Correspondence on pure mathematics and other subjects. The papers include correspondence with A. de Morgan on curves, infinity in mathematics and other theorems; theories of probability by J.V. Lamont; the riddle of the fifteen young ladies; writing by W.J.M. Rankine on the properties of curves; the proceedings of the Mathematical Society; logarithmic tables; algebraic and numerical theory of errors of observations; two proofs and a draft of Airy's 'Partial Differential Equations'; a paper on the Bank of England and gold standard by W.D. Haggard; and work on errors in magnetism by J. Davidson. The correspondents include I. Todhunter and J. Glaisher. There are also 42 photographs of mathematical models of partial differential equations.