DUBLIN Royal Irish Academy, June 11. W. B. MOBTON: The stability and oscillations of certain permanent arrangements of parallel vortices. The arrangements in question are those which formed the subject of an earlier paper, namely, any three vortices at the corners of an equilateral triangle and four, with a definite ratio of strengths, at the corners of a rhombus. The slightly disturbed motions are discussed, and the frequencies and modes of oscillation about the steady motions are determined. It is found that the triangular arrangement is stable when the centre of the vortices lies within the circle circumscribing the triangle and the rhombus when its acute angle exceeds a critical value, arc cos (l/\/3).