462 
move uniformly in a horizontal line, it has a 
re € motion in its curve of oscillation, 
which, if measured from its lower extremity, is 
just equal to the velocity of the point of junc- 
tion, when estimated in the direction of the 
tangent of the curve at the commencement of 
the step. Hence, in quick walking, when the 
Swinging leg is supposed to come to the ground 
.In a vertical position, it describes half of the 
curve during each step. By following the 
same course of reasoning Messrs. Weber have 
ascertained the amount of the vis viva, or vital 
force, communicated to the swinging leg in 
any given time; the amount communicated to 
the body by the standing leg; the proportion 
which the time when the body is supported on 
one leg bears to the whole time of a step; and 
the height at which the centre of gravity is 
borne above the ground.* In order to verify 
* After an elaborate analysis the Messrs. We- 
ber have deduced the following equations, which 
express the general laws of walking. 
At pA = 2 ,... 2. eccccccesses 
(hk — 4 g 8) & 4 pt = 12... eee ee (24) 
< s1+n Cos iad @—«)} 
WN Bo Cabe B) Rives cs icvevesaceseses 
(bak titers tantiee IOS 
In which equations 
—a 
=a/i+r2 . 
" a/ x lg 
= 7 are (Cos = 
w 
). 
x!l- 
(eels 
k= 
(ip rar= sin qit—«) } sn 
The mass of the trunk is supposed to be con- 
centrated in a point m at the upper end of the 
leg, and the mass of the swinging leg in a point 
m’in the leg which is considered as a straight 
line. vy * ; 
lis the length of the hinder leg at the begin- 
ning of a step. . 
h is the height of m above the horizontal plane 
at that time. d 
is the distance between the hinder foot and 
the forward at that time, or the length ofa step. 
@ is the time during which m falls below its ho- 
rizontal line at the end of the time ¢. 
U is the length of the hinder leg at the end of 
the time before it is extended or becomes /, 
+ is the time of one ~~ F : 2 
t is that portion of it during which the leg is 
swinging. 
MOTION. 
the pendulous movements of the legs a person 
was placed upon a small block, and by sup- 
porting himself on one leg, suffered the other, 
measuring thirty inches, to swing, with relaxed 
muscles, as a pendulum. A vi mo 
having been communicated bya slight mov 
of the trunk backwards and forwards, the num 
ber of oscillations made in the time of a minut 
were found to be 84, consequently * 
o = 0”.714285 = time of one oscillation 
and since the lengths of pendulums*at th 
same place vary inversely as the squares of th 
numbers of oscillations in a given tim 
842: 607 :: 39}: 1 (the length of a pendulun 
which vibrates synchronously with the leg) 
602 x 39} _ 140850 _ 19 9¢. 
84? ae 
inches. Now as the whole length of the leg 
was 34 inches, the centre of oscillation must be 
less than two-thirds of that length from the 
point of suspension, and consequently les 
than in a prismatic rod, the length of which 
is such as will vibrate synchronously wit 
the leg. This accords with the known figure 
of the leg, the mass of which diminishes a: 
the distance from the axis of motion in- 
creases. The time of a half oscillation ¢ 
the freely suspended leg which we have found 
0”.714285 __ 0”.3571425 . ical 
aren aay » approximates ve 
closely to that found by the Webers, both m 
the living and the dead subject. 
The second experiment was made 
engraver, Mr. Vasey. In walking at the ra 
of four miles per hour he counted 2000 step: 
15 x_60 _ 0". 
hence / = 
every fifteen minutes; then 
the time of each step ; now as 2000 steps wer 
taken in one mile of 5280 feet, the length of e: ‘ 
oy 
ris the ratio of the distance between m 
m’ to I. 
P gis the accelerating force of gravity = 3% 
eet. 
m is the number 3.1416. 
T is the time of an oscillation of a pen¢ 
whose length is rl. 
w is the ratio of the mass‘of the trunk to 1 
mass of the swinging lege 
The quantities / T, ~ must be previt 
ascertained, and w and g being always the sa 
there will be nine equations for finding the vah 
of the ten remaining quantities; if therefore 
know any one of these ten, the rest may be fou 
In regular progression the force communics 
by the supporting leg to the trunk must e 
re imparted by the trunk to the swingin; 
that is 7 
mi(etrape sin} = (t—a) } ym : 
a Oe, tee 
h t 
SS 
? 
cr. 
from which, by substituting ? for ¢ 
v 
~ we get equation (26.) 
» saa 
