( -4 ) 



must lie (If'teriiiined froui the solution of the equations (8) are 

 ^«0, .'/o. Vm -n-o and — . 



dTi 

 The values of — — for the four satellites are however nof nnitnally 

 at 



independent. The theory gives these differential coefficients as functions 



of the masses of the satellites and the compression of Jupiter. The 



masses need not be considered here. I have tried to determine a 



correction to m,, hut this determination had too small a weight (o 



have any real \alue. The influence of the other masses is even 



smaller. 



The compression enters into the formulas through the factor Jb', 

 where J is the well known constant, which is approximately equal 

 to Q — Va *f (Q = ellii)ticity of the free surface, (p = ratio of centri- 

 fugal force to gravity at the equator of Jupiter) and 6 is the equatorial 

 radius ') of the planet. 



If we introduce as unknown : 



_dJb' 



then the true values of the coefficients- of t arc 



dPi /"drf, 



-\- "i ^ 



lit y dt 

 The coefficients a; depend practically alone on the mean motions, 



dFi 

 and must be treated as absolute constants. They differ little from 



dt 



itself, and conseqnently the ratios of tiie motions of the nodes must 

 be considered as approximately constant. The adopted values accor- 

 ding to Souillart's theory are (daily motions) : 



I — i I = 0M4109, I -"I = O°.0O7O19 



V dt J, y dt J, 



^ ) = 0°.033010 I — i 1 = 0°.001898 • 



dt ;„ V dt Jo 



The 36 equations (8) thus contain the 11 unknowns 



y- -To .p„ «/„ ^ 



These equations must be solved by successive approximations. The 

 conditions for the application of the method of least squares are far 

 from being fulfilled. 



These approximations have been conducted in the following maimer. 



') In the original Dulcli h was erroneously stated to be the diameter, instead 

 of tlic radius. 



