The oscillations of ships under voyage are produced by the ocean waves, and the ocean waves contain randum elements like the other geophysical phenomena. Recently the theory of probability and statistical inference were used as a means of analysis of these geophysical phenomena. That is to say, the record of these phenomena were used as a Time Series that contained the elements of variance that follow the laws of randumness. If the compulsory force upon ships were regarded like this process, the oscillations of ships produced by that force may be regarded similarly. I studied the motions of ships from this standpoint, and succeeded in analizing them as a Stationary Time Series. At frst I made it clear that the Correlogram of the time series of ships oscillation can be regarded as a sample of a certain Auto-regressive Process, and then introduced the method of analysis of the theoretical Correlogram and the Spectrum Density of ships oscllations. As a result, the following things became clear : - (i) The prominent period of oscillations of ship can be found clearly from a rather irregular record by means of the Periodograms of Time Series. (ii) Analiying by the method of Harmonic Analysis, we can get the periods and amplitudes of the elemental waves of oscillations that are tested the level of significance from the standpoint of statistical inference. (iii) By calculating Correlograms from the record of oscillations of ships that are under way on ocean waves, we can get the real period and the damping factor of the elements of its oscillations, which could not be found correctly until now. (iv) By making a Fourier-Cosine Inversion from the Correlogram, we can directly obtain a Spectrum of a ships oscillation and can clarify the construction of the compulsory force upon the ship, composed of the period and the damping of elements of ocean waves. (v) If we synthesize the Correlogram of ocean waves and the nature of a ship's free oscillations, we can obtain a theoretical Correlogram and Spectrum of a ship's motion on waves, and from this the knowledge of a ship's forced motion on irregular waves. And by this method, I analized several records of oscillations of the Aomori-Hakodate Train Ferry Ship, and made clear many points of characteristics of this ship that were unknown for us untill now.