44 Statics. 



If either of the given forces happen to be parallel to one of 

 the straight lines XZ, XY, XT, its components parallel to the 

 two other straight lines, as obtained by the above method, would 

 be each equal to zero. 



Such are the general principles of the composition and de- 

 composition of forces. 



Of the Centre of Gravity. 



74. Before we proceed to treat of the particular effects pro- 

 duced by the forces whose general properties we have been con- 

 sidering, it is necessary to speak of the centre of gravity, a sub- 

 ject of the greatest importance in all inquiries relating to the 

 motion of machines and bodies of a known structure. 



By gravity, we mean the force which urges bodies downward 

 in vertical lines, t>r directions perpendicular to the surface of 

 tranquil waters. If the earth, or the surface of these waters, 

 were perfectly spherical, the directions of gravity would all meet 

 at the centre. But although this surface is not perfectly 

 spherical, the deviation is so inconsiderable, that, for the objects 

 we have more immediately in view, we may, without sensible 

 error, regard the* directions of gravity as meeting at the centre 

 of the earth. 



The earth being considered as a sphere, its radius is estimat- 

 ed at 3956 miles, or 20887680 feet. From this it may be read- 

 ily inferred, that it would require at the surface of the earth an 

 extent of about 100 feet to subtend an angle of one second at the 

 centre. Thus, with respect to a machine of 100 feet in length, 

 the directions of gravity at the extremities would want only one 

 second of being parallel. Hence, on account of the great distance 

 of the centre of the earth, compared with the dimensions of any ma- 

 chine, we may regard the directions of gravity as parallel. We may 

 also for the same reason, consider the force of gravity, exerted upon 

 different parts of the same body, as the same in point of magnitude, 

 and capable of giving the same velocity in the same time. 



