An attack of rheumatic fever at Sanremo in 1849 left him an invalid, and he returned to Cambridge, living at Anstey Hall, Trumpington, next to his friend John Grote, vicar of Trumpington.
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In his second year he became a pupil of the private tutor William Hopkins, and in the Mathematical Tripos of 1839 came out second to Robert Leslie Ellis.
In particular, his Differential Equations and the Calculus of Finite Differences (1839) incorporated the new solution of the Laplacian equation for the figure of the earth as given by Thomas Gaskin in symbolic form; it was the elaboration of this original solution by Robert Leslie Ellis in 1841 which led largely to George Boole's masterpiece On a general method in analysis in 1844 (PRS, 5, 1843–50).