PROJECTILE.) Other cases of fluid motion are too difficult for discussion here. It should be noted, however, that there are two great divisions of such motions: irrotational and rotational. The former is such that, if a small portion of the fluid were suddenly solidified and freed from the rest of the fluid, it would have simply motion of translation, no rotation. The latter is such that if a small portion of the fluid were suddenly solidified and freed from the rest of the fluid, it would be spinning round a definite axis. It was proved theoretically by Lagrange that if a certain portion of a perfect fluid free from viscosity was set in irrotational motion, it would never have its character changed (if certain con ditions are satisfied, as they would be in gen eral). Helmholtz has proved, further, that if a portion of a perfect fluid is moving rotationally, it will always do so; and that it is as impossible to produce this motion in a perfect fluid as it is to destroy it. Ile showed, too, how lines can
be imagined drawn in the fluid so that at each of their points they coincide with the axis of rotation of the portion of fluid at that point. Such a line is called a 'vertex-line ;' and a solid tube made up of such lines is called a 'vortex.' A vortex once existing in a perfect fluid moves through it, keeping its identity, i.e. always being made up of the same particles and preserving certain other properties. If two vortices were to collide they would rebound, being perfectly elastic. It is possible to devise many forms of vortices which are stable and can keep their gem eral shape. Many of the properties of vortices can be imitated by smoke-rings, but the air is„ of course, not a perfect fluid, and so the vortices do not persist.