You may remember that the Commissions which have visited Cambridge originated in a Memorial addressed to the Government by men of respected scientific character: Sabine was one, and I may take him as the representative. He is a man of extensive knowledge of the application of mathematics as it has been employed for many years in the science of the world; but he has no profundity of science. He, as I believe, desired to find persons who could enter accurately into mathematical science, and naturally looked to the Great Mathematical University; but he must have been much disappointed. So much time is swallowed up by the forced study of the Pure Mathematics that it is not easy to find anybody who can really enter on these subjects in which men of science want assistance. And so Sabine thought that the Government ought to interfere, probably without any clear idea of what they could do. I am, my dear Sir, Yours very truly, G.B. AIRY. _Professor Cayley_. * * * * * DEAR SIR, I have to thank you for your last letter. I do not think everything should be subordinated to the educational element: my idea of a University is that of a place for the cultivation of all science. Therefore among other sciences Pure Mathematics; including whatever is interesting as part of this science. I am bound therefore to admit that your proposed extension of the problem of billiards, _if it_ were found susceptible of interesting mathematical developments, would be a fit subject of study. But in this case I do not think the problem could fairly be objected to as puerile--a more legitimate objection would I conceive be its extreme speciality. But this is not an objection that can be brought against Modern Geometry as a whole: in regard to any particular parts of it which may appear open to such an objection, the question is whether they are or are not, for their own sakes, or their bearing upon other parts of the science to which they belong, worthy of being entered upon and pursued.