in ihc Saliii' Sijstem. 25 



The motion of Jupiter's aplielion and Saturn's, since they 

 arise almost entirely from the action of each other, and as 

 their masses are best determined from their nuitual periodical 

 inequalities, it is almost useless to examine the motions of 

 their aphelia from observation : the motion of their nodes, 

 however, depends in a great measure on Venus and Mars; we 

 shall therefore examine tliem. 



For Jupiter there is still some uncertainty ; however, De- 

 lambre makes it about So'l, with a possible error of 2 or 3 

 seconds. Lalande employs this motion in his Tables. For 

 Saturn, Delambre makes the motion 33"'.'35: Lalande, 3l""7. 

 The mean of these, since they agree so nearly, cannot be far 

 from the truth ; we shall therefore suppose it 32"-52. We 

 have therefore the following number : 



Mercurv. Venus. Earth. Mars. Jupiter. Saturn. 



Node... 4-2"-73 3l"-52 ■ 30"-13 35"-7 32 '-52 



Aphelion 5&' 61 "-908 63 "-OO 



Laplace's values for the masses, which I first assumed as a 

 means of examining the above numbers, are as follows : 

 Mercury ojjjjipjn Jupiter 



Venus 55cVo7 Saturn 



Earth TTaTTTT Georgian 



These are all extracted from Laplace, with the exception of 

 that of the Earth, which he has estimated too largel}-, by as- 

 suming the parallax 8"-81 instead of 8"-56, which his own 

 lunar theory and the calculations of Short from the last trans- 

 it point out. I however, for various reasons, have assumed 

 it 8"-7. Laplace says. Mercury's, Venus's and Mars's masses 

 were first determined from their densities upon Lagrange's 

 hypothesis' of their being inversely proportional to their di- 

 stance from the sun, and then corrected from observation. He 

 therefore diminishes Mars's mass so found, in the ratio of -725 

 to unity from Delambre's observations of its effect on the pe- 

 riodical inequalities of the Earth's motion. And from similar 

 observations he increases Venus's mass determined from a se- 

 cular diminution of the obliquity of 50', in the ratio of l-074'3 

 to unity. And finally, Saturn's was first setded at ^-i^ -^, as 

 an elongation of 2' 57" of the fourth satellite required; and 

 then the ine(|ualities in the motion of Jupiter upon this sup- 

 ))osition, compared with fifty oppositions, showed that it must 

 be diminished by j^VTii' "hicli reduced it to j^-^VoiT' ^^® 

 above value. 



With these values we have the following secular motions of 

 the planets' orbits : 



\ ol. ri5. No. 321. J<ni. 1S25. 1) Sidriral 



_ i _ 



35'o'iO'S 



