A critical parameter η0λ2/ｈ3 for long waves was introduced by Ursell in 1953. his course of discussion was developed by the general perturbation series of Lagrangian method and three equations were classified depending on η0λ2/ｈ3＞1, η0λ2/ｈ3～1, η0λ2/ｈ3＜1. In the present paper, the parameter η0λ2/ｈ3 is directly contained in the equations expanded from Friedrich's method, which is modified by the different stretching between the depth and the amplitude, and equations are classified by η0λ2/ｈ3＞1, η0λ2/ｈ3＜1. By this modification it is implied that η0λ2/ｈ3 is used as a method and the other parameter such as σ=(h/λ)2 used in Friedrich's expansion method and the otherparameter η0/ｈ is used for the estimation of approximation. It is also shown, in the case η0λ2/ｈ3＞1, this method gives the same results obtained by Keulegan and Patterson which were derived from the potential theory.