I 



OP THE MOTION OF A SYSTEM. 209 



5s being constant quantities. These equations will give 

 us linear relations between X, Y, and Z, if we extermi- 

 nate t ; whence it follows that the motion of the centre of 

 gravity is rectilinear: and its velocity being equal to ^ 



always constant, and the motion is uniform. 



Scholium. It is obvious from this analysis that the 

 invariability of the motion of tlie centre of gravity of a 

 system of bodies, whatever their mutual actions may be, 

 holds good even in the case of an instantaneous loss of a 

 finite quantity of motion in the separate bodies, by means 

 of their mutual action. 



§ 21. Of the principle of the constancy of areas. It 

 subsists notwithstanding the abruptness of any changes in 

 the system. Determination of a system of coordinates , for 

 which the sum of the ureas described by the projections of 

 the revolving radii vanishes for two of the planes of the 

 ordinates, the sum being a maxiinum on the third, and 

 vanishing for every plane perpendicular to it. P. 56. 

 [^General properties of projections.'] 



323. Theorem. The sum of the areas 

 described by the projections of the revolving 

 radii of any system of bodies, upon any given 

 plane, multiplied respectively by their masses, 

 is proportional to the time, supposing the 

 bodies subject only to their reciprocal actions, 

 and to a force directed to the origin of the 

 radii. 



