he limits of danger.

70. _Q._--Will you explain in what way the various strains subsisting in a
steam engine may be resolved into tensile and crushing strains; also in
what way the magnitude of those strains may be determined?

_A._--To take the case of a beam subjected to a transverse strain, such as
the great beam of an engine, it is clear, if we suppose the beam broken
through the middle, that the amount of strain at the upper and lower edges
of the beam, where the whole strain may be supposed to be collected, will,
with any given pressure on the piston, depend upon the proportion of the
length to the depth of the beam. One edge of the beam breaks by extension,
and the other edge by compression; and the upper and lower edges may be
regarded as pillars, one of which is extended by the strain, and the other
is compressed. If, to make an extreme supposition, the depth of the beam is
taken as equal to its length, then the pillars answering to the edges of
the beam will be compressed, and extended by what is virtually a bellcrank
lever with equal arms; the horizontal distance from the main centre to the
end of the beam being one of the arms, and the vertical height from the
main centre to the top edge of the beam being the other arm. The distance,
therefore, passed through by the fractured edge of the beam during a stroke
of the engine, will be equal to the length of the stroke; and the strain it
will have to sustain will consequently be equal to the pressure on the
piston. If its motion were only half that of the piston, as would be the
case if its depth were made one half less, the strain the beam would have
to bear would be twice as great; and it may be set down as an axiom, that
the strain upon any part of a steam engine or other machine is inversely
equal to the strain produced by the prime mover, multiplied by the
comparative velocity with which the part in question moves. If any part of
an engine moves with a less velocity than the piston, it will have a
greater strain on it, if resisted, than is thrown upon the piston. If it
moves with a greater velocity than the piston, it will have a less strain
upon it, and the difference of strain will in every case be in the inverse
proportion of the difference of the velocity.

71. _Q._--Then, in computing the amount of metal necessary to give due
strength to a beam, the first point is to determine the velocity with which
the edge of the beam moves at that point were the st