106 
FIFTH REPORT— 1835 . 
vatu re to be the utmost the beam would bear without impairing 
its elasticity; but the result would have been the same if we had 
assumed any other constant curvature. In the parabola so 
formed; the deflection in the middle would be to the deflection 
half-way between that and one end, as 1 to *75 ; and it will be 
seen from the mean between the results of our experiments on 
the 5th, 6th, and 7th beams that this ratio was found to be 1 to 
*694, differing T j from the above. 
Theorem .— If an uniform beam be supported at the ends, and 
struck horizontally upon the side, the same blow will be required 
to break it wherever it is given. 
From Cor. 1, Prob. 2, it appears that where the striking body 
and the inertia of the beam remain invariable, the power of re¬ 
sisting impact is as the strength of the beam multiplied by the 
deflection it is capable of. 
From the last theorem the ultimate deflection at any point is 
as the product of the segments at that point, and is equal to 
ex (/ — x). It is shown too by writers on the strength of ma¬ 
terials that the strain from a weight at such point is in the same 
proportion ; the strength therefore is inversely as the strain, or 
as -~t~ -t . Hence the power of the beam to sustain an im- 
x (I — x) L 
pact at any point is as the product of these, 
1 
It is therefore the same in every part. 
For another proof of this see the experiments on the 5th, 6th, 
and 7th beams. 
j Expert men ts.—Horizon tal Imp acts. 
In all the following experiments a ball was suspended by a 
thin string from an elevated object, and so placed that, when 
hanging vertical, its side just touched the beam in the point in¬ 
tended to be struck, which was always the middle , except other¬ 
wise mentioned ; the beam being loosely supported at its ends, 
horizontally and vertically, by immoveable bodies. The impacts 
were made by drawing back the ball through given arcs, as 
measured by their chords, and letting it fall against the beam. 
The deflection of the beam by an impact was measured by the 
quantity which a peg, whose end touched the beam when at rest, 
had been driven into a mass of clay placed on the opposite side 
of the beam to that where the ball was. The use of the peg and 
clay was only to indicate the deflection. 
