Horizontal Motion Under Balanced Forces. The Gradi ent Wind.—Equations (to) and (I I) above form an algebraic statement of the balance between the accelerations relative to the earth and the deviating force, together with any other im pressed forces. If V be the total velocity in the path, at a point The upper sign gives a solution which is continuous near straight isobars, where V = G, while the second solution would demand indefinitely high velocities near straight isobars. Thus the only physically appropriate solution of (i6) is Equation (i7) gives a system of winds blowing clockwise round a centre of high pressure, but everywhere with a veloc ity less than rcosinO. The anticyclone therefore has a slower rate of rotation than the earth beneath it, and is therefore a counterclockwise circulation in space. Equation (i8) gives a sys tem of winds blowing counterclockwise round a centre of low pressure, both when considered relative to the earth and as motion in space. Thus both cyclone and anticyclone have in space the same direction of rotation as the earth beneath them. It can be readily verified that the second solution shown in equa tion (15) is a clockwise rotation in space, for both cyclone and anticyclone. Large scale systems conforming to this solution do not occur in nature, and the solution is to be regarded as an algebraic accident rather than as having a physical meaning. Some evidence has been adduced by Brunt (Proc. Roy. Soc., A., 1924) to show that such systems would be unstable if they could be produced momentarily.
The geostrophic wind is readily evaluated by the use of a scale of reciprocals to measure the distance apart of consecutive isobars. The scale is graduated for standard density, and the small cor rection required for deviations from standard density is readily made. A detailed comparison of observed winds with winds com
puted from synoptic charts was carried out by E. Gold (Baromet ric Gradient and Wind Force, M.O. 190), and it was found that the geostrophic wind gives a close approximation to the wind observed at a height of 2,000 to 3,00o feet.
The computation of the gradient wind requires the solution of equation (13), which demands the evaluation of the curvature of the isobars, denoted by r. The gradient wind is therefore an in convenient quantity to use, and the geostrophic wind is adopted as the most useful first approximation to the actual wind. The nature of this approximation is here emphasised because the major part of modern dynamical meteorology assumes the geostrophic wind as equivalent to the actual wind.
In low latitudes, where 2cosin4 is small, the term usually exceeds 2co Vsin4). Equation (13) then becomes meaningless for anticyclonic curvature, i.e. with the negative sign on the right hand side, showing that closed anticyclonic isobars are not physi cally possible as a steady state in low latitudes.
The hydrodynamical equation of continuity may be written If the effect of changing density be neglected it can be shown that systems of steady geostrophic winds satisfy the equation of con tinuity with no vertical velocity w. There can therefore be no convergence, and consequently no rainfall, in a system of geo strophic winds. The isallobaric components of winds discussed by Brunt and Douglas give convergence into regions of low values and divergence from regions of high values on the isallobaric charts, and so explain the rainfall associated with the low values, and fine weather associated with the high values.