IMPACT UPON BEAMS. 
109 
gently laid on the middle bent it (in the same direction that it 
was afterwards bent by impact), as below : 
28 lbs. bent it *37 inch, 
56 lbs.- *77 inch. Elasticity a little injured. 
In calculating the deflections of the beam and the recoils of 
the striking body, the inertia of the beam was in this case and 
in all others taken as half the weight of the beam between the 
supports (Cor. 2, Prob. 2). Adopting the formulae used in the cal¬ 
culations for the first beam, we have here the inertia r = 3*111 lbs. 
And since 28 lbs. bent this beam “37 inch, calling p = 28, we 
have e = *37* We have also I = 144 inches, w = 8J or 4^ lbs., 
and the other quantities given in each case, or obtained from the 
observed results. 
The deficiency of the deflections in the experimental results, 
compared with the calculated ones, may perhaps arise from the 
resistance of the peg in the clay. 
3rd Beam.—This was a rectangular bar of cast steel, 1*46 
inch by “41 inch section, and 6 feet 9 inches long, weighing 
14J lbs. It was laid horizontally, and placed with its broader 
side against two vertical supports, 6 feet 6 inches asunder; the 
impacts being intended to bend it in its least direction. The 
striking bodies were balls of lead, cast iron, bell metal, and har¬ 
dened steel, and of various weights, as below. 
Leaden ball 8| lbs. weight. 
Chord of arc fall¬ 
en through, in 
feet. 
(Rad. 12 feet.) 
Observed chord 
of arc of recoil, 
in inches. 
Calculated chord 
of arc of recoil, 
in inches. 
Observed deflec¬ 
tion, in inches. 
Calculated de¬ 
flection, in 
inches. 
1 
5-5 
6-37 
“42 
■43 7 
2 
11*5 
12-4 
*82 
•87 
3 
18*3 
18-7 
1-23 
1*31 
4 
24*7 
25*2 
1-66 
1-75 
5 
3U0 
32-2 
2-12 
2-19 
Leaden ball 4^ lbs. weight. 
1 
5*17 
*29 
•27 
2 
8-5 
io-7 
*60 
•54 
4 
17-3 
20-0 
1*12 
1-08 
6 
29-0 
30-8 
1'73 
1-63 
Cast iron ball 8£ lbs. weight. 
Chord of arc fall¬ 
en through,in 
feet. 
(Rad. 12 feet.) 
Observed chord 
of arc of recoil. 
Calculated chord 
of arc of recoil. 
Observed deflec¬ 
tion. 
Calculated de¬ 
flection. 
1 
6 
6-37 
“42 
•437 
2 
12*5 
13*3 
“88 
•87 
3 
18-0 
19-1 
1-26 
1*31 
4 
24-5 
25*6 
1*69 
1-75 
5 
31-5 
32-0 
2-11 
2*19 
Bell metal ball 4| lbs. weight. 
1 
4-5 
5*5 
•31 
•27 
2 
9-0 
11*0 
•62 
•54 
4 
17“5 
20*0 
1-12 
1-08 
6 
27-0 
29*4 
1-65 
1*63 
