ect, is called the _centre of pressure_; and if all the
resistances were concentrated in this point, they would have the same
effect as before in resisting the rotation of the wheel. The resistance
upon any one moving float board totally immersed in the water will, when
the vessel is at rest, obviously vary as the square of its distance from
the centre of motion--the resistance of a fluid varying with the square of
the velocity; but, except when the wheel is sunk to the axle or altogether
immersed in the water, it is impossible, under ordinary circumstances, for
one float to be totally immersed without others being immersed partially,
whereby the arc described by the extremity of the paddle arm will become
greater than the arc described by the inner edge of the float; and
consequently the resistance upon any part of the float will increase in a
higher ratio than the square of its distance from the centre of motion--the
position of the centre of pressure being at the same time correspondingly
affected. In the feathering wheel the position of the centre of pressure of
the entering and emerging floats is continually changing from the lower
edge of the float--where it is when the float is entering or leaving the
water--to the centre of the float, which is its position when the float is
wholly immerged; but in the radial wheel the centre of pressure can never
rise so high as the centre of the float.

553. _Q._--All this relates to the action of the paddle when the vessel is
at rest: will you explain its action when the vessel is in motion?

_A._--When the wheel of a coach rolls along the ground, any point of its
periphery describes in the air a curve which is termed a cycloid; any point
within the periphery traces a prolate or protracted cycloid, and any point
exterior to the periphery traces a curtate or contracted cycloid--the
prolate cycloid partaking more of the nature of a straight line, and the
curtate cycloid more of the nature of a circle. The action of a paddle
wheel in the water resembles in this respect that of the wheel of a
carriage running along the ground: that point in the radius of the paddle
of which the rotative speed is just equal to the velocity of the vessel
will describe a cycloid; points nearer the centre, prolate cycloids, and
points further from the centre, curtate cycloids. The circle described by
the point whose velocity equals the velocity of the ship, is called the
_rolling circle_, and the resis