verification of any general
theorem is the selection of an experiment in proof or disproof of a
theory.

I do not quite understand your reference to Stokes and Adams, as types
of the men who alone retain their abstract Analytical Geometry. If a
man when he takes his degree drops mathematics, he drops geometry--but
if not I think for the above reasons that he is more likely to go on
with it than with almost any other subject--and any mathematical
journal will shew that a very great amount of attention is in fact
given to geometry. And the subject is in a very high degree a
progressive one; quite as much as to Physics, one may apply to it the
lines, Yet I doubt not thro' the ages one increasing purpose runs, and
the thoughts of men are widened with the progress of the suns.

I remain, dear Sir,
Yours very sincerely,
A. CAYLEY.

CAMBRIDGE,
_6 Dec., 1867_.

* * * * *

ROYAL OBSERVATORY, GREENWICH,
LONDON, S.E.
_1867, December 9_.

MY DEAR SIR,

I have received with much pleasure your letter of December 6. In this
University discussion, I have acted only in public, and have not made
private communication to any person whatever till required to do so by
private letter addressed to me. Your few words in Queens' Hall seemed
to expect a little reply.

Now as to the Modern Geometry. With your praises of this science--as
to the room for extension in induction and deduction, &c.; and with
your facts--as to the amount of space which it occupies in
Mathematical Journals; I entirely agree. And if men, after leaving
Cambridge, were designed to shut themselves up in a cavern, they could
have nothing better for their subjective amusement. They might have
other things as good; enormous complication and probably beautiful
investigation might be found in varying the game of billiards with
novel islands on a newly shaped billiard table. But the persons who
devote themselves to these subjects do thereby separate themselves
from the world. They make no step towards natural science or
utilitarian science, the two subjects which the world specially
desires. The world could go on as well without these separatists.

Now if these persons lived only for themselves, no other person would
have any title to question or remark on their