Abstract

The unit vectors el, e2, e3 form a fixed orthogonal coordinate frame. The unit vectors el', e2', e3' form a movable orthogonal frame with the same origin as the fixed frame. All orientations in space of the movable frame are assumed to be equally probable. Under these conditions the average of exp 2i(3i,j = 1aijei.e'j) is calculated. As an application the average of exp 2i(h.x + k.y + l.z) is calculated where the vectors h,k,l are specified and where the magnitudes of the vectors x,y,z and the angles between them are specified. This integral is of importance in utilizing a priori knowledge of molecular structure as an aid in solving the phase problem.