About two years ago, by the kindness of the University, an opportunity was presented to me of orally stating what I conceived to be deficiencies in the educational course of the University as regards mathematical physics.  Since that time, the consideration of those deficiencies, which had long been present to me, has urged itself on my attention with greater force:  and finally I have entertained the idea that I might without impropriety communicate to you my opinion, in a less fugitive form than on the occasion to which I have alluded:  with the request that, if you should deem such a course appropriate, you would bring it before the Board of Mathematical Studies, and perhaps ultimately make it known to the Resident Members of the Senate.

I will first give the list of subjects, which I should wish to see introduced, and to the prosecution of which the generally admirable course of the University is remarkably well adapted:  and I will then, without entering into every detail, advert to the process by which I think it probable the introduction of these subjects could be effected.

In the following list, the first head is purely algebraical, and the second nearly so:  but they are closely related to observational science, and to the physical subjects which follow.  Some of the subjects which I exhibit on my list are partially, but in my opinion imperfectly, taught at present.  I entirely omit from my list Physical Optics, Geometrical Astronomy, and Gravitational Astronomy of Points:  because, to the extent to which Academical Education ought to go, I believe that there is no teaching on these sciences comparable to that in the University of Cambridge. (It is, of course, still possible that improvements may be made in the books commonly used.) It might, however, be a question, whether, as regards the time and manner of teaching them, some parts of these subjects might ultimately be associated with the other subjects included in my list.

        I. List of subjects proposed for consideration.

(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.