5. It is clear, then, that an adequate mail speed requires more fuel, more engineers, more firemen, more coal-stokers, and more general expense. The question of fuel is, however, alone the most important of all those affecting the attainment of high speed, and the item whose economy has been most desired and sought, both by those attempting to carry freight, and those who carry the mails and passengers. The principal points of interests concerning it are, the enormous quantity which both theory and practice show to be necessary to fast vessels; the large sum to be paid for it, and the steadily increasing price; and the paying freight room which its necessary carriage occupies. In fast steaming, the supply of coal to the furnaces frequently arrives at a point where many additional tons may be burned and yet produce no useful effect or increase of power. The draft through the furnaces and smoke stacks is so rapid and strong as to take off a vast volume of heat; and this, coupled with a large quantity of heat radiated from the various highly heated parts and surfaces, requires a consumption of fuel truly astonishing. If we reflect that at the twelve principal ports of Great Britain in the year of 1855, the tonnage entered was 6,372,301, and departed 6,426,566, equal to 12,798,867 total, and this during the war, that a large part of this was steam tonnage, and that the total imports and exports of Great Britain for 1856 were 1,600,000,000 dollars, we can somewhat appreciate the present and future uses of coal, and its inevitably large increase in price. The two hundred and seventy steamers in the British Navy, with about 50,000 aggregate horse power, consumed in 1856, according to a report made to a Committee of the "British Association for the Advancement of Science," this year, by Rear-Admiral Moorsom, 750,000 tons of coal. The difficulty and cost of mining coal, its distance from the sea-shore, and the multifarious new applications in its use among our rapidly increasing population, as well as its almost universal and increasing demand for marine purposes, all conspire to make it more costly from year to year; while, as a propelling agent, it is already beyond the reach of commercial ocean steam navigation. Coal has gone up by a steady march during the last seven years from two and a half to eight dollars per ton, which may now be regarded as a fair average price along our Atlantic seaboard. And that we may see more clearly how essentially the speed and cost of steam marine navigation depend upon the simple question of fuel alone, to say nothing further of the impeding causes heretofore mentioned, I will now present a few inquiries concerning THE NATURAL LAWS OF RESISTANCE, POWER, AND SPEED, WITH TABLES OF THE SAME.