Analysis of the Mecanique Celeste of M, La Place. 26"9 



he determines the length of the simple pendulum which 

 would make its oscillations in the same time. The author 

 afterwards takes up the motion of fluids : he establishes the 

 conditions necessary, in order that this movement may take 

 place, and that the continuity of the fluid at the same time 

 may be always satisfied : he discusses certain cases in which 

 these equations are integrable, such as the case where the 

 density being any given function of the pressure, the sum of 

 the velocities parallel to the three rectangular axes, multiplied 

 each by the element of their direction, forms an exact vari- 

 ation ; a condition which will he fulfilled at every instant if it 

 be in one alone. This case takes place when the motions of 

 the fluid are very small ; and the author draws from it the 

 equations which involve the theory of the very small undu- 

 lations of homogeneous fluids. Considering afterwards a 

 homogeneous fluid mass, endowed with a motion of rota- 

 tion uniform around one of the rectangular axes, he shows 

 that this hypothesis verifies the equations of the movement 

 and of the continuity of fluids ; whence he concludes that a 

 similar movement is possible. This case is one of those in 

 which the sum of the velocities multiplied respectively by 

 the elements of their direction is not an exact variation m 7 

 whence it follows, that motion may take place without this 

 condition being fulfilled. 



The author afterwards determines the oscillations of a fluid 

 homogeneous mass, covering a spheroid endowed with an 

 uniform movement of rotation around one of the rectangular 

 axes, supposing this fluid mass to be deranged from the 

 state of equilibrium, by the action of very minute forces r 

 applying these considerations to the sea, and regarding its 

 depth as very small, relatively to the terrestrial radius, he 

 thence deduces the conditions of its motion ; and comparing 

 them with those of its equilibrium, he shows ihat^ach point - 

 of the spheroid covered by the sea is more pressed in the 

 state of motion than in that of equilibrium, from the weight 

 of the smalicolumn of water comprehended between the sur- 

 face of the sea and the surface of level ; this excess of pres- 

 sure becoming negative in the points where the surface 19 

 lowered below the level. It results also from the same ana- 

 lysis, 



