Perhaps it may be of interest to describe, by way of example, the general features of Routh's system. He gave catechetical lectures three times a week to classes of eight or ten men of approximately equal knowledge and ability. The work to be done between two lectures was heavy, and included the solution of some eight or nine fairly hard examples on the subject of the lectures. Examination papers were also constantly set on tripos lines (bookwork and riders), while there was a weekly paper of problems set to all pupils alike. All papers sent up were marked in public, the comments on them in class were generally brief, and, to save time, solutions of the questions were circulated in manuscript. Teaching also was supplemented by manuscripts on the subjects. Finally to the more able students he was accustomed, shortly before their tripos, to give memoirs or books for analyses and commentaries. The course for the first three years and the two earlier long vacations covered all the subjects of the examination--the last long vacation and the first term of the fourth year were devoted to a thorough revision. Under Hopkins and Routh there was no trace of what is called cramming; they might say that a particular demonstration was so long that it could not be required in the tripos, but none the less they expected their pupils to master it. The system had faults, but it had the merit of providing a systematic grounding in a wide field of subjects. The effectiveness of teaching of this kind was dependent on intimate constant personal intercourse, and the importance of this cannot be overrated. The scandal of the system consisted in the fact that a man was compelled to pay heavy fees to the University and his College for instruction, and yet found it advantageous at his own expense to go elsewhere to get it. During the last quarter of the nineteenth century college lecturers began to share with the coaches the general direction of studies. Post-graduate work was also to some extent brought under the influence of professors and university lecturers--these not uncommonly suggesting subjects for dissertations for fellowships, Smith's prizes, etc. But the students thus influenced were not numerous, and it still remains true that the majority of mathematical undergraduates are so out of touch with the professors in the subject as to be unacquainted even with their personal appearance. Such was the mathematical tripos and its history. Whatever its demerits, it dominated the situation, and Cambridge mathematics and mathematicians of the nineteenth century were the direct product of the system it embodied. Judged by the output, I do not think it can be said to have resulted in failure; and perhaps Cayley, Sylvester, Adams, Green, Stokes, Kelvin, and Maxwell--to mention no others--were none the worse for having been compelled to go through the course.