tance due to the difference of velocity of
the rolling circle and centre of pressure is that which operates in the
propulsion of the vessel. The resistance upon any part of the float,
therefore, will vary as the square of its distance from the rolling circle,
supposing the float to be totally immerged; but, taking into account the
greater length of time during which the extremity of the paddle acts,
whereby the resistance will be made greater, we shall not err far in
estimating the resistance upon any point at the third power of its distance
from the rolling circle in the case of light immersions, and the 2.5 power
in the case of deep immersions.

554. _Q._--How is the position of the centre of pressure to be determined?

_A._--With the foregoing assumption, which accords sufficiently with
experiment to justify its acceptation, the position of the centre of
pressure may be found by the following rule:--from the radius of the wheel
substract the radius of the rolling circle; to the remainder add the depth
of the paddle board, and divide the fourth power of the sum by four times
the depth; from the cube root of the quotient subtract the difference
between the radii of the wheel and rolling circle, and the remainder will
be the distance of the centre of pressure from the upper edge of the
paddle.

555. _Q._--How do you find the diameter of the rolling circle?

_A._--The diameter of the rolling circle is very easily found, for we have
only to divide 5,280 times the number of miles per hour, by 60 times the
number of strokes per minute, to get an expression for the circumference of
the rolling circle, or the following rule may be adopted:--divide 88 times
the speed of the vessel in statute miles per hour, by 3.1416 times the
number of strokes per minute; the quotient will be the diameter in feet of
the rolling circle. The diameter of the circle in which the centre of
pressure moves or the effective diameter of the wheel being known, and also
the diameter of the rolling circle, we at once find the excess of the
velocity of the wheel over the vessel.

556. _Q._--Will you illustrate these rules by an example?

_A._--A steam vessel of moderately good shape, and with engines of 200
horses power, realises, with 22 strokes per minute, a speed of 10.62 miles
per hour. To find the diameter of the rolling circle, we have 88 times
10.62, equal to 934.66, and 22 times 3.1416, equal to 69.1152; then 934.66
divided by 69.1152 is equa