2. Another circumstance which modi fies the general results is the velocity of the body. It was ascertained, by Mr. Russell's experiments on canal boats, that the resistance does not follow the ratio of the squares of the velocities, ex cepting when the velocity is small and the depth considerable ; but that the in crements of the resistance are greater than those due to the squares of the ve locities as the velocity approaches to a certain limit depending on the depth of the fluid ; and that immediately after passing this limit the resistance. suffers a sudden diminution, and becomes much less than that due to the square of the velocity. Ina canal about five and a half feet deep, this limit (which is the velo city of the wave generated by the motion of the body) was found to be from 11 to 12 feet per second, or about eight miles per hour.
5. A third cause which modifies the theory is the adhesion of the molecules of the fluid, which is most sensible when the motion is slow and the body small and very long. In such cases, it becomes necessary to add a term depending on the first power of the velocity.
4. The resistance is also influenced by the depth of the body under the surface of the water. When the body is near the surface the resistance is greater than when it is at the depth of six feet. When a body floats, the fluid is heaped up, as it were, before the anterior surface, by which the resistance is increased.
5. In elastic fluids, as the density in creases with the pressure, the density of the fluid before the anterior surface in creases with the velocity, and the inerA ments of the resistance are greater than in the ratio of the square of the velocity.
In this case, also, we may conceive a ve locity so great that the pressure on the posterior surface becomes negative, as in the case of a cannon ball projected with a velocity greater than that with which air rushes into a vacuum. When this takes place the fluid is not even in con tact with the posterior surfaces of the ball, and the character of the resistance is wholly changed.
6. When a body moves in a fluid a portion of the fluid adheres to the body, and accompanies it in its motion ; where by the form of the moving body is alter ed, and the resistance increased. The quantity of fluid thus dragged along is independent of the velocity, and was esti mated by Du Buat, from experiments made on spheres vibrating in water, to increase the quantity of displaced fluid in the ratio of 1 to 1-6. His experiments on prisms also showed that the quantity of dragged fluid was proportional to the bulk of the moving body. Mr. Bally gives, as the mean results of his experi ments on pendulums swinging in air, the ratio 1 to 1.846 as the increase of the displaced fluid from this cause ; and re marks that the quantity appeared to de pend on the form as well as magnitude of the moving body, but not on its weight or specific gravity. This circumstance, which considerably modifies the resist ance, though made known by Du Buat in 1786, was overlooked by other experi menters, until re=discovered by Bessel in 1826, when engaged on experiments to determine the length of the seconds' pen dulum.