FORCES OPERATIVE DURING PROGRESSION. 271 



on the left-hand side of the figure leaves the ground, the push of the leg 

 would be in the direction of the arrow ca (Fig. 160). If the line ca 

 represents the push of the leg in amount and direction, and the line cb 

 the force of gravity, by completing the parallelogram we obtain the 

 actual displacement of the centre cd, which would take place under 

 the influence of these two forces. The push of the leg under discussion 

 and gravity combined would cause the body to be projected forwards 

 and downwards, but for the fact that at this very time the other leg- 

 touches the ground in the extended position, and prevents this down- 

 ward displacement of the body. The momentum of the body, therefore, 

 carries it forward, and it swings forward on the second les, which is like 

 the travelling radius describing the arc of a circle. Thus the centre of 

 gravity is raised upon the extended leg, and then falls, until raised again, 

 when the first foot next reaches the ground. 



The resistance of the air is not a very considerable force, but its rate 

 of increase is in proportion to the square of the rate of progression. 



Fig. 161. — To illustrate the surface of body exposed to the resist- 

 ance of air (a) in bicycling, (b) in running, (c) in walking. 

 The centrdid is indicated by a white spot. 



This resistance is met by the changes in the posture of the body 

 which invariably accompany progression. During the act of rapid 

 walking or running the body is bent forward, so that a diminished 

 surface is presented in the direction of movement. In bicycling, the 

 racer also bends down upon his handles, presenting a diminished surface 

 in the direction of resistance. Fig. 161 is constructed from three 

 photographs taken at equal distances from the same individual bicycling 

 (a), running (b), and walking (c), the areas being respectively 100, 73, 

 and 72. 1 



Not only does the act of bending forward diminish the surface 



^The areas were calculated by projecting the photographs upon pieces of cardboard, 

 outlining the figures, cutting them out and weighing them. The centre of the surface 

 (centroid) was found in the usual way, by suspending each of them from two different 

 points and finding the point of intersection of the plumb-lines of these points. 



