or less illustrated in nature, but he never succeeded in uniting the three equations in one comprehensive system. The Germans approached more nearly a satisfactory solution, but as already stated, the assumption that cyclones and anticyclones are symmetrical, respectively, about warm and cold centers, is no longer tenable. We have already made the assertion that the asymmetrical cyclone, as it occurs in nature, does not conform satisfactorily to any homogeneous vortex. It will be possible to show how this is by giving a few details regarding waterspouts, tornadoes and hurricanes, which will lead up to this conclusion.
Local Vortices in the Earth's Atmosphere
A large waterspout was seen at Cottage City, Mass., in the Vineyard Sound, on August 19, 1896, about eight miles distant from Cottage City. Fortunately a series of good photographs was secured of the waterspout and its cloud, which together with the meteorological data, have enabled us to compute the dimensions and the velocities of motion in all parts of it by means of the vortex formulas. It happens that the same cloud developed two types of vortex, at short intervals of time between them. One is the funnel-shaped vortex and the other is the dumbbell-shaped vortex. Fig. 1 gives an illustration of a section
through the funnel-shaped vortex, and shows the boundary of the several vortex tubes. The horizontal dimensions are multiplied by ten for the sake of showing the relative dimensions more plainly which exist from one tube to another. It will be noted that the distances between the successive tubes get smaller and smaller in a geometric ratio towards the axis. They concentrate at the lower part, and expand so that the lines become parallel to a horizontal plane in a region at
