Similarly, the zonal component of the geostrophic equation may be rearranged to give
The density of the atmosphere is given by p = mp/RT, where m is the mean molecular weight of the air and R is the molar gas constant. Substituting this into the hydrostatic equation we find fdz) 1 RT
which may be differentiated with respect to x, holding p constant, to give g = R f^T) (522)
Similarly, if we differentiate the meridional component of the geostrophic equation (Equation 5.19) with respect to p, holding x constant we find
and thus equating Equation (5.22) and Equation (5.23) we derive
A similar manipulation of the zonal wind component of the geostrophic wind equation (Equation 5.16) leads to
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