MOTION. 



461 



allowed to accompany the movements of the 

 legs without muscular effort. When the body 

 is put in motion, the momentum generated re- 

 quires an equal force in the opposite direction 

 to stop it, for which purpose the trunk is thrown 

 back; and this, with the resistance of the feet on 

 the ground, will commonly suffice. When, 

 however, this is not the case, the motion must 

 be arrested gradually, or, as it often happens 

 when the plane of position is composed of ice, 

 the leg goes on without the trunk, arid the cen- 

 tre of gravity comes to the ground. 



In walking, the trunk is also elevated and 

 depressed at each step vertically, as well as 

 oscillated in other directions. By the assist- 

 ance of a rod graduated into millimetres, which 

 was carried at the head of the trochanter major 

 by the ambulator, and viewed through a tele- 

 scope, Weber was enabled to ascertain the 

 amount of the elevation and depression of the 

 trunk. He found that when the length of the 

 steps treading on the whole sole of the foot 

 measured 2.39 feet, the mean elevation and de- 

 pression were 1.1 inches. The plane in which 

 the rod vibrated, and the magnitude of the 

 oscillations, did not appear to vary materially, 

 whether the speed was accelerated or retarded. 

 In walking on the ball of the great toe the 

 mean elevation and depression of the trunk 

 was 0.8 inch. 



Estimate of the forces employed in walking. 

 The forces which we have to estimate in walk- 

 ing are, first, that of the extension of the leg ; 

 secondly, the gravity of the body ; thirdly, the 

 resistance which the body encounters in pro- 

 gression. Of these, the first is that force which 

 the leg exerts by its extension to bring it into 

 a straight line, as if both of its extremities (viz. 

 the head of the femur, and that part of the foot 

 which is in contact with the ground) endeavoured 

 to push each other away. The direction of this 

 force depends on the position of the extremi- 

 ties of the leg ; but whatever that direction may 

 be, it is always resolvable, on the principle of 

 the parallelogram of forces, into a vertical and a 

 horizontal component. The vertical portion of 

 the extension upwards is equal to the second 

 force, or the gravity of the body acting vertically 

 downwards ; in this case the centre of gravity 

 remains at the same height above the plane of 

 progression. The horizontal portion of the ex- 

 tension produces an increased velocity in the 

 horizontal direction, the magnitude of which 

 depends on the position of the supporting leg. 

 By means of these forces the body is propelled 

 forwards. At the moment the body receives the 

 impulse of extension it is accelerated until the 

 third force, namely, the resistance,* augmenting 

 continually with the velocity, is equal to that 

 of the acceleration ; when these two forces neu- 

 tralize each other, the body will move forwards 

 with an uniform velocity. 



Hitherto the forces which influence walking 



* The principal resistance is occasioned by the 

 advanced leg when it reaches the ground. Other 

 resistances are the frictions of the joints, of the sole 

 of the foot upon the earth, of the air, &c., but these 

 are very trifling when compared with the retard- 

 ation caused by the advanced leg. 



have been considered as if they were uniformly 

 accelerating forces ; but though they are not 

 strictly such, yet as they recur at the end of 

 each step, the mean velocity of the body will 

 remain the same as if they actually were so.* 



Let us assume a common point of application 

 of the forces, and consider this as the centre of 

 the body, or the point of separation between the 

 trunk and the legs. The three forces may be re- 

 presented (Jig- 250) by three straight lines meet- 



250. 



ing at this point, thus : Let c be the centre of the 

 body ; draw c a in a vertical direction, c b 

 in a horizontal, and c d in the direction of the 

 prolongation of the leg on which the body is 

 supported. These three lines will represent in 

 magnitude and direction the forces which are 

 in action during progression, if they be so taken 

 that either of them equals the diagonal of the 

 parallelogram formed by the other two, and 

 will coincide in direction with that diagonal 

 produced beyond c. Messrs. Weber do not 

 consider those physiologists worth refuting who 

 state that the forces which propel the body for- 

 wards exceed those that drive it back, for in 

 that case, from the continued preponderance of 

 force in one direction, there would result, not 

 an uniform, but a continually increasing velo- 

 city. An uniform motion in a straight line 

 can only take place either when no force what- 

 ever is exerted on the moving body, or when all 

 the forces by which it is affected are in equi- 

 librium. 



In order to investigate with greater precision 

 the laws which regulate the movement s of the 

 body, the Messrs. Weber have considered the 

 weight of the trunk to be collected at the point 

 of junction of the legs, and the weight of each 

 leg, supposed a straight line, to be collected in 

 a point at a given distance from that junction. 

 The movements of these points are supposed to 

 take place in the same vertical plane. They 

 have then applied the general equation for the 

 motion of a system of material points,f and 

 deduced by means of it that the raised leg, in 

 walking, swings forward like a pendulum, the 

 length of which is the above-mentioned given 

 distance, but in consequence of the motion of 

 the point of junction, which is supposed to 



* The three forces which influence walking are so 

 related to each other, that each of them is equiva- 

 lent and opposite to the resultant of the other two. 



i See Poisson's Traite de Mechanique, Paris, 

 1833, vol. ii. 531. 



