Analysis of the Mccanique Celeste of M. La Place, 265 



nomena with care, compares them with each other, and, 

 removing the illusions of imagination and of the senses, 

 penetrates to the true laws of nature. In these respects the 

 task fitted M. La Place exactly, who from the outset of 

 his career directed his researches towards the celestial phe- 

 nomena, and who has since taken an active part in the 

 progress of this science, by publishing, upon every point 

 connected with the system of the world, a crowd of Me- 

 moirs filled with important discoveries. It is principally 

 from these memoirs that M. La Place has derived the ma- 

 terials of this great work : and if he has connected them 

 with each other by an admirable coincidence, it has arisen 

 from all of them having become peculiar to himself, either 

 because he had been the first to discover them, or from the 

 new form which he has given to them. 



Astronomy, considered under the most general point of 

 view, is a great problem in mechanics, the elements of 

 which are furnished by observations. This problem is very 

 susceptible of being submitted to calculation ; because the 

 immense distances which separate the celestial bodies, at- 

 tenuating the secondary causes, which might act upon them, 

 in order to bring into view only the principal forces which 

 animate them, give to their movements a rigour and preci- 

 sion truly mathematical. To develop the relations which 

 exist between the motions and forces which produce them; 

 to deduce from thence the nature of the force which ought to 

 animate celestial bodies, in order that their movements may 

 be such as are presented to us by observation ; thus to raise 

 ourselves to the principle of universal gravity, and to re-de- 

 scend from this principle to the explanation of all the ce- 

 lestial phenomena, even to their minutest details, such is the 

 object of the Mccanique Celeste, and such has been the ob- 

 ject of the labours of M. La Place. 



BOOK FIRST. 



After having first detailed the principles of the compo- 

 sition and decomposition of forces, the author establishes 

 the conditions of equilibrium for any point wanted, by any 

 number of forces acting in any given directions; conditions 



which 



