254
[Mec. Cel.
CHAPTER XI.
ON THE LIBRATION OF THE THREE INNER SATELLITES OF JUPITER.
29. We have seen, in [6629], that the mean motions of the three innersatellites of Jupiter are subjected to the following law, which holds goodrelative to any variable axis, moving according to any law whatever [6632].The mean motion of the first satellite , plus twice that of the third , is
exactly equal to three times the mean motion of the second satellite.
To show how accurately this law agrees with observation, we shall givethe mean secular motions of these three bodies, as Delambre has determined
them, by the discussion of an immense number of eclipses. He has found
that, in one hundred Julian years, these motions, relative to the variable
*
equinox, are,
First Satellite, 8258261°,63313;
Second Satellite, 4114125°,81277 ;
Third Satellite, 2042057°,90398 ;
[7253]
[7254]
[7255]
[7255']
[Fourth Satellite, 875427°,45956]. [7281]
* (3574) The motions of the satellites from the variable equinox in 100 Julian years,is given in [7253—7255]. Dividing these by 100, we get the motions in one Julian year,which is taken for the unit of time in [7283']. Subtracting the annual precession 154",63[4357], we get the motions from the fixed equinox 825826009", 411412427",
204205635", 87542591", which agree nearly with the values of n, n', n", ri" [6025&].
the preceding value of n"', we obtain, from [6840], the expression of M— 337211"[6025m] ; agreeing nearly with Bouvard’s tables 337212",094. These values ofn, n', n", n"', agree very nearly with those used by Delambre, in his new tables
[72535]
[7253c] [6781A, &c.], as is evident by subtracting the precession for 100 years 1°,5463 from thenumbers in [6781o—r] ; then dividing by 100, and reducing to seconds.