radii 2.9067; and adding to this the depth of the paddle board, we have 4.9067, the fourth power of which is 579.64, which, divided by four times the depth of the paddle board, gives us 72.455, the cube root of which is 4.1689, which, diminished by the difference of the radii of the wheel and rolling circle, leaves 1.2622 feet for the distance of the centre of pressure from the upper edge of the paddle board in the case of light immersions.  The radius of the wheel being 9.6667, the distance from the centre of the wheel to the upper edge of the float is 7.6667, and adding to this 1.2622, we get 8.9299 feet as the radius, or 17.8598 feet as the diameter of the circle in which the centre of pressure revolves.  With 22 strokes per minute, the velocity of the centre of pressure will be 20.573 feet per second, and with 10.62 miles per hour for the speed of the vessel, the velocity of the rolling circle will be 15.576 feet per second.  The effective velocity will be the difference between these quantities, or 4.997 feet per second.  Now the height from which a body must fall by gravity, to acquire a velocity of 4.997 feet per second, is about .62 feet; and twice this height, or 1.24 feet, multiplied by 62-1/2, which is the number of Lbs. weight in a cubic foot of water, gives 77-1/2 Lbs. as the pressure on each square foot of the vertical paddle boards.  As each board is of 20 square feet of area, and there is a vertical board on each side of the ship, the total pressure on the vertical paddle boards will be 2900 Lbs.

557. Q.—­What pressure is this equivalent to on each square inch of the pistons?

A.—­A vessel of 200 horses power will have two cylinders, each 50 inches diameter, and 5 feet stroke, or thereabout.  The area of a piston of 50 inches diameter is 1963.5 square inches, so that the area of the two pistons is 3927 square inches, and the piston will move through 10 feet every revolution; and with 22 strokes per minute this will be 220 feet per minute, or 3.66 feet per second.  Now, if the effective velocity of the centre of pressure and the velocity of the pistons had been the same, then a pressure of 2900 Lbs. upon the vertical paddles would have been balanced by an equal pressure on the pistons, which would have been in this case about .75 Lbs. per square inch; but as the effective velocity of the centre of pressure is 4.997 feet per second, while that of the pistons is only 3.66 feet per second, the pressure must be increased in the proportion of 4.997 to 3.66 to establish an equilibrium of pressure, or, in other words, it must be 1.02 Lbs. per square inch.  It follows from this investigation, that, in radial wheels, the greater part of the engine power is distributed among the oblique floats.

558. Q.—­How comes this to be the case?