3 



Eesearches on the Distribution of the Mean Motions of the Asteroids. 49 



The mean value of the angle of eccentricity of all the asteroids, 

 791 in number, is 8 '50. Accordingly the mean value in the 

 outer portion is less than the total mean by 0*53 and that in the 

 inner portion, by 1°19. Thus it seems quite certain that the 

 eccentricity in the portion near the gaps, especially on the inner side, 

 is smaller than that in the other portions. 



60. In order to determine the types of the motion near the 

 commensurable points I have computed the quantities (7, E, Eo, 

 F^ and E% for each asteroid by the formulae — 



x=—-\ d=sXl-l') + (s-s')(w-l') 



no 



E.=Fo + ^^^îfl, {-Q^f^ (approximately) 



which may be easily deduced from the equations in Chapter II. 

 The constants ;)i2,. were computed by Leverrier's formulée, and 

 the elements of the asteroids, n, e, vs and /, according to the data 

 in the Berliner Jahrbuch for 1917. 



61. For the class 2/1 taking 41 asteroids with n—n^ within 

 the limits— 35" and + 25", the results are as follows: — 



2/1 «0=598 26 p/^^xlO^'rrrO-Tie 



No. Epoch m I V n xXlQSeXlO 6 CXlO* -Exl02 F0XIO2 FjXlOS Type 



790 1914 VII 10-5 235 6 274°0 319'-0 564-31 -5-68 1-48 281-6 +30-99 + 5-97 52-03 371 Ri 

 76 1911 VII 6-0 87-5 309-6 227-5 564-54 -5-64 1-73 3021 +27-86 + ^I'o 4206 352 Ei 



