CONTENTS. IX 



of the subject of motion where the centre of forces is immoveable, 

 ib. 



(SECTION XI. Principia.) Motion in orbits where the centre is dis 

 turbed, or where other forces disturb the motion divided into 

 three heads, 



i. Disturbance produced by the mutual action of two bodies 

 revolving round one another, 104. Demonstration of their 

 motion round each other, and round the common centre of 

 gravity, 105. Motion referred to a body in the centre of 

 gravity, 107. Amount of the body which must be in the im- 

 moveable centre that it may act there, as the bodies would act 

 on each other, were one to be in the fixed centre, ib. Deter 

 mination of their absolute trajectories in space, ib. Application 

 to the earth and moon, 108. 



ii. Disturbances produced by the action of the whole bodies of any 

 subordinate system on each other, and by the bodies of other 

 systems on any given subordinate system, illustrated from Laplace, 

 ib. Remarks on Newton s investigations, and the problem of 

 three or more bodies, 109- Comparative disadvantages under 

 which he laboured, ib. Improvement, first, of the calculus 

 itself, and secondly, by the introduction of that of variations, 

 peculiarly fitted to facilitate these inquiries, 110. How the 

 latter especially bears on the subject, ib. Motion of the moon s 

 apsides and nodes, 112. Variation in the rate of both their 

 motions, ib. Acceleration of the moon s motion, ib. The cause 

 discovered by Laplace from the algebraical expression, 113. 

 Connexion between the transverse axis and the mean motion, ib. 



Kepler s law demonstrated, 114. Proved by the mere exami 

 nation of the algebraical expression only to be true if there are no 

 disturbing forces in action, 115. Same inspection likewise shows 

 the retardation of the apsides and nodes to be caused like the 

 moon s acceleration by the decrease of the earth s eccentricity, ib. 



Confirmation of the calculus by actual observation, ib. Slow 

 secular inequality of the moon discovered by Laplace, in dimi 

 nution of her secular acceleration, 11 6. Irregularity of other 

 orbits and motions, ib. Motion of earth s apsides produced by 

 the disturbing forces of the greater planets, 117. Variation of 

 orbits of other planets, ib. Disturbances at first seem not reduc 

 ible to any fixed rule, 118. Euler s attempt and errors, ib. 



His important discovery, ib. Discovery by Lagrange and 

 Laplace of the stability of the system, and universal operation of 

 the rule, 118. Mean motions of Jupiter and Saturn commen 

 surable, 119. Proportion of motion and distances of Jupiter s 

 satellites, ib. Laplace s remarks on Jupiter and Saturn, ib. 

 No satellite but the moon disturbs its primary, 120. The 

 greater axes of the planetary orbits do not vary from one long 

 period to another, 121. The period of their change being 



