Papers relating to transactions with the Royal Society, including correspondence with its members. The material includes nominations for new members; computation of the wave length of light corresponding to spectrum lines; computation of wave lengths; comparison of magnetic disturbances recorded by self-resisting magnetometers; diurnal inequalities of terrestial magnetism as deduced from observations, 1858-1863; magnetic disturbances inferred from galvanic currents; and correspondence with the Board of Trade on meteorological observations. There are also reviews of scientific works by Airy and other correspondents, including G.G. Stokes, W.H. Miller, W. Huggins, J. Glaisher, A. de Morgan, C. Pritchard, N.C. Flammarion, B. Price, J. Challis, C.E. Delaunay, C.F. Varley, W. De La Rue, R.S. Robinson, W. Smyth and J. Tyndall.