The resistance to bodies moving through the water increases as the square of the velocity; and the power, or coal, necessary to produce speed varies or increases as the cube of the velocity. This is a law founded in nature, and verified by facts and universal experience. Its enunciation is at first startling to those who have not reflected on the subject, and who as a general thing suppose that, if a vessel will run 8 miles per hour on a given quantity of coal, she ought to run 16 miles per hour on double that quantity. I think that it may be safely asserted that in all cases of high speed, and ordinary dynamic or working efficiency in the ship, the resistance increases more rapidly than as the squares. The _rationale_ of the law is this: the power necessary to overcome the resistance of the water at the vessel's bow and the friction increases as the square; again, the power necessary to overcome the natural inertia of the vessel and set it in motion, increases this again as the square of the velocity, and the two together constitute the aggregate resistance which makes it necessary that the power for increasing a vessel's speed shall increase as the cube of the velocity. But whatever the _rationale_, the law itself is an admitted fact by all theoretical engineers, and is proven in practice by all steamships. In evidence of this, I will give the following opinions. In his treatise on "The Marine Engine," Mr. Robert Murray, who is a member of the Board of Trade in Southampton, England, says in speaking of the "Natural law regulating the speed of a steamer," page 104: "These results chiefly depend upon the natural law that _the power expended in propelling a steamship through the water varies as the cube of the velocity_. This law is modified by the retarding effect of the _increased resisting surface_, consequent upon the weight of the engines and fuel, so that the horse power increases in a somewhat higher ratio than that named." It must be understood that when he speaks of power, horse power, etc., it is simply another form of representing the quantity of coal burned; as the power is in the direct ratio of the quantity of fuel. Bourne, the great Scotch writer upon the Screw Propeller, in his large volume published by Longmans, London, page 145, says, in concluding a sentence on the expensiveness of vessels: "Since it is known that the resistance of vessels increases more rapidly than the square of the velocity in the case of considerable speeds." Again, at page 236, on "the resistance of bodies moving through the water," he says: "In the case of very sharp vessels, the resistance appears to increase nearly as the square of the velocity, but in case of vessels of the ordinary amount of sharpness the resistance increases more rapidly than the square of the velocity."