150 Remarks oh Dr. Enfield's Institutes 



editions concerning the retrogradation of the primary plan- 

 ents ; and, should, like them, have been rectified or struck 

 out. All that can be said with truth is, that during the spe- 

 cified interval the motion of the secondary is retrograde 

 relatively to its primary ; and even this statement can 

 scarcely be extended to the satellites of Herschel.* 



Prop. 114. " The greatest elongations of a satellite on 

 each side are equal." This proposition has several excep- 

 tions. The orbits of the third and fourth satellites of Ju- 

 piter have a very sensible excentricity ; and the same is true 

 of the fourth (now more generally numbered as the sixth) 

 satellite of Saturn. See Laplace: Syst. du Monde. The 

 latter, according to Delambre, (Ast. III. 510,) has an ellip- 

 ticity nearly equal to that of our moon. 



Prop. 123. Several of the particulars inserted in the an- 

 nexed scholium from Sir I. Newton, have now become ob- 

 solete. In particular, the quantities of matter in Jupiter 

 and Saturn, instead of being to that in the sun in the ratios 

 of 1 to 1100 and 2360, are now known to be in the ratios of 

 1 to 1067 and 3534.f 



Prop. 135, is founded on the erroneous theory of retro- 

 gradation previously laid down ; and therefore should have 

 been corrected. 



Prop. 155. The demonstration of this proposition is in 

 part fallacious. It is said to be contrary to prop. 51. cor. of 

 Book 11, that the centre of gravity of two gravitating bod- 

 ies should move ; and is inferred that if one of the bodies 

 is projected in any direction, the other must acquire (by 

 what means we are not told) an equal motion in the oppo- 

 site direction. Now this is so far from following as a ne- 

 cessary consequence, that the other body will not in fact 

 acquire any such motion; and if a projectile movement be 



* We have not attempted, in the general list of coiTecfions insei'ted, p. 

 14fi, to rectify the periodical times of the satellites of Herschel ; for with, 

 the exce[)tion of the second and fourth, their distances from their primary 

 are wholly conjectural ; nor is even their nymber res;arded by Dr. Herschel 

 as yet fully ascertained. His last determination of die synodical revolutions 

 of the second and fourth, given in the Philos. Trans, for 1815, is as follows : 

 II. 8d. 16h.56/5". 

 IV. 13d. llh.8'59". 



The inclination of their orbits to the ecliptic he finds to be 78° 58', — 

 much farther from perpendicularity than has been heretofore supjjosed, 



t Mec. Celeste. Fart. U. Ch. 9. 



