( 718 ) 



Newcomb litis already pointed oiil that oppositions of Pol^'hymnia, 

 as favourable as the one used in his work, will not recnr till the 

 end of the twentieth centurj', and a similar statement is true for 

 Themis. Hill has pointed out ^) that Jupiter produces in the motion 

 of certain nnnor planets (those of the Hecuba type) perturbations of 

 long periods, which amount to several degrees. Thus e. g. Freia is 

 subject to a perturbation, whose geocentric amplitude is 12^.7 with 

 a period of 121 years. The length of the period makes it impossible 

 to derive an improved value of the mass by this method in the 

 near future. 



Derivation of the jinal masses. 



The right-hand-members of the equations of condition, which have 

 served to determine the corrections to the values {B) of the masses, 

 have been derived, as explained above under I to IV, from: 



I. the motions of the nodes 6^ and 6^ (those of 6^ and 6^ I 

 leave out of consideration, as having too small weights), 



II. the motion of the perijove to^, 



III. the great inequalities .t'l, .v^, x^, 



IV. the period of the libration. 

 The equations are : 



I. 



- . 0266 o\' —. 0030 o\ — . 000 1 o v, _ . 0040 ^'v, _ . 0002 V4 =^ — . 000 10+. 000 08 

 — .0051 —.0003 —.0007 —.0007 ==- .000 41 ± 15 



II. 



■j-.OOOlloy' -f.00004!?vi +.00007^^2 +.000820 V3 — .00005v4 =— .OOC036 +.000020 



These three equations depend in part on the values of the elements 

 in 1750, which were determined from eclipse-observations. It has 

 already been ])ointed out above that practically the same results 

 would be found from extra-eclipse observations alone. 



III. 1«U1 1901 1902 Adopted 



— . 003 -^vi -I - . 4 03 V. —.014 5 V3 = -[- . 080 +.051 — . 058 + . 020 + , 040 



+ .195 -.008 +.816 = + .019 +.087 +.169 +.050 + 40 



— .001 +.060 —.006 =—.004 —.014 — .02J —.009 + 10 



The probable errors of the separate determinations have been given 

 in Table III. The p.e. of the adopted values were estimated according 

 to the agreement of the separate values. 



IV. 



+2 . 40-' ov^ +0 . 245 o\ +1 , 35» 0.^ = . 000 + .18 

 ij Collected works J, page 105. 



