As before mentioned, when speaking of the experiment with a thin sheet of metal, the resistance to passage through the water increases very rapidly with the increase of speed, and careful observation has shown that _such increase is proportionate to the square of the speed_, so that an immersed body has four times the resistance when moving at twice the speed, and since it will travel double the distance in the same time the power required is eight times as great; that is, _the power needed to propel a ship varies as the cube of the speed_. It was also discovered that the _power varied with the cube root of the square of the displacement_; although more correct modern experiment has shown that this variation is not strictly true, it is sufficient for the purpose of this article to assume that it is so. [Illustration: The Impérieuse going at Full Speed. (From an instantaneous photograph.)] [Illustration: The North German Lloyd Steamer Kaiser Wilhelm II.] The indicated horse-power [called I. H.-P. for brevity], or that power developed by the engine as registered by the indicator, is not all usefully applied to the propulsion of a steamship. A large portion of it is used up in overcoming the resistance of the engine itself, as well as the necessary adjuncts of it, amounting often to thirteen per cent. Then, again, another portion is absorbed in overcoming the resistance of the propeller and its shafting; and as at present there is no accurate method of determining these portions, the net effective horse-power, or that usefully employed in propelling the vessel, can only be guessed at, or approximated to by calculations more or less abstruse. It is, however, the gross, or _indicated_, horse-power that has to be obtained and paid for, and that, therefore, is the element that has to be considered in practice; so that, from this consideration alone, any great increase in speed has to be very dearly paid for. Moreover, as has already been said, to admit of a higher speed the ship must be made much finer, which means that her carrying capacity for cargo and fuel has to be decreased; besides which the greater engine-power will add to the dead load, thus still further diminishing the vessel’s capability for carrying. This may be better understood by taking a steamer of moderate dimensions, and such as for many years was deemed sufficient for the Atlantic trade, say 300 feet long, 40 feet beam, and having a draft of water of 20 feet. Such a craft would have a displacement of about 4,800 tons, could steam 10 knots per hour with 1,000 I. H.-P., and carry 3,000 tons of cargo, fuel, stores, and equipment. Taking the distance to be steamed at 3,200 knots, and the consumption of fuel at 4 pounds per I. H.-P., it will be seen that the net consumption of coal is 571 tons; adding to this twenty-five per cent. for contingencies of weather, for raising steam, cooking, heating, etc., the ship would have to leave port with 714 tons of fuel