206 AimhjHs of the Alccanique Celeste of M. La Place. 



fluid would begin to be dissipated in consequence of a very 

 rapid rotatorv motion. Tbe author shows that this is not 

 the case, since at this Hmit the gravity at the equator still 

 surpasses ti;e (liird of the gravity al the pole ; whence it 

 follows, thai ii the cijuilibriuni ceases to be possible, it is 

 because with a more rapid motion we could not give to the 

 fluid mass an elliptic figure, so as to make the result of its 

 attraction and of the centrifugal force perpendicular to the 

 surface. ^ 



The author aficrwardi examines if ecjuilibrium can sub- 

 sist with a figure elongated towards the poles, and proves 

 that this could not take place. What has been said a,s to 

 the possibilitv of two states of eijuilibriuin relative to the 

 same aniiular motion of rotation, jloes not carry with it 

 this possibility relative to one and the same primitive force: 

 in order to know what ought to be concluded in this re- 

 spect, the author considers a fluid mass primitively agitated 

 by any given forces, and then abandoned to itself and to 

 the mutual attraction of all its parts : by the centre of gra- 

 vity of this mass supposed to be iimnoveablc, he conceives 

 a plane on which the sum of the areas, described by the 

 projections of the radii vectores of each molecule, and mul- 

 tiplied by the respective masses of these molecules, to be 

 al the coimnencement. of the motion a maximum. This 

 plane will constaiuly maintain this property; also, when 

 after a great nimtber of oscillations the fluid mass shall 

 assun)e an uniform rotatory motion about a fixed axis, 

 this axis will be perpendicular to the plane just trientioned, 

 which will consequently become that of the equator, and 

 the rotatorv motion will be such that the sutn of the areas 

 on this plane will remain the same as at the origin of the 

 motion. This consideration determines the motion of ro- 

 tation and the figure of the body ; whence it follows, that 

 with respectto tliesaiiie primitive impulse, there is only one 

 elliptic figure which can satisfy the eciuiiibrium. The au- 

 thor observes, that the axis about which the rotatory motion 

 is established, being, from the origin of the triotion, per- 

 pendicu'lar to the plane of the maxinium of the areas, was 

 also at this period the axis of the greatest moments, and 

 we find that it still preserves this property during the mo- 

 tion. 'I'his constancy in the initial properties forms a re- 

 markable and hitherto uimoticed analogy belwcin the axis 

 of the greatest nivmcnts and the place of the maximum of 

 the areas. 



The author, iawhal precedes, has shown that the elliptic 



figure 



