( m ) 



the oscalating elements wo wish to derive not only the valnes of 

 these elements, bnt also of the masses, it is necessaiy that the expres- 

 sion of the perturhations as functions ot the masses be known. 

 The masses which form the basis of Souillart's theory probably 

 reqnire considerable corrections. In consequence of the mutual com- 

 mensnrability of the mean motions the perturbations of higher orders 

 are very large — : in some cases larger than those of the first order. 

 For these reasons the perturbations cannot be assumed to be linear 

 functions of the masses. The formulas needed to compute the correc- 

 tions to the perturbations corresponding to given corrections to the 

 masses have been developed by me, on the basis of Souillart's 

 numerical theory. They have been published in (rro/i. Fuhl. 17, art. 17. 



The data required for the determination of the masses are: 



I. The motions of the nodes, especially of 6^. The inclination of 

 satellite I is too small to allow tlie motion of its node to be deter- 

 mined with accuracy, and the motions of 6^ and 6^ are too slow to 

 be of aiiy importance for the determination of the masses, compared 

 with 6*,. The motion of 6.-^ is the datum trom which the constant of 

 compression Jb"^ must be derived. 



II. The motions of the perijoves, especially of to^. The excentri- 

 cities of I and II are again too small to allow a determination of 

 the motion of the perijove to be made. The motion of Wg on the 

 other hand, if it could be accurately determined, would be of little 

 value for the determination of the masses on account of the small 

 coefficients of these masses. The motion of (Ji^, which owing to the 

 large excentricity of this satellite can be very accurately determined, 

 is used for the derivation of the value of m^. 



Illrt. The great inequalities in the longitudes and radii-vectores 

 of the first and third satellites. These depend chiefly on m^, and 

 serve to determine this mass. 



lllb. The great inequality of the second satellite. This furnishes 

 an equation involving m^ and m^. 



These data are those used by Laplace. To these I have added: 



IV. The period of the libration. This depends on m^, m^ and m^. 

 Of these m^ only has a small coefticient, consequently the observed 

 period practically gives an equation between m^ and m^, from which 

 combined with III6 these two masses can be found ^). 



ij See "Over de Ubratie der drie binnenste satellieten van Jupiter, en eene 

 nieuwe methode ter bepaling van de massa van satelliet I," door Dr. W. de 

 Sitter. Handelingen van het 10e Ned. Nat. en Geneesk. Congres, (Arnhem 1905) 

 pages 125—128. 



