PIERRE SIMON LAPLACE 147 



proached very near to the relation which renders the mean motion of 

 the first, minus three times that of the second, plus twice that of the 

 third, equal to nothing. Then their mutual attraction rendered this 

 ratio rigorously exact, and it has moreover made the mean longitude 

 of the first minus three times that of the second, plus twice that of 

 the third, equal to a semicircumference. At the same time, it gave 

 rise to a periodic inequality, which depends on the small quantity, by 

 which the mean motions originally deviated from the relation which 

 we have just announced. Notwithstanding all the care Delambre 

 took in his observations, he could not recognize this inequality, which, 

 while it evinces its extreme smallness, also indicates, with a high de- 

 gree of probability, the existence of a cause which makes it to dis- 

 appear. In our hypothesis, the satellites of Jupiter, immediately after 

 their formation, did not move in a perfect vacuo ; the less condensa- 

 able molecules of the primitive atmospheres of the Sun and planet 

 would then constitute a rare medium, the resistance of which being dif- 

 ferent for each of the stars, might make the mean motions to approach 

 by degrees to the ratio in question ; and when these movements had 

 thus attained the conditions requisite, in order that the mutual attrac- 

 tion of the three satellites might render this relation accurately true, 

 it perpetuahy diminished the inequality which this relation originated, 

 and eventually rendered it insensible. We cannot better illustrate 

 these effects than by comparing them to the motion of a pendulum, 

 which, actuated by a great velocity, moves in a medium, the resistance 

 of which is inconsiderable. It will first describe a great number of 

 circumstances ; but at length its motion of circulation perpetually 

 decreasing, it will be converted into an oscillatory motion, which it- 

 self diminishing more and more, by the resistance of the medium, 

 will eventually be totally destroyed, and then the pendulum, having 

 attained a state of repose, will remain at rest for ever. 



