THE COURSE OF MATHEMATICAL STUDIES. 427 



it rapidly and well, generally attains to more honour than he 

 quite deserves ; and though the undue influence of mere memory 

 is somewhat diminished by papers consisting of original pro- 

 blems, yet at any rate the student is trained to be quick and 

 ready rather than wise and thoughtful. In devising problems 

 it is difficult to avoid mere puzzles things to be solved only 

 by some happy guess ; and if, on the other hand, examiners 

 were to confine themselves to tolerably obvious deductions from 

 known propositions, the problem papers would cease to be a 

 counterpoise to the rest of the examination. If the candidates 

 for high honours were, as in the Smith's prize examination, 

 examined apart from the rest, it might be possible, so far as 

 they were concerned, to diminish these difficulties by varying 

 the modes of examination. In a select examination there could 

 be no excessive inconvenience in giving almost unlimited time 

 for the consideration of the questions proposed, and in these 

 questions the candidate might be required to state accurately, 

 and in detail, the grounds of his views on fundamental prin- 

 ciples in analysis, geometry, or physics. Again, in such an 

 examination books might perhaps be introduced, and if so, in- 

 teresting questions might be proposed of a kind now inadmis- 

 sible; to mention one class only the candidate might be re- 

 quired to form an opinion on any controverted point, to examine 

 for instance the correctness of Sir James Ivory's doctrine, that 

 in certain cases the ordinary condition of fluid equilibrium is 

 insufficient, and to state his reasons for adopting or rejecting it. 



It must, however, be remembered that after all possible im- 

 provements the complaint that schools " lack profoundness and 

 dwell too much on seeming," will always be more or less just. 

 A course of study, of which the most obvious purpose is to pre- 

 pare the student for an &rt$6Jft?, can never be quite what a 

 course of study ought to be, and might be made if higher ends 

 could always be kept in view. 



CAMBRIDGE: PRINTED BY c. j. CLAY, M.A. AT THE UNIVERSITY PRESS. 



