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)