The writer has been studying in the manner of expression of the damping properties of the rolling motion of ships and the method of analysis which is simple and is to be employed in various calculations, having just achieved some of the results as follows. In the general case of the curve of extinction to be expressed by an arbitrary function of amplitude θ as having an entire approximation the expression of the damping properties of the rolling motion of ships is considered to be appropriate as explained in the following sequence. (1) In order to express, of the first significance, the damping properties of the motion peculiar to hulls the number of swing for the rolling to decrease to one-half amplitude μ is employed in the amplitude θ=10°. Furtheremore to express the degree of increase in the damping of the rolling for the augmentation of amplitude, μ₂/μ₁, ratio of the number of swing for the rolling to decrease to one-half amplitude μ₂ and μ₁ in amplitude θ=20° and 10° is employed. (2) The value of these μ₂ and μ₁ can be obtained directly from the experimental result of the rolling motion. (3) The damping properties of the rolling motion among waves are expressed by maximum amplitude in synchronous rolling θ_max in the simplified imaginary standard condition on the utmost audacious assumption. In this case the damping forces among waves are taken for those in the still water and that which is learnt from Zimmermann's study is taken for the standard condition of waves. (4) If the damping properties of the rolling motion of ships are expressed by the number of swing for the rolling to decrease to one-half amplitude μ in an arbitrary amplitude, μ is found from μ₁ and μ₂/μ₁ as shown below; μ=1/ a_e (1+Δ _e θ){1-1/2(1+Δ _e θ)} where{ a_e =2/3μ₁(1-1/μ₂/μ₁) Δ _e =0.15/2μ₂μ₁-1(1-μ₂-μ₁) (5) The maximum amplitude in synchronous rolling among waves θ_max is found by graphic method from the following expression. γΘ _w /θ=2/π a ₂(1+Δ _e θ) where{Θ _w ; the slope of the surface trochoid γ; the coefficient of the effective wave slope a_e Δ _e ; by using the above expression can be round μ₁ and μ₂/μ₁.