With regard to the second and chief cause by which the resistance is influenced - the wave - Mr. Russell concludes, from his investigations, that the restoration of the equilibrium amongst the particles of the fluid which has been disturbed by the motion of a floating body, is effected not so much by the generation of currents in the fluid, as has been hitherto generally assumed, as by the generation of waves, which form elevations in front of the moving body. These waves travel to a great distance, with a velocity which is nearly uniform, and which depends solely upon the depth of the fluid; and in channels of rectangular section does not differ sensibly from that which is acquired by a heavy body falling freely by gravity, through a space equal to half the depth of the fluid. In a channel 5.5 feet deep, the velocity of the wave is about 8 miles per hour.

The resistance will chiefly depend upon the relative velocities of the wave and of the vessel; the resistance increases rapidly as the velocity of the vessel approaches that of the wave.

When the vessel moves slower than the wave, the elements of increased resistance are:-


Increased immersion of the bow in the anterior wave.


Inclination of the longitudinal axis of the floating body, so as to change the form of the displacing body.


Increased vertical section opposed to resistance=thesineof the inclination.


Increased velocity of the lateral current.

The following table shows the rapid increase of resistance in approaching the velocity of the wave. It is extracted from the experiments of 1838.

Experiment I

Miles per Hour.

Resis. lbs.











Velocity of Wave, 8 Miles.

Experiment II

Miles per Hour.

Resis. lbs.











Velocity of Wave, 8 Miles.

Let it now be supposed that the vessel had created a wave by its motion, and suppose it possible to lift the vessel entirely out of the water, and place its centre on the top of the wave, the stem being anterior to the wave, and its stern behind it, and suppose the vessel to be of such form as to remain in a state of equilibrium on the surface of the fluid having the form of the wave, and that the velocity of the vessel be such as to keep it in the same relative position to the wave, the following results would be obtained:-


The vessel would recover its horizontal position, and would present the minimum transverse section of resistance.


The immersion of the vessel being increased by the height of the crest of the wave around its centre of gravity, the head and stern displacements would be diminished (the total immersion being a constant quantity) by the amount of excess of central displacement.


The velocity of the vessel being now increased beyond that of the wave, the waves of displaced fluid continually falling behind the points where they were raised, would form a series of great central waves, bearing the vessel on their summit.

When the velocity is greater than the wave, it might be expected that the wave would be left behind; but, in this case, it should be observed that a new wave is formed at every instant by the motion of the vessel through the water, whatever be its velocity; for the displaced fluid thrown aside at the bow generates a series of waves, which move with a less velocity than the vessel, and fall back behind the bow.

It is always found that the commotion produced in the fluid at velocities less than the wave is greater than at velocities exceeding that of the wave. The stem of the vessel in the latter case enters water which is perfectly smooth and undisturbed, because no wave has previously passed before the vessel to produce any anterior derangement.

It is to the diminished anterior section of displacement produced by raising a vessel with a sudden impulse to the summit of the progressive wave, that a very great improvement recently introduced into canal transport owes its existence. The isolated fact was discovered accidentally on the Glasgow and Ardrossan canal, which is a canal of small dimensions. A spirited horse, in the boat of Mr. William Houston, took fright, and ran off, dragging the boat with it, and it was then observed, to Mr. Houston's astonishment, that the foaming stern surge, which used to devastate the banks, had ceased; and the vessel was carried on through water comparatively smooth, with a diminished resistance. Mr. Houston, perceiving the mercantile value of this fact, devoted himself to introducing on that canal vessels moving with this high velocity. The result of this improvement has been to bring from the conveyance of passengers at a high velocity a large increase of revenue to the canal proprietors. The passengers and luggage are conveyed in light boats about GO feet long, and six feet wide, made of thin sheet iron, and drawn by a pair of horses.

The boat starts at a slow velocity behind the wave, and at a given signal, it is, by a sudden jerk of the horses, drawn up on the top of a wave, where it moves with diminished resistance, at the rate of 7, 8, or 9 miles per hour.

It appears, from the experiments of 1835, that a vessel has conveyed on a canal given weights with the following forces:-

Moving Force.

Weight Moved.


71.5 lbs.

19.222 lbs.

4 Milesper Hour.

86. "

19.222 "

4.5 "

112. "

19.222 "

5.2 "

246. "

8022 "

11.3 "

264. "

9262 "

13.6 "

331. "

10.262 "

15.1 "

In these experiments the vessel which experienced the least resistance was one designed by Mr. Russell, and to which he gave the name of The Wave.

This vessel was of very peculiar form, which suggested itself to Mr. Russell as a form of least resistance, and which even surpassed the expectations he had formed of the facility of her motion. The lines of entrance are parabolic tangent arcs, having a point of contrary flexure between the maximum transverse section and the stem. The run is formed of elliptical arches, and is by no means so fine as runs usually are. Mr. Russell was led to devise this form, from an opinion, confirmed by long observations, that the maximum resistance to a vessel of ordinary form is experienced in the immediate vicinity of the stem; that the water there is thrown aside with a velocity much greater than is requisite to remove the particles from the space to be passed over by the succeeding points of the bow. This head of water at the bow, instead of being merely thrown aside, is also thrown upwards and forwards, so as very much to increase the resistance beyond what appears necessary for the transit of the vessel. It occurred to him, that a form might, perhaps, be obtained which wrould not, at any given velocity, raise a head of water above the level, but merely give to the particles displaced the minimum of lateral motion required to permit the transit of the vessel.

From his investigations he obtained a curve which appeared to him to be a curve of least resistance, and the vessel named The Wave was built conformably thereto; and the truth of his theory, being tested by experiment, was fully confirmed. This vessel, when deeply laden, and moving with a velocity of seventeen miles an hour, causes no spray, foam, surge, nor head-water at the bow, but the water is parted smoothly and evenly asunder, and quietly unites after the passage of the vessel; adhesion, alone, to the vessel drags forward a film of adjacent fluid; all else remains quiet and smooth.

The form of The Wave has been followed, as nearly as circumstances would admit, in some steamers recently constructed, and the results have been highly satisfactory.