Researches on the Distribution of the Mean Motions of the Asteroids. 57 



stable, the eccentricity must always be very small. On the 

 positive (inner) side of x, the asteroids which made the libration 

 previously with negative value of C remain near the critical point 

 with small eccentricities, as was shown in Chapter III, The 

 asteroids which were removed from the negative side do not stay 

 long near the critical point, and therefore will not affect the mean 

 value of the eccentricity, although they may have unusually great 

 values. 



In concluding the present paper I wish to express my 

 gratitude to Prof. Brown of Yale University, and to Prof. Eichel- 

 berger of the Naval Observatory at Washington, both of whom read 

 the first part of this paper and gave valuable and encouraging 

 suggestions in connection with my investigation. 

 ' Astronomical Observatory, Tokyo, Nov. 6, 1917. 



