272 



ANIMAL MECHANICS. 



FIG. 162. In A, the erect position, 

 the centre of gravity (c) plumbs 

 above hip h. B represents 

 the body of a man running, 

 the resistance of the wind is 

 represented by the line cb, and 



(c) the centre of gravity plumbs tion of be, namely, Jib. 

 in front of the v; ~ *-*-* /Z ' N Jt 



exposed to the resistance of the air, but it is a necessary action, which 

 must occur if equilibrium is to be established without the aid of 

 excessive muscular exertion. This will be readily understood on refer- 

 ence to Fig. 162. 



In the erect position the centre of gravity of the body is approxi- 

 mately above the centre of rotation of the hip, and it is steadied upon 



the hip by the aid of muscular effort. Were 

 the body to progress forwards in the erect 

 position, and encounter the resistance of the 

 air, it would be toppled backwards, unless 

 for muscular adjustments. In point of 

 fact, we instinctively lean forwards, so 

 that the centre of gravity is well in front 

 of the hip-joint, as in B (Fig. 162). If, as 

 in the figure, we consider the centre of 

 the vertical surface exposed to the resist- 

 ance of the air (the centroid) as correspond- 

 ing with the centre of gravity, we may 

 consider the line be as repressing in force 

 and direction the resistance of the wind. 

 Its moments around A, the centre of rota- 

 tion of the hip, will be be multiplied by the 

 shortest distance between k and the direc- 

 Now the centre of 

 equilibrium 



be established, move forwards, until its moments are equal, until the 

 force of gravity multiplied by hd is equal to the resistance of the air 

 multiplied by lib. In more rapid progression, resistance of the air 

 increases as the square, and, in consequence, the movement forward 

 of the centre of gravity must be much greater. 



The reaction of the ground upon 

 which progression is made is the 

 last of the external forces acting 

 upon the body which we need 

 discuss. Were the ground perfectly 

 smooth, a condition which is not 

 reached by the smoothest ice, we 

 should be unable to progress, for 

 a perfectly smooth surface has a 

 reaction in the vertical direction 

 only, and the feet would at once 

 slip backwards. On smooth ice pro- 

 gression is difficult, because of the 

 large amount of slipping which 

 takes place, but on an ordinary 

 floor there is sufficient roughness to 

 give a grip to the foot. 



When the foot is about to leave 

 the ground, pushing the body for- 

 wards, the thrust or reaction of the 

 of the arrow (Fig. 163, ab). 



d a 



FIG. 163. The thrust of the ground repre- 

 sented by the arrow ab may be resolved 

 into a vertical component ac and a 

 horizontal component ad. This latter 

 is the force which will prevent the leg 

 from slipping backwards. 



ground will be in the direction 

 If ab represents this reaction in force and 



direction, we may resolve it by the parallelogram of forces into a vertical 

 force (ac) and a horizontal force (ad). The vertical force is that which 



