Correspondence on various mathematical theories and calculations, mainly pure, but some applied, and miscellaneous papers on scientific matters. The correspondents include, among others, C. Brooke, R.C. Carrington, W.J. Rankine, L.S.X.B. Aousts, R.H. Manners, A. Strange, J.N. Lockyer, J. Tyndall, A.R. Clarke, A. de Morgan, J.C. Adams, E.J. Routh and W. Shanks. The material includes a paper by Airy 'on the factorial resolution of a given trinomial formula'; a printed paper by W. Shanks 'On the Calculation of the Numerical Value of Euler's Constant'; eight concentric calculators sent to Airy by J.D. Everett on a proportional table and testimonials to it; a printed paper titled 'Two Tables of LogaritHMS to Natural Numbers and Natural Numbers to LogaritHMS for all Numbers from l to 99999 and all LogaritHMS from .00001 to .99999' by Erskine Scott; a paper endorsed by Airy titled 'Note on Scientific Education, submitted to the Royal Commission on Scientific Instruction and the Advancement of Science'; printed papers on state aid to science, including a 'First Report of the Royal Commission on Scientific Instruction and the Advancement of Science'; pages extracted from 'Nature' on various subjects; a paper by W.J.M. Rankine 'On Thermodynamics'; and an examination paper on mixed mathematics for the Civil Service of India Open Competition of 1870.