IMPACT UPON BEAMS. 
107 
In all the experiments the radius or length of the pendulum 
was 12 feet, except another radius be mentioned; and the mag¬ 
nitudes of the impacts were measured by the chords of the arcs 
through which the ball fell, because the velocity of impact is 
in that ratio, as will easily be seen; for the velocity is as the 
square root of the versed sine, (or of the height fallen through,) 
and the chord is in the same ratio. 
1st Beam.—This was a rectangular bar of cast iron, 1 inch by 
inch section, and 4 feet 6 inches long, weighing 7^ lbs. It 
was placed horizontal, and laid with its broader side against two 
vertical supports 4 feet asunder. The blows were given hori¬ 
zontally in the middle of the beam to bend it in that direction. 
The impinging body was a cast iron ball S^-lbs. weight. 
Chord of arc 
fallen 
through, in 
feet. (Ra¬ 
dius 12 feet.) 
Observed 
chords of 
recoil of 
ball, in 
inches. 
Calculated 
chords of 
recoil of 
ball, in 
inches. 
Observed 
deflections 
of beam, 
in 
inches. 
Calculated 
deflections 
of beam, 
in 
inches. 
Difference 
between ob¬ 
served and 
calculated 
recoils. 
Difference 
between ob¬ 
served and 
calculated 
deflections. 
1 
7 
8-3 
■25 
•26 
1 
IT 
TlV 
2 
15 
145 
•44 
•53 
. l 
HIT 
l 
5 
3 
21 
21-8 
•66 
•79 
_l 
2 (T 
1 
TT 
4 
31 
29 1 
•88 
105 
_ l 
1 6 
l 
IT 
5 
39 
383 
1-16 
1*32 
l 
5 IT 
i 
‘S* 
6 
46 
47'2 
1-43 
1-58 
1 
T'S* 
l 
T JT 
7 
52 
53-5 
162 
1-84 
l 
T5* 
1 
"S' 
8 
Broke it. 
Prior to the experiments above, the beam was laid flat on two 
horizontal supports 4 feet asunder; and weights, suspended from 
the middle and gently laid on, produced deflections in the bar 
(in the direction that it was bent by impact) as below : 
28 lbs. bent it *32 inch, 
56 —— -63 — 
The quantity of the recoil in the preceding experiments was 
calculated from the formula c = h ^ ^ 
(Prob. 1.) 
€ (w + r)' 
This formula, like all the others, is calculated on a supposition 
that the beam is perfectly elastic and the striking body devoid 
of elasticity. 
J 
In Cor. 2, Prob. 2, it is shown that the inertia of uniform 
beams, struck in the middle, is nearly equal to one half of the 
weight of each between its points of support; and as this beam 
was 4 feet 6 inches long, and 7*25 lbs. weight, the weight of 4 
feet was 6*44 lbs. Whence the inertia r = 3*22 lbs. We have 
