But, it will be urged, it is just the same thing to drive a large body of water astern at a slow speed as a small body at a high speed. This is the favorite fallacy of the advocates of hydraulic propulsion. The turbine or centrifugal pump put into the ship drives astern through the nozzles at each side a comparatively small body of water at a very high velocity. In some early experiments we believe that a velocity of 88 ft. per second, or 60 miles an hour, was maintained. A screw propeller operating with an enormously larger blade area than any pump can have, drives astern at very slow speed a vast weight of water at every revolution; therefore, unless it can be shown that the result is the same whether we use high speed and small quantities or low speed and large quantities, the case of the hydraulic propeller is hopeless. But this cannot be done. It is a fact, on the contrary, that the work wasted on the water increases in a very rapid ratio with its speed. The work stored up in the moving water is expressed in foot pounds by the formula W v squared / 2g where W stands for the weight of the water, and v for its velocity. But the work stored in the water must have been derived from the engine; consequently the waste of engine power augments, not in the ratio of the speed of the water, but in the ratio of the square of its speed. Thus if a screw sends 100 tons of water astern at a speed of 10 ft. per second per second, the work wasted will be 156 foot tons per second in round numbers. If a hydraulic propeller sent 10 tons astern at 100 ft. per second per second, the work done on it would be 1,562 foot tons per second, or ten times as much. But the reaction effort, or thrust on the ship, would be the same in both cases. The waste of energy would, under such circumstances, be ten times as great with the hydraulic propeller as with the screw. In other words, the slip would be magnified in that proportion. Of course, it will be understood that we are not taking into account resistances, and defects proper to the screw, from which hydraulic propulsion is free, nor are we considering certain drawbacks to the efficiency of the hydraulic propeller, from which the screw is exempt; all that we are dealing with is the waste of power in the shape of work done in moving water astern which we do not want to move, but cannot help moving. If our readers have followed us so far, they will now understand the bearing of Rankine's proposition, that that propeller is best which moves the greatest quantity of water astern at the slowest speed. The weight of water moved is one factor of the thrust, and consequently the greater that weight, other things being equal, the greater the propelling force brought to bear on the ship.