Equations and theorems governing the flow of an inviscid, incompressible, continuously-stratified fluid in a gradually varying channel with an arbitrary cross section are developed. The stratification and longitudinal velocity are assumed to be uniform in the transverse direction, an assumption that is supported under the assumption of gradual topographic variations. Extended forms of Long's model and the Taylor-Goldstein equation are developed. Interestingly, the presence of topographic variation does not alter the necessary condition for instability (Richardson number < 1 4 ) nor the bounds on unstable eigenvalues (the semi-circle theorem). The former can be proved using a new technique introduced herein. For the special case of homogeneous shear flow, generalized versions of the theorems of Rayleigh and Fjørtoft do depend on the form of the topography, though no general tendency toward stabilization or destabilization is apparent. Previous results on the bounds and enumeration of neutral modes are also extended. The results should be of use in the hydraulic interpretation of exchange flow in sea straits.

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Accurate real estate appraisal relies upon good market analysis, sound feasibility studies and correct professional practice. This paper discusses, by way of case study, how a failure to comply with these criteria, coupled with loose management and inadequate auditing, can lead to insolvency in leading financial institutions. It concludes that there is a need for real estate appraisers to re‐examine their own practices and to return to basics in their appraisal and thus provide precise, accurate valuation advice for clients.