48 STATEMENTANDEXPOSITIONOP 



there should have been a very close approximation to the conformity in question, 

 and then the mutual attraction of the satellites would rigorously establish such a 

 conformity j" and hence, moreover, " make the mean longitude of the first satellite 

 minus three times that of the second, plus twice that of the third, always equal to 

 a semi-circumference." 



At the same time, as he says, this would originate a periodical inequality depend- 

 ant on the small quantity by which the mean motions " primitively deviated from 

 the relation which Ave have announced. Notwithstanding all the care which 

 Delambre took to make out this inequality by observation, he could not discover it ; 

 which proves its extreme minuteness, and consequently indicates with very great 

 probability a cause which made it disappear." 



M. Laplace then proceeds to show that, on his own hypothesis, the satellites of 

 Jupiter, immediately after their formation, did not move in a perfect vacuum; but 

 that the less condensable molecules of the primitive atmospheres of the sun and of 

 the planet furnished a resisting medium^ the effect of which would be different on 

 every one of the satellites in question, and w^hen their motions attained the con- 

 ditions requisite to the establishment of the conformity of motions, the same resist- 

 ance diminished the inequality to which this relation gave rise, and finally rendered 

 it insensible. 



All this may well be extended to the case of tlie conformiiy of periodic-times in 

 Saturn^s system, as well as those of the periodic-times of the outer planets already 

 specified. 



M. Laplace illustrates the process in question by the retarded motion of a pen- 

 dulum in a resisting medium; entire revolutions being reduced to oscillations 

 diminished continually by the resistance of the medium, and in the end annihi- 

 lated; the pendulum coming to rest, and ever after remaining so. 



The original passage in which this illustration occurs, is the closing one of the 

 Systeme du Monde ; and is as follows : — 



" On ne peut mieux comparer ces effets, qu'au mouvement d'un pendule anime 

 d'une grande vitesse, dans un milieu tres peu resistant. II decrira d'abord un 

 grand nombre de circonferences ; mais a la longue, son mouvement de circulation 

 toujours decroissant se changera dans un mouvement d'oscillation, qui diminuant 

 lui-meme de plus en plus, par la resistance du milieu, finera par s'aneantir; alors 

 le pendule arrive a I'etat du repos, y restera sans cesse." 



The changes indicated in the quotation in the next article, contemplate a veri- 

 table oscillation, in some measure like this. 



Special Characteristics of the Moon, and other Satellites. 



(68) M. Laplace, commenting on his own hypothesis, in the connexion already 

 referred to, (67), thus expresses himself: "One of the most singular phenomena 

 of the solar system is the rigorous equality observed between the angular motions 

 of rotation and revolution of every satellite. We may wager infinity to one that 



' The italics are our own. 



