hence a double speed requires that the liquid should be impelled with almost a double force. But besides this, it is to be considered, that when the vessel acquires a double speed, it moves in the same time through a double space, and therefore must impel a double quantity of the liquid. Since, therefore, it impels a double quantity, and every portion of that with almost a double force, the resistance which it has to overcome must be increased in a threefold proportion. Hence we see, that to give a vessel moving in a liquid a double velocity, requires that the power of traction or impulsion should be increased in a threefold proportion. In the same manner, it will be easily made out, even by the general reader, that a threefold velocity will require about sixfold power of traction or impulsion, and so on; the resistance and the necessary power of traction increasing not merely in the proportion of the speed, but in the proportion of what arithmeticians call the square of the speed.
Even this statement must be received in a qualified form, and limited in its application to moderate rates of motion; because it is demonstrable, that there is a practical limit of speed, beyond which a vessel cannot be impelled through a fluid, and that limit is by no means a wide one. Notwithstanding the application of the immense power of steam to vessels plying between points of great intercourse. I believe that a greater speed than from ten to twelve miles an hour has never yet been attained independently of the effect of currents.
To the power of impelling a vessel through water we see, therefore, that there is a narrow limit; but if this limit be narrow as applied to vessels in the open sea, it is still more so when applied to vessels in confined channels, such as canals. In this case the
