§ 17. Orbital Motion and Displacement,— Experimental Demonstration.—The displacement of the fluid and the form of the orbit can be roughly demonstrated by a simple smoke experiment. If a smoke cloud be viewed against a dark background during the passage of a body of streamline form in its vicinity, the retrograde movement of the air is clearly visible. So long as the surface of the body is not too close, the movement is clean and precise, and the general character of the orbit form can be clearly made out; it is found to be, so far as the eye can judge, in complete accord with the foregoing theory. The commencement and end of the orbit, where the motion should be in the same direction as the body, is most difficult to observe, though even this detail is visible if the orbit selected be sufficiently near to the axis of flight. The difficulty here is that the latter part of the orbit is generally lost in consequence of the "frictional wake,"[1] i.e., the current set up by viscous stress in the immediate neighbourhood of the body in motion. In all actual fluids a wake current of this kind is set up, and the displacement surface b, b, b, Fig. 5, is obliterated in the neighbourhood of its cusp by a region of turbulence.
§ 18. Orbital Motion,—Rankine's Investigation.—The form of the orbits of the fluid particles has been investigated theoretically for a certain class of body by Rankine (Phil. Trans., 1864).
Rankine closely studied the streamlines of a body of oval form, generated by a certain method from two foci (§ 77), and by calculation arrived at the equation to the orbit motion of the particles. The result gives a curve whose general appearance is given in Fig. 6 (actual plotting), in which the arrows represent the motion of the particle, the direction of motion of the body being from left to right. Discussing the particular case in which the eccentricity of the oval vanishes, and the form merges into that of a circle. Rankine says,—". . . The curvature of the orbit varies as the distance
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- ↑ A term, used in naval architecture.
