*A.*—The weight of a malleable iron
rim of one square inch sectional area and 7 feet diameter
is 21.991 feet x 3.4 lbs. = 74.76, one half of which
is 37.4 lbs. Then by the same process as before,
8,000/37.4 = 213.9, the centrifugal force in terms
of the weight: 213.9 x 7, the diameter of the
wheel = 1497.3, the square root of which, 38.3 x 4.01
= 155.187 feet per second, the highest velocity of
the rims of railway carriage wheels that is consistent
with safety. 155.187 feet per second is equivalent
to 105.8 miles an hour. As 4,000 lbs. per square
inch of sectional area is the utmost strain to which
iron should be exposed in machinery, railway wheels
can scarcely be considered safe at speed even considerably
under 100 miles an hour, unless so constructed that
the centrifugal force of the rim will be counteracted,
to a material extent, by the centripetal action of
the arms. Hooped wheels are very unsafe, unless
the hoops are, by some process or other, firmly attached
to the arms. It is of no use to increase the
dimensions of the rim of a wheel with the view of giving
increased strength to counteract the centrifugal force,
as every increase in the weight of the rim will increase
the centrifugal force in the same proportion.

CENTRES OF GRAVITY, GYRATION, AND OSCILLATION.

31. *Q.*—What do you understand by
the centre of gravity of a body?

*A.*—That point within it, in which
the whole of the weight may be supposed to be concentrated,
and which continually endeavors to gain the lowest
possible position. A body hung in the centre of
gravity will remain at rest in any position.

32. *Q.*—What is meant by the centre
of gyration?

*A.*—The centre of gyration is that
point in a revolving body in which the whole momentum
may be conceived to be concentrated, or in which the
whole effect of the momentum resides. If the
ball of a governor were to be moved in a straight
line, the momentum might be said to be concentrated
at the centre of gravity of the ball; but inasmuch
as, by its revolution round an axis, the part of the
ball furthest removed from the axis moves more quickly
than the part nearest to it, the momentum cannot be
supposed to be concentrated at the centre of gravity,
but at a point further removed from the central shaft,
and that point is what is called the centre of gyration.

33. *Q.*—What is the centre of oscillation?

*A.*—The centre of oscillation is
a point in a pendulum or any swinging body, such,
that if all the matter of the body were to be collected
into that point, the velocity of its vibration would
remain unaffected. It is in fact the mean distance
from the centre of suspension of every atom, in a
ratio which happens not to be an arithmetical one.
The centre of oscillation is always in a line passing
through the centre of suspension and the centre of
gravity.