Dynamically, the tornado may be treated as a rotating pillar of air in which each mass of fluid fairly retains its angular momentum. This means that for any mass of the whirling air the radius of its path, multiplied by its circular speed, remains a constant product; in other words, the velocity of whirl varies inversely as the radius. Accordingly, the circular velocity is exceedingly rapid where the radius is very small. Now, when any mass runs round a circle its centrifugal force is known to be directly as the square of the speed of its centroid and inversely as the radius. But by the above assumption the speed itself is inversely as the radius. Hence, the centrifugal force varies inversely as the cube of the radius of the inflowing mass of air. This centrifugal force, acting on the inner layers of air of the rotating column, must be supported by the pressure against them exerted by the outer layers as they pass inward. Thus there is a strong barometric gradient from the remote still air toward the swiftly whirling parts of the vortex. It follows from the above argument that inside a tornado the barometric pressure may be much below the normal; and it is easy to see that if a barometer, starting from some point on the tornado base, be moved vertically upward it must show a declining pressure, but if moved upward and outward it may be made to show a constant pressure all the way to the upper portion of the vortex. The instrument would thus travel along an isobaric, bell-shaped surface opening upward. On a series, therefore, of concentric circles on the base of a tornado, we may erect a family of coaxial bell-shaped surfaces to mark the points of equal pressure, and thus map out the isobars of the vortex. Inside these coaxial surfaces reaching to earth, others of still lower pressure may be drawn tapering downward to a rounded point and terminating at various places on the axis. In an actual tornado one of these infinitely numerous funnel-shaped isobaric surfaces may become distinctly outlined and visible, if the air has sufficient moisture to start precipitation when it reaches a surface of suitably low pressure. This quite usually occurs in Nature, the funnel sometimes reaching to earth, sometimes only part way, according to the pressure at which precipitation begins, this pressure depending, of course, on the percentage of humidity of the uprushing air.