MOTION. 



409 



site direction toil, will produce an equilibrium. 



Fig. 206. 



r 



Let N (fig. 205) be the point acted upon by 

 any two forces N F, N F', which form an angle 

 F N F', and the line N R their resultant, which 

 will draw ihe point in the direction NR. But 

 if a third force NR', equal and opposite to NR, 

 be applied, it will destroy the motion in 

 NR, and the point N will remain at rest by 

 the simultaneous action of the three forces 

 NR', NF, NF. 



Fig. 207. 



D 



11 



Fig. 208. 



Centre of gravity. The centre of gravity 

 of any body is a point about which, if acted 

 upon only by the force of gravity, it will ba- 

 lance itself in all positions ; or, it is a point 

 which, if supported, the body will be sup- 

 ported however it may be situated in other 

 respects; and hence the effects produced by 

 or upon any body are the same as if its whole 

 mass were collected into its centre of gravity. 



To find the centre 

 of gravity of any plane 

 body mechanically, 

 let the plane a e d b 

 (fig. 208) be sus- 

 pended freely by a 

 string from the point 

 a, to which a plumb- 

 line ft b is also at- 

 tached the latter 

 will coincide with 

 the vertical line a b, 

 which is to be marked 

 with a pencil : then 

 suspend the plane 

 and plumb-line from 

 a second point f, 

 when the plumb-line 

 will hang vertically 

 in the line e d, inter- 

 secting a b in c , the point c will be the centre 

 of gravity of the plane. 



To find the distance of the head and feet 

 from the centre of gravity of the human body 

 in a horizontal position ; balance the body 

 placed upon a plane a b on a triangular prism 

 d e, as in fig. 209 ; then draw a line on the plane 



Fig. 209. 



at? **& 



d 



close to the edge of the prism ; again balance 

 the body in another position and draw a line 

 as before, the vertical line passing through c, 

 the intersection of these lines will pass through 

 the centre of gravity. 



After the plan of Borelli, Weber balanced a 

 plank across a horizontal edge, and stretched 

 upon it the body of a living man : when the 

 whole was in a state of equilibrium, in which 

 the method of double weighing was adopted, 

 by accurate measurements he found the total 

 length of the body 



m.m. in. 



= 1669.2 = 65.30853 



the distance of the centre of gravity below the 

 vertex = 721.5 = 28.406455 



above the sole of the foot 



= 947.7 = 37.310949 

 above the transverse axes of the hip-joints 



= 87.7 = 3.454729 



above the promontory of the sacrum 



= 8.7= 0.341519 



As the horizontal plane of the centre of gravity 

 lies between three-tenths and four-tenths of an 

 inch above the promontory of the sacrum, it 

 must traverse the sacro-lumbar articulation 

 which is intersected by the mesial plane, be- 

 cause the body is symmetrical, and by the 

 transverse vertical plane, the sacro-lumbar arti- 

 culation must, therefore, contain the common 

 point of intersection of all three planes, which 

 coincides with the position of the centre of gra- 

 vity of the body when standing; but this point 

 varies in different individuals in proportion to 

 the difference of the weight of the trunk to that 

 of the legs, as well as by any change of the 

 position of the limbs. 



The centres of gravity of particular figures 

 may be found geometrically and analytically, 

 as shewn in mechanical treatises; but these 

 methods require computations too detailed for 

 our limits. 



The attitudes and motions of every animal 

 are regulated by the positions of their cen- 

 tres of gravity, which, in a state of rest and 

 not acted on by extraneous forces, must lie in 

 vertical lines which pass through their bases 

 of support. Thus, if (Jig. 210, A and u) be the 

 common centre of gravity of two bodies whose re- 

 spective centres of gravity are g, II, in A 



