(1) Partial Differential Equations to the second order, with their arbitrary functions: selected principally with reference to the physical subjects. (2) The Theory of Probabilities as applied to the combination of Observations. (3) Mechanics (including Hydraulic Powers) in the state which verges upon practical application, and especially including that part in which the abstract ideas of _power_ and _duty_ occur. (4) Attractions. This subject is recognized in the existing course of the University: but, so far as I can infer from examination-papers, it appears to be very lightly passed over. (5) The Figure of the Earth, and its consequences, Precession, &c. I believe that the proposal is sanctioned, of adopting some part of this theory in the ordinary course; but perhaps hardly so far as is desirable. (6) The Tides. (7) Waves of Water. (8) Sound (beginning with Newton's investigation); Echoes; Pipes and Vibrating Strings; Acoustics; the Mathematical part of Music. (9) Magnetism, terrestrial and experimental, and their connection. (I omit for the present Mineralogy and Mathematical Electricity.) This list of subjects appears formidable: but they are in reality easy, and would be mastered in a short time by the higher Wranglers. II. _Mode of introducing these subjects into the University_. After much consideration, and after learning the opinions of several persons whose judgment claims my deepest respect, I propose the gradual introduction of these subjects into the Examination for Honors at admission to the B.A. Degree, as soon as the preparation of Books and the readiness of Examiners shall enable the University to take that step. I conceive that, by a judicious pruning of the somewhat luxuriant growth of Pure Algebra, Analytical Geometry, and Mere Problems, sufficient leisure may be gained for the studies of the undergraduates, and sufficient time for the questions of the examiners. I do not contemplate that the students could advance very far into the subjects; but I know the importance of beginning them; and, judging from the train of thoughts, of reading, and of conversation, among the Bachelors with whom I associated many years ago, I believe that there is quite a sufficient number who will be anxious to go deep into the subjects if they have once entered into them. If six Wranglers annually would take them up, my point would be gained. The part which these gentlemen might be expected, in a short time, to take in the government of the University, would enable them soon to act steadily upon the University course: the efficiency of the University instruction would be increased; and the external character of the University would be raised.