478 
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 “eC ye ad legs, as designed 
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 
81 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 
seb e thes 5 
rmer case ; ut as neiti 
that mode of leaping ch eset. Betas i. 
merely consists of a both legs, 
* 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, 
Barthez has chosen to deny without attempting to 
disprove the conclusion of Borelli. (See Barthes, 
Nouv. Mecan. p. 97,) 
Fig. 270. 
at the 
with 
MOTION. 
succession of isolated movements, there bein 
always a pause between each two, we shal 
vestigate the latter case as the only one w 
admits of a continued uniform progre 
the only one, therefore, which is proper 
the scope of the present article.* - 
In the alternate movement of the legs, th 
swinging leg is not placed on the ground ¢ 
soon as it has reached the vertical position, as’ 
quickest walking and running, but it is sufferet 
to swing beyond it, and the placing it on t 
ground is delayed until it comes a second tim 
to the vertical position, consequently the — 
swings freely in the air for a longer peri 
in running, whereby a longer step is é 
Fig. 271 represents the various is « 
the centre of gravity and of each leg im sue 
cessive instants of time: a is the right foot 
b the left, and ¢ the centre of gravity. a,,, 
signifies that while c moves a c, toc 
and c,, and b from 6, to 6, and by a Fe 
mains at the point a,,,. The spaces a, 
= &c. the lengths of the steps. 
body i J 
DC 
b = Co, C 
It ‘will be observed that whilst the 
advancing from c, to cy, it is su 
rojected by the right leg. From c, to ¢, 
egs are off the ground, from c, to c, the body i 
supported and projected by the left leg, anc 
from c, to c, both legs are again off the grount 
and so on successively. 
TaBLe 13. a 
Table shewing the length and duration of # 
steps in leaping with various velocities. a 
Doda Vv 
Length of on 
steps. Duration, Velocity. | 
1.243 0.460 2.702 
1.578 0.468 3.372" 
1.688 0.455 3:710/' = 
1.809 0.411 4.402 
1.977 0.404 4.894 
* In leaping, the equations (29) (32) (34) 
the same as in running. Equations (30) and (; 
are omitted, for @ = 0, since the centre of 
vity of the body does not sink, because at 
beginning of each step the leg is bent, and th 
is, therefore, no depression, as is necessarily 
case in walking and running. Instead of equat 
(31) and (33), we have, 
27 = TH+E+(1 +— 
dt 
T 
cos pRB 
2s 
1 2(1— — 
ais ide 3a «cececcunl 
r(2—~r) ‘ 
The condition for regular progression in leapi 
in walking and running, is that the Vital 
communicated by the supporting leg to the tr 
equals that communicated by the trunk to 
swinging leg. In the present case the 
force is, 
st 
m’ cr (2 _ r) eee Rr a 
and the former is the same as in running, 
y é 
