470 



MOTION. 



Fig. '260. 



vertical line, not only the time of swinging 

 the leg has increased, but also the time in 

 which both legs are resting on the earth; for 

 the latter commences at the instant when the 

 forward leg has reached the ground, and termi- 

 nates when the head of the femur has arrived 

 at the vertical line, passing through the point 

 of support of the same foot. The time aug- 

 ments in proportion to the distance which the 

 swinging leg passes beyond the vertical posi- 

 tion, or half oscillation. The time when both 

 legs are resting is greatest in fig. 260, because 

 it must be sufficiently great for the head of 

 the femur, together with the whole trunk, to 

 advance to a position directly over the foot, 

 during which the head of the femur moves 

 very slowly, and by the direction of the for- 

 ward leg its action is to retaid the horizontal 

 advance of the centre of gravity. The time is 

 less infg. 259, because the head of the femur 

 has to pass through a less space, and the sup- 

 porting leg acts against the trunk at a less 

 angle; but in Jig. 258 the time of both legs 

 resting at the same time, disappears altogether. 

 The two legs complete the least portion possi- 

 ble of the vibrating curve, and the duration of 

 each step amounts only to the time of half an 

 oscillation. In walking very slowly we may 

 suffer the swinging leg to vibrate so long, that 

 it partly returns to its former position before it 

 reaches the ground. 



We have seen in quick walking that during 

 the time both legs rest on the ground, the ad- 

 vanced leg continually forms a smaller angle 

 with the vertical than the hinder leg ; but in 

 very slow walking the forward leg may form a 

 greater angle with the vertical than the hinder 

 k 1 ^; the magnitude of this angle determines the 



kind of gait the walker acquires. In order to 

 accomplish this, the swinging leg is suffered 

 nearly to complete its curve of oscillation be- 

 fore it is placed on the ground, and during this 

 time the centre of gravity moves so little, that 

 half the length of the step may not be at once 

 described, and the entire duration of the step will 

 be about four times greater than in the quickest 

 pace.* In this case the forward leg really 

 makes a greater angle than the hinder as it 

 reaches the ground, but during the time that 

 both legs are on the ground, the angle of the 

 forward leg diminishes, whilst that of the 

 hinder leg augments, and there is an instant 

 when both legs form equal angles. When the 

 angle of the forward leg becomes zero, or in other 

 words, when it is directed vertically, the hinder 

 leg rises from the earth ; for example, in Jig. 

 261, where a c represents the right leg, be 

 the left, in the beginning 

 of a step, or the instant the 

 foot a is raised from the 

 ground ; c c"' is the magni- 

 tude of the step, or the 

 space which the centre of 

 gravity passes through in 

 the time of a step, c" being 

 the centre of that space. 

 ~& TJ - <r Now, if the foot a, which 

 was raised at the begin- 

 ning of the step, were placed again on the 

 ground at a', at the instant when the centre of 

 gravity reaches the middle point c", then both 

 legs would form equal angles with the vertical ; 

 or, the angle b c" a, = a c" a,, in which 



fig. 261. 



c" at is the vertical through c" ; but if the angle 

 of the hinder leg to the vertical be less, when 

 the right leg is set down in ', the centre of 

 gravity will not have arrived at the middle 

 point c", but at c'; however, whilst both legs are 

 on the ground, the centre of gravity is pro- 

 pelled from c' toe", after which the angle b c' a, 

 increases and the angle ' c" . diminishes 

 (where c' a. is the vertical through c'); when 

 the centre of gravity is propelled onwards from 

 c" to c'", the angle a c" a. is less than b c" a., 

 until the termination of the step. 



In this slow method of walking a very mea- 

 sured pace results, in which the body is carried 

 very erect, and remains for a considerable time 

 in the rear of the forward leg after it first reaches 

 the earth ; consequently the duration of the 

 step will be very considerable, nearly one se- 

 cond and a half, the length of the step very 

 .short, and the velocity of the centre of gravity, 

 which is very little at the middle of the step, 

 varies considerably during each step, so that 

 there is an instant in which the body is nearly 

 at rest. This is denominated by Weber the 

 grave or procession step.-\ 



A remarkable difference may be observed in 

 the duration of the steps of two different per- 

 sons, one of whom has long and the other short 

 legs. In quickest walking the duration of 



( That is, where T represents the entire duration 

 of an oscillation of the leg, the time of a step in the 

 quickest to that in the slowest walking will be as 

 ^T to 2T, or four times that of quickest walking, 

 t Viile Weber, loc. cit. sect. 139, p. 344. 



