University has taken a course different from that which I had recommended in the first part of this book: and on these points also I may hereafter be led into some further discussion.

I had recommended (282) that the attainment of a Mathematical Honour (Junior Optime at least) should be made a condition of admission to the competition for the new Science Triposes, as it is made for the Classical Tripos. But in the scheme as voted by the Senate, the new Honours are made accessible to all who have passed the Ordinary examination for the degree of B.A., that is, to the Polloi (204). I conceive that the reason for not requiring a Mathematical Honour as a condition for the new Tripos was, the wish to encourage, by all reasonable facilities, the competition for the Honours in the Moral and Natural Sciences; since there does not exist for them, as yet, the encouragement which arises from knowing that they are the doors to station and emolument in Colleges, as the Mathematical and Classical Honours are. Their connection with such advantages, may, at a future period, become very close and effective; but at present, it is a distant and doubtful speculation. And even with the facility which the scheme, as now established, offers, it may be doubted whether the new Honours will, for a time at least, attract so many competitors as might be desired. This, however, is a matter which we shall have further to consider in these pages.

292 The admission of competitors to the new Triposes without the condition of Mathematical Honours was the principal argument for the relaxation of that condition with regard to the Classical Tripos, which was recommended by a portion of a Syndicate and voted by a Grace Oct. 31, 1849. This also is a point which will be further discussed hereafter.

293 In the former part, it was suggested (258)

;

that the Previous Examination which now takes place in the course of the second year of the student's residence, might be transferred to the beginning of residence and made an Initial Examination; and that this change would have certain advantages. This suggestion has not been put in any more definite form nor am I disposed to urge it at present. But the question of the establishment of an Initial Examination without disturbing the Previous Examination has been brought before the University; and it was decided by the vote of February 15, 1848, that the University disapproves of such a plan as was then proposed. On this subject I will insert, in the Appendix*, a paper which was circulated at the time among the Members of the Senate, and of which the arguments appear to me well worthy of consideration.

294 Some alterations intended to remedy defects to which, I believe, I had not specially referred in my former publication, were made by confirming the Report of a Syndicate appointed for that purpose, which was done by Grace of the Senate, on the 23rd of March 1849. The point in these alterations which principally affects the general course of Cambridge studies as here discussed, was the introduction into the Previous Examination of a small quantity of Mathematics. It was decreed that the first two Books of Euclid and a certain amount of Arithmetic should be introduced among the subjects of examination. By this regulation, it was conceived that the students would be prevented from delaying their Mathematical reading till near the time of their final examination, which it was supposed persons averse to Mathematics often did.

295 I may mention also, that I had recommended (246 and 259) that an Examination viva voce should be

introduced into the Examinations both for Mathematical and Classical Honours; but that this recommendation does not appear, as yet, to have met with any response on the part of those who turn their thoughts to the improvement of our University system.

I had recommended (254) that some of the best of the answers to Mathematical questions, given on paper, should be made publicly accessible to Members of the University. This suggestion has been adopted (with regard to the answers in general, not the best only,) in the regulations respecting the new Triposes.

I will now make a few remarks on some of the subjects which are thus undergoing alteration.

SECT. 2. The Classical Tripos.

296 In the previous part of this book, I have (218 and 256) stated that the Classical Tripos was established in 1822; and that the access to the Honours of this List was restricted to those who had obtained the Mathematical Honour of Junior Optime at least; just as the two Medals given by the Chancellor to the best proficients in Classical learning among the commencing Bachelors had already been restricted to Senior Optimes. This limitation of the Honours of the Classical Tripos to those who have already obtained Mathematical Honours was, for several years, generally approved of as reasonable and wise. More recently, however, it has been objected to, as imposing unreasonable burthens upon those who aim at Classical Honours; and lately, the asserted analogy of the new Triposes being added to the previous arguments for a relaxation of this condition, the First Class of the Polloi, as well as the Wranglers and Senior and Junior Optimes, are hereafter to be admitted to compete for the Classical Tripos Honours, as I have already said.

As the discussion upon this subject is probably by

no means at an end in the University, and as it is one of very great importance, I will proceed to offer some remarks upon it.

297 The subject is of very great importance, and the discussion of it involves such questions as these:Whether a Liberal Education ought to include Mathematical Knowledge as well as Classical Literature:Whether the Schools at which boys are taught, ought to regulate the conditions on which the University shall grant its Honours :-Whether the University shall have for its aim to teach its students something which they had not learned as boys, or merely to reward their proficiency acquired by other teaching.

298 On the question whether a Liberal Education ought to include Mathematical Knowledge as well as Classical Learning, I have already repeatedly declared my opinion. A knowledge of Mathematics is requisite in order to familiarize students with exact Reasoning, as an acquaintance with the Classics is requisite in order to familiarize them with standard examples of the power and effect of Language. As I have already said (115), "No education can be considered as liberal which does not cultivate both the Faculty of Reason and the Faculty of Language; one of which is cultivated by the study of Mathematics, and the other by the study of Classics. To allow the student to omit one of these is to leave him half educated. If a person cannot receive such culture, he remains, in the one case, irrational, in the other, illiterate." Such an imperfect education, I conceive, the University ought not to give; and undoubtedly, it has been the aim of all those who have hitherto endeavoured to preserve or to promote the beneficial character of our University Education to show that they have taken this large view of its objects. It will be a novelty, and I believe, a very disastrous one, if, in our discussions respecting the rules by which University Honours are to be

assigned, our arguments come to turn, not upon the point, What is a good and Liberal Education; but upon such points as this, Whether it be not hard upon a particular class of men, specially Classical Students, for example, to require them to read Mathematics, which they dislike.

299 But though this would, as I think, be a very narrow and unworthy mode of arguing respecting our University Education, there are certain influences which tend to give such arguments currency among us. The persons who come to the University have been, for the most part, educated at schools at which the Classics form, we may almost say, the sole study. I have the highest opinion of many of the excellent men who are at the head of our several great Schools : and so far as I am acquainted with the present state of those institutions, I admire greatly both the improvements of system and the elevation of their general spirit and character which have taken place in many of them of late years. But still, they may be regarded as exclusively Classical schools. No other subject than Classical studies attains, comparatively, any hold upon the minds of the scholars. În particular, the Mathematics are not, at most of these schools, taught generally and effectually, as part of the business of the school. How it happens, I do not pretend to say; but at several of the great schools the attempts to teach Mathematics to the boys, as a preparation for their University studies, have in a majority of cases failed. Young men highly intelligent and well instructed in the Classics, come to the University most of them knowing little of the Mathematics; many, nothing. Not only so, but such persons have often acquired a repugnance to Mathematics, from the aspect under which they have seen the subject at school; and I believe would, in many cases, study it with more advantage if they were to begin it afresh