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.