The form of the funnel-like cloud ere it reaches the earth is interesting. Being an isobaric surface, it would support in static equilibrium a free particle resting on it and sharing its rotatory motion. The lower rounded part of the funnel is parabolic, the upper outer part hyperbolic; the two together delineating the well-known Rankine double vortex of hydrodynamics. Students of hydrostatics know that when a glass of water is spun round its axis at a fixed velocity, the dimple observed is of parabolic form, and if frozen will sustain in repose a small shot resting on its surface and whirling with it. Similarly the lower part of the funnel is parabolic because in it the air rotates, as one solid body, while the broader part of the funnel is hyperbolic because in it the air has a speed inversely proportional to its radius of motion. If everywhere in a tornado the circular velocity of the inflowing air were inversely proportional to the radius, as above assumed, the speed near the axis would be indefinitely great. This cannot be admitted. Practically, the inflow ceases when the centrifugal force of the gyrating stratum equals the pressure urging it toward the axis. Within this stratum is a column of air rotating everywhere with constant angular velocity about the vortical axis, and thus having quite calm air at its center. Outside this solidly rotating core the air spirals radially inward and upward. Some idea of the stream lines in such spiral flow may be obtained from Fig. 50 if a rapid circular motion be added to the inward and upward velocity represented by the arrows. In the foregoing discussion no account of friction was taken. Near the earth’s surface this dampens the whirl and centrifugal force, so that the air flows more directly into the vortex, while farther aloft the centrifugal force near the axis so effectually checks the inflow as to allow the central core of air to rush up nearly unimpeded, as in a walled flue, taking its draught mostly from the lower part. As a consequence, the upward speed of the heated air in the tornado tube may be enormous, supporting in its stream objects of considerable mass. [Illustration: FIG. 50.—FUNNEL-LIKE CLOUD SOMETIMES OBSERVED IN A TORNADO.]