε2h and to discuss the problems relatedto the conjecture of Ankeny-Artin-Chowla.