The proportion which the power ot the engines should bear to the size of the vessel depends greatly upon the nature of the service for which the vessels are intended. Post-office packets, and vessels depending chiefly upon passengers, for instance, require and will admit of engines of larger power than vessels employed principally in the transport of goods; in which latter, less space can be afforded for the machinery and fuel, on account of the room required for the cargo. The proportional power must likewise depend partly upon the size of the vessel, for, as the resistance to a vessel's progress depends principally upon the area of the transverse section immersed, which area does not increase in the same proportion as the capacity of the vessel, larger vessels require less power in proportion than smaller ones. For instance, if two vessels be built upon the same model, but one of them of double the tonnage of the other, their proportional linear dimensions will be as 126 to 100, and their sectional areas as 158 to 100; therefore, to obtain the same velocity, the power will only require to be increased in the same ratio as the sectional area, or as 158 to 100; if the power in each vessel were in the direct ratio of the tonnage, or as 200 to 100, the ratio of the power to their sectional areas would be 200 to 158.

Viewed solely as a question of economy without regard to speed, it might at first sight be concluded that vessels must be worked at less cost with engines of small power than with large ones, for the resistance to a vessel's motion through the water increases more rapidly than in the ratio of the velocities. The resistance of a fluid to a body moving therein is generally stated to be as the square of the velocities; a double speed occasioning a fourfold resistance, so that if it required 100 horse power to propel a vessel at the rate of 5 miles an hour, it would require 400 horse power to produce a speed of 10 miles per hour. This ratio, however, applies only to the resistance of the particles of the fluid in a quiescent state, and also assumes hat the area of the immersed section is the same at all velocities; but the progress of vessels is influenced by various other causes, besides the inertia of the water, as tides or currents, and the force of the wind and sea; resistance from these causes has little or no relation to the speed of the vessels, and will require a certain amount of power to overcome them, independent of that which is required to overcome the inertia of the water; and the greater the amount of the resistance from the former causes in proportion to that from the latter, the more will the result vary from the theoretical calculation.

In some circumstances, therefore, the consumption of fuel may be even less in going a given distance with large engines than with small ones. Let us suppose that a vessel, fitted with engines of 100 horse power, will go 10 miles an hour in still water, and that another vessel with 50 horse power will in the same circumstances go 7 miles per hour; if these vessels have to stem a current of 4 1/2 miles per hour, the effective speed of the first will be reduced to 5 1/2 miles per hour, and that of the second to 2 1/2 miles per hour; the former, therefore, would perform a distance of 100 miles in 18 hours, and the latter in 40 hours; and as the large engine would only consume twice as much fuel per hour as the small one, it would consume in 18 hours only as much fuel as the smaller would in 36 hours, and, consequently, the consumption would be as 36 to 40 in favour of the larger power. But independently of these casual resistances, the resistance from the inertia of the water is found not to increase as rapidly as the square of the velocity; from the circumstance that with a considerable increase of speed, the vessel has a tendency to rise from the water, or diminish her draught, so that the area of the immersed section becomes less, and the head wave also decreases.

This circumstance may appear paradoxical, but it seems to be well ascertained by a careful observation of facts, both in this country and in America. The Great American Steam Raft is stated frequently to have attained a speed of 20 miles per hour, at which time her draught of water was 7 inches less than when still, and there was no head wave. The same facts have been elicited by numerous experiments in this country with boats upon canals and drawn by horses, and will be found to be noticed in the experiments of Sir J. Robinson and Mr. Russell, of which we have already given extracts.

From the foregoing considerations, which have been confirmed by experience, the proportion of the power to the tonnage in seagoing steamers has been gradually augmented, vessels recently built having generally engines of greater power than old vessels of the same tonnage. Small engines are also frequently removed from vessels, and others of greater power substituted for them, with decided advantage, not only as to speed, but also with respect to the economy of fuel; their consumption per voyage, or for the same distance, being less with the large engines than it had previously been with the smaller ones.

The measured tonnage of a vessel, however, affords rather an uncertain criterion of the comparative amount of power required, as, from the improper mode of estimating the sizes of vessels or measuring them still in practice, a small vessel may be made to measure a great deal, and a large vessel may be made to measure very little. In all steamers, the vessel displaces considerably more than the measured tonnage.

Mr. Morgan, who has had considerable experience in this matter, and who has paid great attention to this subject, in his evidence before the committee on steam communication with India, assumes the displacement of the vessel as a better standard, and for vessels going long sea voyages deems 1 horse power to 4 or 4 1/2 tons displacement a good proportion. He, however, advocates building the vessels of asharper form than is generally done, so as to make the measurement and displacement nearly accord. We select from this gentleman's evidence the dimensions of some of the government steam packets, which will show the great discrepancy between the measurement and displacement.