The problem considered is that of the buckling of a right-angled isosceles triangular plate subjected to shear along the two perpendicular edges together with uniform compression in all directions. Four combinations of boundary conditions are considered, and the buckle is assumed to be symmetrical about the bisector of the right angle. In each case it is shown that, if the plate is subjected to shear only, the critical stress is changed considerably upon reversal of the shear. The larger value occurs when the shear is tending to decrease the right angle. Because of this fact, the interaction curve, giving critical combinations of compression and shear, is unsymmetrical and the critical compressive stress can be appreciably increased by the application of a suitable amount of shear.

In this paper the Janzen-Rayleigh method is used to calculate the velocity potential for the steady subsonic flow of a compressible, inviscid fluid past a prolate spheroid. The fluid velocity at a point on the body is calculated. The analytic form obtained for this velocity differs, from that giving the velocity which an incompressible fluid would possess at the same point on the body, by a correction factor. The factor is an infinite series of first derivatives of Legendre functions of the first kind and odd order. The first three coefficients in this series are computed for bodies of certain axis ratios, and graphs of the values of these coefficients against axis ratio are plotted. The behaviour of the nth coefficient for large values of n is given. Results for slender ellipsoids, considering these as a limiting case of the family of ellipsoids just referred to, are obtained and are found to agree with the usual slender-body theory. Using these an attempt is made to continue the graphs of the first three coefficients in the correction factor series for the whole range of axis ratios of the ellipsoids in the system, namely zero to unity. The results obtained for the bluff-nosed ellipsoids may be used to estimate the effects of compressibility on the pressure distribution over the front of a general bluff-nosed body in steady flow.