A.—­The screw steamer Fairy, if enlarged to three times the size while retaining the same form, would have twenty-seven times the capacity, nine times the sectional area, and nine times the power.  The length of such a vessel would be 434 feet; her breadth 63 feet 4-1/2 inches; her draught of water 16-1/2 feet; her area of immersed section 729 square feet; and her nominal power 1080 horses.  Now as the lengths of the Fairy and of the new vessel are in the proportion of 1 to 3, the speeds will be in the proportion of the square root of 1 to the square root of 3; or, in other words, the speed of the large vessel will be 1.73 times greater than the speed of the small vessel.  If therefore the speed of the Fairy be 13 knots, the speed of the new vessel will be 22.49 knots, although the proportion of power to sectional area, which is supposed to be the measure of the resistance, is in both cases precisely the same.  If the speed of the Fairy herself had to be increased to 22.29 knots, the power would have to be increased in the proportion of the cube of 13 to the cube of 22.49, or 5.2 times, which makes the power necessary to propel the Fairy at that speed equal to 624 nominal horses power.

STRUCTURE AND OPERATION OF PADDLE WHEELS.

551. Q.—­Will you describe the configuration and mode of action of the paddle wheels in general use?

A.—­There are two kinds of paddle wheels in extensive use, the one being the ordinary radial wheel, in which the floats are fixed on arms radiating from the centre; and the other the feathering wheel, in which each float is hung upon a centre, and is so governed by suitable mechanism as to be always kept in nearly the vertical position.  In the radial wheel there is some loss of power from oblique action, whereas in the feathering wheel there is little or no loss from this cause; but in every kind of paddle there is a loss of power from the recession of the water from the float boards, or the slip as it is commonly called; and this loss is the necessary condition of the resistance for the propulsion of the vessel being created in a fluid.  The slip is expressed by the difference between the speed of the wheel and the speed of the vessel, and the larger this difference is the greater the loss of power from slip must be—­the consumption of steam in the engine being proportionate to the velocity of the wheel, and the useful effect being proportionate to the speed of the ship.

552. Q.—­The resistance necessary for propulsion will not be situated at the circumference of the wheel?