The method developed in Part I for treating the difficulty in the case when the secular periods determined from the so-called secular determinant are nearly commensurable with each other, was applied to the theory of the secular perturbation of the third degree of the asteroids under the action of Jupiter and Saturn. An interval in the distribution of the mean motions of the asteroids extending from 716."5 to 719."4 was suspected t o be a gap. This interval falls accidentally near to the commensurability-point of a simple type of the first order in the secular periods. By the method, which I have demonstrated in Part I, I tried to find out whether there occurs any exponential factor in the expression of the motion of the asteroids in and near this interval. The result was contrary to the supposition. To treat more rigorously we must consider all the eight principal planets in the solar system. Some of the asteroids near the suspected gap belong to the Coronis Family. The fact that the eccentricities of the asteroids of this family are small, was pointed out to be related closely to the stability of their motion. One may strongly argue against this method for the fact that this method breaks down for large values of the eccentricities, while in the actual case in the solar system some of the asteroids are furnished with rather large eccentricities. I am thankful to Prof. K. Hirayama for his taking interest in this work

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