CORRESPONDENCE, 184G-55. 227 



erectly, and to decide wisely, he has been well educated, and the 1853. 



loss of the positive knowledge which I suppose him to have lost 



is comparatively a small matter. I do not underrate knowledge ; 



I would educate for it, even if it gave no powers ; but I am sure 



that if we take care of the habits, the acquirements will take 



care of themselves. 



Throughout the whole of the requisitions runs a tone which 

 would give anyone the notion that the study demanded is sought 

 only for its results, and that it will be tested only by the know- 

 ledge of results shown. I look at the programme of the mathe- 

 matical propositions required, and I find the implication that as 

 long as a certain list of truths is known, it matters not how. I 

 admit that the examiners by setting this list at defiance, by pro- 

 posing questions which try the knowledge of principles, and 

 which necessarily require them to travel out of the list, have done 

 much to neutralise its evil tendency. But I cannot suppose the 

 necessity for a complete alteration is thereby done away. We 

 are informed that the principal properties of triangles, squares, 

 and parallelograms (when did the square cease to be a paral- 

 lelogram ?) are to be treated geometrically. Among the principal 

 properties of parallelograms are those of similar parallelograms ; 

 their study involves a doctrine of proportion. But only the first 

 of the six books of Euclid are demanded. Must similar paral- 

 lelograms be treated by what is called a geometrical theory of 

 proportion ? If not, how are the principal properties of 

 parallelograms to be treated geometrically, as demanded? If 

 yes, what is that geometrical theory of proportion, other than 

 Euclid's, so well known that it may be trusted to implication ? 

 The only proportion alluded to in any part of the list is alge- 

 braical proportion, which, as usually understood, is the doctrine 

 of the ratios of commensurable quantities, expressed by letters, 

 with either every possible amount of gratuitous assumption 

 about incommensurable quantities, or else a total refusal to 

 consider them. 



Might not what we may well hope, and what I am inclined 

 to believe, will be the greatest University founded in the nine- 

 teenth century dare to promulgate definite views on the mode 

 in which study should be conducted, its ends, its uses, and the 

 proofs of its efficiency ? Is it not the duty of that University to 

 make it apparent that she receives and cherishes the sound 

 principle so long maintained by her predecessors without pledg- 

 ing herself to the abuses which time and negligence have allowed 



Q 2 



