Horace was taking the examination for the BA degree in the mathematical tripos at the University of Cambridge. The examination consisted of several parts. On the first three days the basic subjects in geometry and algebra were examined, followed by easier parts of advanced subjects like calculus on the fourth day. There was then an interval of ten days after which those declared to deserve honours were admitted to the rest of the examination. The examination began on the first Monday following 29 December, which in 1874 was 5 January. Horace went on to complete the more advanced part of the examination, which included differential calculus and analytic geometry, and was ranked sixth among senior optimes (second class honours; see Cambridge University calendar 1874).

Horace had told CD about the demand for a new edition of Coral reefs in Cambridge; CD included this information in his letter to Smith, Elder & Co, 17 December [1873] (Correspondence vol. 21).