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 devotion to this barren subject. But a Cambridge Examiner is not in that position. The University is a national body, for education of young men: and the power of a Cambridge Examiner is omnipotent in directing the education of the young men; and his responsibility to the cause of education is very distinct and very strong. And the question for him to consider is--in the sense in which mathematical education is desired by the best authorities in the nation, is the course taken by this national institution satisfactory to the nation? I express my belief that it is _not_ satisfactory. I believe that many of the best men of the nation consider that a great deal of time is lost on subjects which they esteem as puerile, and that much of that time might be employed on noble and useful science.