Correspondence on various mathematical theories and calculations, mainly pure, but some applied, and miscellaneous papers on scientific matters. The correspondents include Lord Wrottesley, A. de Morgan, B.A. Gould, J.D. Forbes, G. Rennie and D. Brewster. There are papers on 'Pierce's criterion for the rejection of doubtful observations, with tables for facilitating its application' by B.A. Gould; the 1/17 division of the circle; supplementary calculations of e2[Pi] and e-2[Pi] formulae for using tables of logaritHMS; the trisection of an angle; the square root of surds; improving navigation; 'the quantity of heat developed by water when violently agitated' by G. Rennie; 'The dynamic theory of the formation of the Earth' by A.T. Richie; and testimonials to Dr A.H. Hassal.