50 



NATURE 



l^Nov. 21, 1878 



admit of being really well taught only by men specially 

 devoted to them, which clearly the private tutors as a class 

 could not very well be. The higher subjects must accord- 

 ingly for some time be taught in an uncertain way, and 

 meanwhile we are deprived of the evidence, which would 

 have been useful in the present emergency, as to how 

 the Cambridge system would work if these subjects 

 were completely in the hands of the lecturers, as they 

 should be. 



As between college lecturers and private tutors we have 

 some reason to hope that one effect of the introduction of 

 the new subjects will be that the former will rise in im- 

 portance and the latter will, at least relatively, decline. 

 We wish to write nothing but good of the private tutors 

 personally, but if that result should really take place we 

 should regard it as a decided boon. There may be some 

 cases in which private tuition may have merits of its own, 

 but for the ordinary student to have a private tutor per- 

 petually at his elbow when he meets with a difficulty is to 

 give him the worst possible education. In like manner 

 we do not admire the system of more than paternal super- 

 vision practised by many of the college tutors over their 

 pupils, the natural effect of which is that the pupil is not 

 allowed to act or to think for himself. He is perpetually j 

 asking and getting advice about very trifling matters, and i 

 receives a great amount of what is called individual atten- 

 tion on a variety of subjects. But though he may thus 

 gain a little knowledge, if he ultimately learns habits of 

 self-reliance he learns them from other sources. 



If the system of private tuition could be done away with, 

 and if more vigour could be instilled into the collegiate 

 system of lecturing, so that complete and adequate courses 

 of lectures could be given, there would be a healthier tone 

 and spirit in the studies of the University, and we are con- 

 vinced the students would learn more and, learn better. 

 In proof of this we may state that the most successful of 

 the private tutors in mathematics really do what ought to 

 be the work of the college lecturer ; that is, they deliver 

 lectures to their classes and examine written work for 

 them. We may also state that in the department of 

 classical studies most of the students depend solely upon 

 the college lectures. 



We have made these remarks because it seems to us 

 that the Tripos examination is only one phase of the 

 broader question of the whole system of mathematical 

 teaching. Certain proposals will to-day be made to the 

 University, and if these be carried the scheme of college 

 lectures will have to be remodelled : if at the same time 

 a new spirit and energy could be infused into them, it would 

 be a good thing for Cambridge teaching. 



The proposed alterations in the examination may be 

 briefly described as follows : — The subjects are in the first 

 place thrown into two grand divisions. On the one side 

 there are what may be called the easier subjects, cover- 

 ing all the ground which a moderately good candidate, 

 whether his tastes incline him towards analysis or physics, 

 may be expected to take up. On the other side there are 

 the higher subjects of pure mathematics and physics. 

 It is proposed that those two divisions should constitute 

 the subjects of two distinct examinations. 



The examination in the first division will, as regards 

 class lists, take the place of the present Tripos, that is, the 

 results will be given in the old form of Wranglers, Senior 



Optimes, and Junior Optimes, arranged in order of merit. 

 This examination will take place in the June of the third 

 year of residence, and only the Wranglers will be per- 

 mitted to take up the second examination. 



The subjects of the second examination which will take 

 place in the following January are subdivided into four 

 groups, and the results upon them will be given in classes, 

 the names in each class being this time arranged in alpha- 

 betical order. It will be possible to attain a first class by 

 doing well in one or two groups. 



Those who bear unqualified hostility to competitive ex- 

 aminations, especially in their intensified form, when they 

 are followed by an order of merit, will probably be satis- 

 fied for the present, hoping that at some future time they 

 will succeed in abolishing the order of merit entirely. 

 There are others who approve of the proposed changes, 

 and who yet think that when confined within reasonable 

 bounds such competitions can do no harm and may do 

 good. Undergraduate human nature being as it is, 

 a good contest, even such as can be had in a Tripos ex- 

 amination, is rather enjoyable than otherwise, and brings 

 out qualities which are worth reckoning for something. 

 It is also a good thing that an undergraduate should learn 

 to have a piece of hard work well done in a given time. 

 What has to be seen to is that the competition does not 

 react injuriously on the course of study. There are 

 many reasons which commend the proposed changes in 

 that connection, and to one or two of these we will now 

 advert. 



In the first place, the higher subjects are not suitable for 

 purposes of examination, because the questions which are 

 likely to be put on them require long work and probably 

 much reflection. It is good, therefore, not only that these 

 subjects should be studied leisurely, but that the element 

 of hurry should be as far as possible excluded from an 

 examination upon them. It is true that the last remark i 

 will apply also to the lower subjects, but we are to con-| 

 sider that the latter subjects which usually consist of a fe\i 

 simple principles, admitting of an almost infinite varietj 

 of simple applications, are in a measure the tools of the 

 mathematician who ought to be well skilled and expert ii 

 their use. 



Again, if there is to be strict competition it is as well 

 that the area should be narrowed and that the combatant^ 

 should meet one another on common ground. In the pre 

 sent state of things that cannot be, but under the proposed 

 system it will be possible for a clever lad who has read 

 but Uttle when he enters the University, to hold his owi 

 against a competitor, his inferior, who does not begin hi^ 

 undergraduate course till he has been pushed, or ha| 

 plodded on a good way towards his mathematical degree." 



The opponents of the proposed changes affirm that the 

 Tripos will lose its prestige, and that the students under 

 the new system will entirely neglect the second examina- 

 tion. It seems sufficient, in answer to the first of these 

 objections, to point out that the first examination will not 

 be so insignificant either in extent or difficulty, as not to 

 compare in those respects with the Tripos examination of 

 forty or fifty years ago. And as to the best students neglect- 

 ing the second part, that is a circumstance which seems 

 very unlikely to occur, but the colleges will have the matter 

 in their own hands, and it is to be expected they would be 

 patriotic enough to refuse their fellowships and certainly 



