70 Statics. 



found the moments of these different parts with respect to a hori- 

 zontal plane, supposed to pass through the keel ; and the moments 

 with respect to a vertical plane taken at pleasure perpendicular 

 to the keel ; we divide each of these two sums by the whole weigh! 

 of the vessel, and we obtain the height of the centre of gravity, 

 and its distance from the vertical plane with respect to which 

 the moments were considered ; and as it must also be in the 

 vertical plane which passes through the keel,- we shall have 

 its position. But it may be remarked, that in the calculation of 

 these moments, we must multiply, not the bulk of each part, 

 but its weight, by the distance of the centre of gravity of this 

 part ; which centre is easily determined after all that has been 

 said upon this subject. 



Properties of the Centre of Gravity. 



115. It is evident from what we have said upon the subject 

 of the centre of gravity, and upon the resultant of parallel forces, 

 that if the parts of a body or system of bodies have each the 

 same velocity, or tend to move with the same velocity, it is evi- 

 dent, I say, that the resultant of all these motions or tendencies 

 would pass through the centre of gravity of the body or system, 

 and that consequently the system would move, or tend to move, 

 as if the several masses were all concentrated at the. centre of 

 gravity ; and were together urged with a velocity equal to that 

 which urges each of the parts. 



116. We must infer reciprocally, that if any force be applied 

 at the centre of gravity of a system of bodies ; all the equal parts 

 of this system will partake equally of this motion, and will all 

 proceed with an equal velocity, obtained by dividing the quantity 



2 ' of motion applied at this centre by the entire mass of the system, 

 and this velocity will have for its direction that of the force ap- 

 plied at the centre of gravity. 



Indeed, whatever be the motions distributed among the parts 

 of the system, we see clearly that they must have for a resultant 

 " the very force applied at the centre of gravity, since it is sup- 

 posed that the system is free, and that there is consequently 

 nothing to destroy any part of the force thus applied. 



