100 
FIFTH REPORT- 1835. 
whether the impact be great or small, provided the beam and 
striking body are the same, since then — and w + r are con¬ 
stant, It is, moreover, inversely as the square root of the stiff- 
ness of the beam, since measures that quality. 
Cor, 1. Since, from above, 
j / 2 he 
V i 
h = 
p (w 8- ?'Y 
p h 9 (w + r) 
2 e w 4 
If e = the utmost deflection the beam will bear, and b = o, 
, _ p e [w + r) 
h = ' 2~uY 5 
the greatest height of impact the beam will bear from a given 
weight w. 
If the weight of the beam be small and neglected, r = o, and 
The two last values of h being the measures of the power of 
a heavy and a light beam to resist impact, we have this propor¬ 
tion -the power of a heavy beam : the power of a light one 
p e (tv + r) p e 
2 iv~ 2 iv 
: iv + r : iv. 
Whence it appears that in beams, whose strength and flexi¬ 
bility are the same, the power of bearing impacts from a given 
body may be increased to any extent by augmenting the weight 
of the beams. This, however, can only apply to horizontal im¬ 
pacts, otherwise the weight of the beam itself might break it 
without any blow. 
* Dr. Young, speaking of the results of impact upon elastic bodies ( Natural 
Philosophy , vol. i. p. 143), says, “ It follows from the nature of resilience that 
a body of a pound weight falling from the height of a yard will produce the 
same effect in breaking any substance as a body of three pounds falling from 
the height of a foot.” This it appears from above is only correct when the 
body struck is without weight, and the impact is given horizontally. And 
when the Doctor (at p. 148 and elsewhere) represents the resilience of a beam, 
or its resistance to impact, to be simply proportional to the bulk or weight of 
the beam, it was necessary to consider that the striking body was without in¬ 
ertia or weight. 
