IMPACT UPON REAMS, 
95 
pact, as appears from our experiments on the collision of im¬ 
perfectly elastic bodies ( Fourth Report of the Association) . But 
a cast iron beam throws back a ball with a velocity much more 
nearly approaching to what would arise from perfect elasticity. 
This will be seen by comparing the observed results with the 
calculated ones in the experiments upon the 1st and 2nd beams, 
the calculated results being obtained from problem 1 following, 
where the beam is assumed to be perfectly elastic. 
Conclusion 4.—The effect of bodies of different natures striking 
against a hard flexible beam seems to be independent of the 
elasticities of the bodies, and may be calculated, with trifling 
error, on a supposition that they are inelastic. 
If the calculation be formed on a supposition that the time of 
the collision, in the first approach of the impinging body, is 
small compared with the time of deflection of the beam, and that 
the beam and striking body both proceed together afterwards as 
one mass (as is done in our following problems); the calculated 
deflections are somewhat greater than the observed ones, the dif¬ 
ference sometimes amounting to one fifth or one eighth, as will 
be seen from the experiments on the 1st, 2nd, and 3rd beams. 
But the observed deflections in our experiments, excepting, per¬ 
haps, those on the 3rd beam, must be rather too small, arising 
from the resistance of the clay, into which a peg used for mea¬ 
suring the deflections was driven by the impacts. 
This fourth Conclusion must only be admitted when there is 
nothing struck upon but the beam. When there is any other 
heavy body intervening between the striking body and the beam, 
touching the latter, and which must be struck before the beam 
can be deflected, then the elasticities of the concurring bodies 
exhibit their influence, and the result is greater than that ob¬ 
tained by calculation as above. This might be expected; and 
it is shown by the experiments on the 4th beam. 
Dr. Young, in his Natural Philosophy , and Mr. Tredgold, in 
his Treatise on the Strength of Cast Iron , reason on this sub¬ 
ject as if the striking body were inelastic, and we have here 
shown that this may be assumed, whatever the hardness and 
elasticity of the striking body may be*; or, probably, its weight 
with respect to that of the beam. 
* Of this curious fact the Author would beg to suggest the following as a 
possible explanation. In the first moment of the impact upon the middle of 
the beam, each half of it, if its ends were not fastened, would have a tendency 
to turn round its centre of oscillation, or a point two thirds of the distance from 
the middle to the end, which is seen in experiment by the ends springing up 
after a blow. But it is probable that, besides this, the whole beam is thrown 
by the blow into a state of nodal vibrations, like as in a musical chord; there 
