of the particle from a line parallel to the axis of X, and midway between that axis and the undisturbed position of the particle. This is the property of the looped or coiled elastic curve; therefore when the water-lines are cyclogenous the orbit of each particle of water forms one loop of an elastic curve." Further, he says—"The particle starts from a, is at first pushed forward, then deviates outwards and turns backwards, moving directly against the motion of the solid body as it passes the point of greatest breadth, as shown. The particle then turns inwards, and ends by following the body, coming to rest at b in advance of its original position."
This orbit in some respects resembles that arrived at by the
Fig. 6.
author, but differs in the one very important point that, whereas the author's method gives a retrograde displacement of the fluid as the net consequence of the passage of the body. Rankine's conclusion is exactly the contrary.
As the author's result is capable of experimental verification, it is evident that some subtle error must exist in Rankine's argument, the exact nature of which it is difficult to ascertain.
§ 19. Bodies of Imperfect Streamline Form.—In an actual fluid, bodies of other than streamline form experience resistance apart from that directly due to viscosity.
In the practical shaping of a streamline body it is found essential to avoid corners or sharp curves in the line of flow. Bodies in which due precaution is not taken in this respect offer considerable resistance to motion, and the regions of abrupt curvature give rise to a discontinuity in the motion of the fluid. Thus Fig. 7 represents a double cone moving axially, and it will be noticed that the flow has not time to close in round the run,
20
