More difficult problems in astronomy, motions of heavenly bodies, tides, lunar irregularities, the Principia and other parts of "Newton's Philosophy," to those sufficiently advanced. This, together with fortnightly lessons in seamanship, weekly lessons in ship construction, an occasional cruise round the Isle of Wight in a small vessel, and practical gunnery, forms a pretty full programme, and argues a somewhat optimistic and enthusiastic view of the capacities of his pupils on the part of the learned Professor. An examination was to be held every six months, and the best and second students were to receive respectively a gold and silver medal. The silver medal was awarded at Midsummer, 1830, to John Irving, who, when he went out in the _Terror_ with Sir John Franklin's expedition in 1846, had it with him. It was buried with him in King William's Land, when, in common with all the members of the ill-fated expedition, he perished, in 1848 or 1849; was found and brought home by Lieut. Schwatka, U.S.N., in 1880, and is now in the Museum of the Royal United Service Institution. The periodical reports show that the programme was carried out regularly; and after some years Inman introduced a novel system of recording progress. The total number of marks obtained by each student was supplemented by a second column headed "number expected"; this was arrived at by multiplying the number of hours at each subject by twenty; this number denoting the progress expected to be made in one hour, if the student completed his course in the full term of three years. If the number obtained exceeded the number expected, the student might be expected to finish his course in a proportionately shorter period. This was a genuine mathematician's device, and was very instructive. A glance at the two final columns of a report practically told the whole story; and it is satisfactory to note that a large percentage of the lads usually exceeded expectations: in one report, for instance, the number was forty-seven out of sixty-five. Notions of discipline were severe, according to the spirit of the times. The Professor on one occasion, reporting the misconduct of some of the students, deplores the abolition of the rod; and mentions that, though a dark cabin is used for confinement, a "black hole" is much needed! There is no mention of such a place of confinement being instituted; but the Admiralty revokes the abolition of flogging. In 1816 the regulations for entry, the composition of the staff, and the course of study were modified.