The problem considered is that of determining the stress distribution in an infinite plate which contains a straight crack terminated at one end by a circular hole, and is in a state of plane strain or generalized plane stress under given loads. The problem has some relevance to the engineering practice of “stress relief”, in which holes are made at the ends of a crack with the object of reducing the concentration of stress. When the diameters of the holes are small compared with the length of the crack, the distribution of stress near one hole will not be greatly influenced by the presence of the other, and will then be approximately the same as in the simpler case considered here.

It is well known that a first approximation to the flow of a viscous liquid in the neighbourhood of a boundary with a corner may be obtained by solving the linearized equations of momentum neglecting the inertia terms. This has been done by Dean and Montagnon [1] for the plane steady flow near a corner formed by two inclined planes. The following is a similar analysis of the modes by which a liquid can form a free surface starting at the edge of a rigid boundary. The formulation differs from that of Dean and Montagnon mainly in that the angle at which the free surface is formed is in the first place unspecified and has to be determined from the analysis.