safety. Indeed, this limit should
not be approached in practice on account of the risks of fracture from
weakness or imperfections in the metal.

30. _Q._--What is the velocity at which the wheels of railway trains may
run if we take 4,000 lbs. per square inch as the greatest strain to which
malleable iron should be subjected?

_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 nea