426 THE COURSE OF MATHEMATICAL STUDIES. 



of symmetrical functions, nor is there any difficulty in the de- 

 monstration by which an intelligent student can be embarrassed. 

 Likewise Abel's method for the division of the complete elliptic 

 function might with advantage replace Gauss's solution of the 

 binomial equation. It includes this solution as a particular case, 

 and from its generality is far more intelligible: Boscovich's 

 doctrine, that the more generally a subject is considered the 

 more easily is it understood, being for the most part true. 

 These instances, in which portions of the theory of the com- 

 parison of transcendents serve to complete and illustrate the 

 theory of equations, tend to show that a course of mathematical 

 study cannot well be made to adhere precisely to any definite 

 classification of the different branches of mathematics. 



VI. One of the obstacles which hinder our mathematical 

 studies from being quite what they ought to be is touched on 

 in the tenth query*. It is there asked whether the number 

 of problems proposed in the Senate-House examination is not, 

 regard being had to the time allowed for solving them, greater 

 than it should be. It may be answered that it is necessary to 

 set before the candidates for high honours more problems than 

 any one is supposed capable of solving in the given time, in 

 order by the variety of subjects to provide sufficient employ- 

 ment for each, and at the same time to leave a certain freedom 

 of choice ; and, further, that if no more problems were proposed 

 than the ablest questionists might be presumed capable of solv- 

 ing, the number would still be too great for those of inferior 

 ability. All this is true, and it is therefore much less easy to 

 point out a remedy than to perceive the evils which result from 

 the present state of things, not only in the problem papers but 

 throughout the examination. He who for a season can remem- 

 ber a great deal, and who while he remembers it can reproduce 



* The tenth query is : Is it your opinion, or the contrary, that the problems 

 proposed in the examinations bear too large a proportion to the questions derived 

 either immediately or by a very simple deduction from the books which are com- 

 monly read ? Are they for the most part so proposed, as to admit of their being 

 readily apprehended and their solution effected by a Student who thoroughly 

 understands the principles and applications of the branches of Mathematics upon 

 which they depend, or are they not unfrequently involved in such a form as to 

 require for their solution a peculiar tact distinct from accurate and philosophical 

 knowledge ? Are you not disposed to think the number of problems proposed to 

 be solved in the time allowed (as many, generally, as seven or eight in one hour of 

 time) is greater than the best prepared Student can be expected to complete 1 



