MOTION. 



465 



sive ; that is, it swings forwards by the force of 

 gravity alone, independently of muscular ac- 

 tion. The supporting leg is regarded by 

 the Messrs. Weber as a substitute for the pro- 

 pelling weight of a clock, and the swinging leg 

 as the substitute for the pendulum, both ex- 

 changing their offices alternately. The distance 

 from the point where the ball of the foot of the 

 swinging leg quits to the point where it is again 

 placed on the earth, is equal to the length of a 

 double .step. This outline of the action of the 

 legs in walking depends on principles which we 

 shall now proceed to investigate more strictly, 

 in doing which we shall draw largely from 

 the theoretical and experimental researches of 

 the Messrs. Weber, whose labours have con- 

 tributed so extensively to advance our know- 

 ledge in this interesting branch of human phy- 

 siology. 



The positions of the body in walking at va- 

 rious instants of time have been described both 

 by Borelli and Weber; it is thus represented 

 by the latter. Let Jig. 253 be the vertical, and 

 Jig. 254 the ground plan, on planes in a straight 



Fig. 253. 



ctt 



Fig. 254. 

 U.-J.2, 134&6 



ao 



horizontal path. In Jig. 253 the simultaneous 

 positions of the two feet are represented at 

 the moment when they reach ' the ground, 

 also the position of the centre of gravity of the 

 body in the vertical plane. The position of the 

 right leg is shown by the continued lines, and 

 that of the left leg by the dotted lines. The 

 extremity of the right foot is designated by the 

 letter a, that of the left by the letter b, and the 

 centre of gravity by r, the contemporaneous 

 positions of these points being denoted by the 

 numerals annexed to these letters. In the 

 horizontal projection,^-. 254 represents the si- 

 multaneous position ot both legs and of the cen- 

 tre of gravity : the letters and figures are the same 

 as in the preceding diagram. At the instant when 

 the hinder leg is raised from the ground at the 

 commencement of each step, the extremity of the 

 forward leg and the centre of gravity lie in the 

 normal plane of the line of progression ; for 

 example, at the beginning of the fust step, 6 

 and r , of the second step a ? and c a , and of 

 the third step, 6 4 and c 4 , lie in the normal 

 plane of the direction of progression. 



In each step the extremity of one leg must 



VOL. III. 



be advanced as far before the foot of the other 

 as in the preceding or following steps the other 

 leg was placed before the first, for example : 

 in the first step, the foot, , 2 3 4 must ad- 

 vance so far before l> , 2 , as in the second 

 step b 3 4 5 6 must advance before , 2 3 4 . 



The time of each step, that is, the space of 

 time between the raising of each foot in succes- 

 sion, is subdivided by Borelb and the VVebers 

 into two parts, namely, one part in which 

 one leg, and the other when both legs are 

 on the ground : for instance, during the first 

 step, while the centre of gravity advances 

 from r to c,, one leg, and, while it advances 

 from c, to r a both are on the ground. In the 

 second step, while the centre moves from r 2 to 

 r 3 , one leg only, but while it advances from 

 c 3 to r 4 both legs are again on the ground, and 

 so on in succession. But there is no instant in 

 walking in which the body moves freely through 

 the air without either leg touching the ground, 

 as in running. 



The sum of the squares of the elevation of the 

 centre of the body above the horizontal plane, 

 and the length of the step, is equal to the square 

 of the length of the extended leg.* This pro- 

 position depends on the circumstance that the 

 forward leg stands vertical to the ground at the 

 instant the hinder leg quits it ; and that the 

 two legs, with the horizontal distance between 

 them, form, at this moment, a right-angled tri- 

 angle. According to the Webers, the body, in 

 walking, continues to be affected by the exten- 

 sor power of one leg only, because the expen- 

 diture of the extensor power of the legs to 

 support the body is only just sufficient to sus- 

 tain it; and this expenditure is at a minimum 

 only when the forward leg bears the whole 

 burden during that period in which they are 

 both on the ground, for as the forward leg acts 

 at a less angle than the hinder leg, it is capable 

 of supporting the body at a much greater me- 

 chanical advantage, which is at a maximum 

 when it stands vertically. MM. Weber also 

 find that the body is accelerated whilst one 

 leg, and is retarded whilst both legs are on 

 the ground ; for, in slow walking, the forward 

 leg being placed on the ground in advance of 

 the centre of gravity, it tends for an instant to 

 check the horizontal velocity of the body. 



We shall now take a brief view of the velo- 

 city in walking, and of the principles on which 

 it depends. MM. Weber have shewn that 

 the velocity in walking varies with the height 

 at which the head of the femur is carried from 

 the ground; as this height increases, the velo- 

 city decreases.\ The length of each step de- 

 creases as the height of the centre of gravity in- 

 creases ; for the greater the elevation, the less 

 will be the distance to which the leg will ex- 

 tend ; therefore corpulent persons, and porters 

 with heavy burdens on the shoulders, take steps 

 of diminished length. The duration of a step, 



* Hence we get eq. 23. 



f The velocity being uniform J_ a:ul 



T 

 therefore increases as h decreases. 



2 u 



