NF, NF'. _ 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 aedb (fig. 208) be sus pended freely by a string from the point a, to which a plumb line a b is also at tached — the latter will coincide with the vertical line a b, which is tobe marked with a pencil: then suspend the plane and plumb-line from a second point e, when the plumb-line will hang vertically in the line c d, inter secting a b in c, the point c will be the centre of gravity of the plane.
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 Boren', 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 = 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 fonr-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 g (fig. 210, A and a) be the common centre of gravity of two bodies whose re spective centres of gravity are g, II, in A In the third order of lever the power acts between the prop and the resistance (fig. 213), the whole mass will be supported, whilst in B it will fall over on the side of II.
In most animals moving on solids, the centre is supported by variously adapted organs; during the flight of birds and insects it is suspended ; but in fishes, which move in a fluid whose density is nearly equal to their specific gravity, the centre is acted upon equally in all directions.
The lever.—Levers are commonly divided into three kinds, according to the relative po sitions of the prop or fulcrum, the power, and the resistance, or weight. The straight lever of each order is equally balanced when the power multiplied by its distance from the fulcrum equals the weight, multiplied by its distance, or P the power, and W the weight, are in equilibrium when they are to each other in the inverse ratio of the arms of the lever, to which they are attached : the pressure on the fulcrum however varies.
In straight levers of the first kind, the ful crum is between the power and the resistance, as in fig. 211, where F is the fulcrum of the lever A B; P is the power, and W the weight or resistance. We have P:W:: BF:A F, hence P. AF=W. BF, and the pressure on the fulcrum is both the power and resistance, or P-FW.
In the second order of levers (fig. 212) the resistance is between the fulcrum and the power ; and, as before, P : W : : BF : AF, but the pressure of the fulcrum is equal to W-P, or the weight less the power.
where also P : W : : BF : AF, and the pressure on the fulcrum is P—W, or the power less the weight.
In the preceding computations the weight of the lever itself is neglected for the sake of sim plicity, but it obviously forms a part of the elements under consideration, especially with reference to the arms and legs of animals.
To include the weight of the lever we have the following equations: P. AF+AF. AF=