THE Cambridge Examination for Mathematical Honours has for a long time enjoyed a high reputation, especially among Cambridge men, who have been accustomed to point to it as the model of what an examination should be. The credit thus claimed has been in past times more or less deserved, but to what extent it is so now is a question on which there may be variety of opinion. Like every other institution, the practical usefulness of which depends upon the ease with which it can adjust itself to external conditions, the Tripos examination must undergo changes to meet corresponding changes from the outside; and there may come a time when the external conditions operate so powerfully that mere modifications are insufficient, and when the changes made must be both radical and extensive. The old Tripos system has recently been put to a severe strain, and it is admitted on all hands that the result has proved unsatisfactory. We propose to inquire into the causes which have brought this about, and to discuss the measures by which it is hoped the evil will be met.