NEWTON S PRINCIPIA. 119 



and discovered, while investigating these motions, the 

 great law of the stability of the universe. 



The circumstance which mainly contributes to render 

 the irregularities in the motions of two planets great, and 

 which especially augments the disturbance of Jupiter s 

 satellites, is that their mean motions should be commen 

 surable, which those of Jupiter and Saturn are after a very 

 remarkable manner. Five times the mean motion of 

 Saturn are equal to nearly twice that of Jupiter ; and the 

 three first satellites of Jupiter are so related to each other, 

 that the mean motion of the first, added to twice the mean 

 motion of the third, is equal to three times that of the 

 second ; while the longitude of the first added to twice that 

 of the third, and subtracted from three times that of the 

 second, makes up exactly 180. Laplace showed, that this 

 proportion, if it was not originally fixed between those 

 satellites, must have been established by the action of the 

 attractive and disturbing forces *; and it is a truly remark 

 able thing, that when the theory had given a value for the 

 three mean motions, M 3 m -f 2 \L = 0, the comparison 

 of the eclipses for a century was found to make the expres 

 sion only 9&quot;, and consequently to tally with the theory 

 within that very small difference. The observation of the 

 effects which were produced upon the equations which 

 resulted from the analysis, by the proportions above stated 

 between the mean motions of Jupiter and Saturn, induced 

 Laplace to suspect that this made quantities become of 

 importance, which from the high powers of the denomi 

 nators might otherwise have been insignificant. For one 

 of the terms in the equation to 8 r (variation of the radius 

 vector of the first satellite), for example, had for its deno- 



* Mec. Cel. liv. vi. ch. 1.2. 12. 13.; also for the analytical investiga 

 tion, see liv. viii. throughout, and liv. ii. ch. 8. s. 65. 



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