Dr. Bowditch, President of the American Academy. xxxiii 
head, La Place considers the Equilibrium and Composition of Forces 
which act on a Material Point; the Motion of a Material Point; 
the Equilibrium of a System of Bodies; the Equilibrium of Fluids ; 
the General Principles of the Motion of a System of Bodies ; the 
Laws of Motion of a System of Bodies, in all the relations mathe- 
matically possible between the Force and Velocity; the Motions 
of a Solid Body of any Figure whatever; and the Motion of Fluids. 
The investigation of these great problems, in this very general 
form, it will be perceived, prepares the way for the consideration 
of the systems of bodies, and the individual bodies composing 
those systems, both solid and fluid, which are the constituent parts 
of the universe. 
La Place then proceeds to the second principal division of his 
work; which is, the Law of Universal Gravitation, and the Mo- 
tions of the Centres of Gravity of the Heavenly Bodies ; and, under 
this part of his subject, he considers the Law of Universal Gravity, 
deduced from observation ; the Differential Equations of the Motion 
of a System of Bodies, subjected to their Mutual Attractions; the 
First Approximation of the Motions of the Heavenly Bodies, or 
Theory of the Elliptical Motion; the Determination of the Elements 
of the Elliptical Motion ; the General Methods of finding the Mo- 
tions of the Heavenly Bodies by successive Approximations ; the 
Second Approximation of the Celestial Motions, or Theory of their 
Perturbations ; the Secular Inequalities of the Motions of the Heav- 
enly Bodies; and the Second Method of Approximation to the 
Motions of the Heavenly Bodies, which is founded on the Varia- 
tions, which the Elements of the Motion, supposed to be Elliptical, 
suffer by means of the periodical and secular inequalities. All 
these profound and complicated questions, particularly the secular 
inequalities, — whose progress and effects are so extremely slow, 
as to have eluded the calculation of all La Place’s predecessors, — 
6 
