478 



MOTION. 



has been briefly described in the last section, 

 and our limits will not permit further illustra- 

 tions. We shall therefore proceed to the in- 

 vestigation of the leap in the human race. 



Fig. 269. 



Preparing to leap with both legs, as designed 

 by Flaxman. 



In Man the leap is 

 accomplished with con- 

 siderable expenditure 

 of muscular action, 

 amounting, according 

 to Borelli, to no less 

 than 2900 times the 

 weight of the body;* 

 but since, notwith- 

 standing the increased 

 exertion, the velocity 

 of this kind of motion 

 is much less than in 

 running, it is rarely 

 adopted as a means of 

 continued progression, 

 but rather for passing 

 over the greatest pos- 

 sible space without re- 

 gard to the time taken 

 to accomplish each 

 step. In leaping, either 

 both legs are employed 

 simultaneously to pro- 

 ject the body, as in 

 Jig. 269, or each leg is 

 used alternately. Bo- 

 relli has confined his 

 observations to the 

 former case ; but as 

 that mode of leaping 

 merely consists of a 



Fig. 270. 



Position of the body at the 

 termination of a leap with 

 both leys. 



* This estimate is calculated by Borelli in the 

 same manner as the force of the muscles in Sec- 

 tion I. On this, as on several other occasions, 

 Darthez has chosen to deny without attempting to 

 disprove the conclusion of Borelli. (See Marthez, 

 Nouv. Mecan. p. 97 ) 



succession of isolated movements, there being 

 always a pause between each two, we shall in- 

 vestigate the latter case as the only one which 

 admits of a continued uniform progression, 

 the only one, therefore, which is properly within 

 the scope of the present article.* 



In the alternate movement of the legs, the 

 swinging leg is not placed on the ground as 

 soon as it has reached the vertical position, as in 

 quickest walking and running, but it is suffered 

 to swing beyond it, and the placing it on the 

 ground is delayed until it comes a second time 

 to the vertical position, consequently the body 

 swings freely in the air for a longer period than 

 in running, whereby a longer step is effected. 

 Fig. 271 represents the various positions of 

 the centre of gravity and of each leg in suc- 

 cessive instants of time : a is the right foot, 

 b the left, and c the centre of gravity, a, 2 3 

 signifies that while c moves from r, to c 2 



b,, a re- 



and 



and b from b, to 



6 a and 



mains at the point a, 2 $ . The spaces , 2 3 , 

 > 4 s 6 = c 2 , c s = &c. the lengths of the steps. 

 It will be observed that whilst the body is 

 advancing from c, to r s , it is supported and 

 projected by the right leg. From r s to c 4 both 

 legs are off the ground, from c 4 to r 6 the body is 

 supported and projected by the left leg, and 

 from c 6 to r 7 both legs are again oft' the ground, 

 and so on successively. 



TABLE 13. 



Table shewing the length and duration of t/ie 

 steps in leaping with various velocities. 



" In leaping, the equations (29) (32) (34) are 

 the same as in running. Equations (30) and (35) 

 are omitted, for = o, since the centre of gra- 

 vity of the body does not sink, because at the 

 beginning of each step the leg is bent, and there 

 is, therefore, no depression, as is necessarily the 

 case in walking and running. Instead of equations 

 (31) and (33), we have, 



2T-T+(3 + (l+ )< ....(38) 



cos 



T 



h = 



2.<, 

 37 



(39) 



The condition for regular progression in leaping, as 

 in walking and running, is that the vital force 

 communicated by the supporting leg to the trunk, 

 equals that communicated by the trunk to the 

 swinging leg. In the present case the latter 

 force is, 



wi'c-'r (2 - r) (40) 



and the former is the same as in running-. 



