Abstract
SummaryThe paper contains a generalisation of the conformal transformation by means of which a circle is converted into Joukowski aerofoils. The transformation is applied to a cascade of oval bodies which is the corresponding generalisation of the isolated circle; and it converts the oval bodies into a wide variety of cascades of curved shapes, which are generalisations of the isolated Joukowski aerofoils. In one particular case, the transformation yields a grid of flat laminae. Since the perfect fluid flow through such a grid is known (it appears to have been first given by Joukowski) the perfect fluid flow past the ovals, in any direction, and with equal but otherwise arbitrary circulation round each, is obtained. Accordingly, the perfect fluid flow through any of the derived cascades can be obtained.
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