has necessarily to be counteracted by the elasticity of the beam; and the
beam will, therefore, be momentarily bent to a greater extent than what is
due to the load, and after a few vibrations up and down it will finally
settle at that point of deflection which the load properly occasions. It is
obvious that a beam must be strong enough, not merely to sustain the
pressure due to the load, but also that accession of pressure due to the
counteracted momentum of the weight and of the beam itself. Although in
steam engines the beam is not loaded by a weight, but by the pressure of
the steam, yet the momentum of the beam itself must in every case be
counteracted, and the momentum will be considerable in every case in which
a large and rapid deflection takes place. A rapid deflection increases the
amount of the deflection as well as the amount of the strain, as is seen in
the cylinder cover of a Cornish pumping engine, into which the steam is
suddenly admitted, and in which the momentum of the particles of the metal
put into motion increases the deflection to an extent such as the mere
pressure of the steam could not produce.

74. _Q._--What will be the amount of increased strain consequent upon
deflection?

_A._--The momentum of any moving body being proportional to the square of
its velocity, it follows that the strain will be proportional to the square
of the amount of deflection produced in a specified time.

75. _Q._--But will not the inertia of a beam resist deflection, as well as
the momentum increase deflection?

_A._--No doubt that will be so; but whether in practical cases increase of
mass without reference to strength or load will, upon the whole, increase
or diminish deflection, will depend very much upon the magnitude of the