96 
FIFTH REPORT -1835. 
In the elaborate paper on the “ Measure of Moving Force/’ 
by Mr. Ewart, (Manchester Memoirs , vol. ii., second series ,) 
there are, among other important matters, some ingenious in¬ 
quiries respecting impact and the force of springs. These, how¬ 
ever, do not appear to be easily applicable to our present sub¬ 
ject generally; and the clay used by Mr. Ewart, in his experi¬ 
ments with pendulous balls, was the resisting medium, while in 
our case it was employed only to indicate the deflections. 
Conclusion 5.—The power of a uniform beam to resist a blow 
given horizontally is the same in whatever part it is struck. 
From the experiments on the 5th, 6th, and 7th beams, it ap¬ 
pears that the beams, when supported at the ends, required the 
same blow to break them, whether they were struck in the 
middle, or half-way between that and one support. From a 
future investigation, too, it appears that the same is the case 
wherever the beam is struck. 
Conclusion 6.—The power of a heavy uniform beam to resist 
a horizontal impact is to the power of a very light one as 
half the weight of the beam, added to the weight of the striking 
body, is to the weight of the striking body alone. 
This is shown by Cor. 1. Prob. 2 ; for, from Cor. 2, the in¬ 
ertia appears to be half the weight of the beam; and the greater 
resistance of a large mass than of a small one may be inferred 
from the experiments on beam 4, and others. 
Conclusion 7-—The power of a uniform beam to resist frac¬ 
ture from a light body falling upon it (the strength and flexi¬ 
bility of the beam being the same,) is greater as its weight in¬ 
creases, and greatest when the weight of half the beam, added 
being one, two, or more nodes on each side of the middle. This will be un¬ 
derstood from the adjoining 
figure, which represents the 
beam, when bent by an im¬ 
pact from the ball A, and the 
small excursions of the parts 
between the nodes. The time of a vibration of one of these parts is very small 
compared with the time of a vibration of the whole beam. Chladni has shown 
that if a uniform rod have its ends supported and be put into a state of double 
vibration as above, the number of nodes being n, there will be (n -j- l) 2 of these 
secondary vibrations for one whole vibration of the rod (Biot, Traite de Physique , 
tom. ii., p. 77-8). Hence, after the first concussion of a ball upon a heavy 
beam, the ball and beam in proceeding together are not constantly in contact, 
or in a state of equal pressure if they are. Their connexion appears to be a 
series of small impacts, or of approaches and retreats, the intervals between 
each of which are the time of one of these secondary vibrations. And during 
these intervals it is presumed that the compressed surfaces of the ball and beam 
recover themselves after the first concussion, leaving the eifect the same whether 
the ball be elastic or not. 
