one of the subjects to be entitled to pass the examination. The names of those who have satisfied the examiners are arranged in two classes alphabetically; the first consisting of those who have passed the examination with credit; and the second, of those to whom the examiners have only not refused their certificate of approval.

The names of those students who have passed the examination in the additional subjects, to the satisfaction of the examiners, are placed alphabetically in one class.

If a student should not succeed in satisfying the examiners either in the ordinary subjects of the Previous Examination, or in the additional subjects, he may attend the next examination; and if he fails at his second trial, he may make a third, a fourth, &c., as there is no law or statute which limits the number of trials an unsuccessful yet persevering student may make to pass this very elementary examination.

It is generally considered that there is no credit in passing an examination so elementary, so limited and defined, as to be within the ordinary diligence of an ordinary capacity. Any student, therefore, who fails in satisfying the examiners at his first trial, necessarily incurs disgrace for a failure he might have avoided if he would, and the payment of the penalty in time and labour, in revising his knowledge, which he might have escaped. The large number of failures which take place from year to year is to be mainly attributed to the want of due care and timely preparation on the part of the student in acquiring a sound and accurate knowledge of the subjects of examination.

THE PROFESSORIAL CERTIFICATE.

On October 31, 1848, it was determined, by Grace of the Senate, that all students candidates for the ordinary degree of B.A. should, before admission to their final examination, attend the lectures delivered during one term at least by one or more of the following Professors :

Regius Professor of Law,

Regius Professor of Physic,

Professor of Moral Philosophy,

Professor of Chemistry,

Professor of Anatomy,

Professor of Modern History,

Professor of Botany,

Woodwardian Professor of Geology,

Jacksonian Professor of Natural and Experimental

Philosophy,

Downing Professor of the Laws of England,

Downing Professor of Medicine,

Professor of Mineralogy,

Professor of Political Economy;

and shall obtain a certificate of having passed an examination satisfactory to one of the professors, whose lectures they have chosen to attend.

Also, that students who have been candidates for mathematical honours, and have failed in obtaining the lowest honour, shall not, on offering themselves for the B.A. degree, be excused the condition of producing a professor's certificate; but it shall not be necessary for such students to have attended the professor's lectures before their examination for the B.A. degree.

On February 25, 1855, it was determined, by Grace of the Senate, that in the examinations for professorial certificates, there shall be joined with each professor an assistant examiner every year, and that the assistant examiner for each subject shall be of equal authority with the professor of the same subject in the examination. The payment of £3 3s. is required from every student to entitle him to attend the lectures and the examination for the certificate. The sum so raised is called the Professorial Fund, out of which each assistant-examiner receives £5, and the residue is divided between the registrary and the professors, in the manner agreed upon among themselves.

It was also determined that the names of the successful candidates shall be published in the Senate House, and that this publication shall be accepted as the eertificate required by the University.

F

THE ORDINARY DEGREE OF B.A.

All candidates for the ordinary degree of Bachelor of Arts are required to have passed the Previous Examination, and to have attended a course of professors' lectures, and passed the examination for the Professorial Certificate, before they are admitted to the final examination for the degree.

A student who has resided nine terms, or who has resided eight terms and entered upon the ninth term, may offer himself as a candidate for the examination of the ordinary degree of B.A.

The general examination for this degree commences on the Thursday before the end of the first two-thirds of the Easter Term, unless that day be Ascension Day; in which case the examination, which would otherwise have been held on that Thursday, is to be held on the preceding day. Besides the general examination, there are two additional examinationsone commencing on the Thursday before the end of the first two-thirds of the Michaelmas Term, and one on the Thursday before the end of the first two-thirds of the Lent Term.

The fixed subjects of the examination are :—(1) The Acts of the Apostles, in the original Greek; (2) History of the English Reformation; (3) The first four books and part of the sixth book of Euclid; (4) The elements of Algebra, including ratio and proportion, and equations of a degree not higher than the second, involving one or two unknown quantities, and questions producing such equations; (5) Elementary Mechanics and Hydrostatics.

The changeable portion of the examination consists of one subject from the Greek, and one from the Latin Classical Authors,* ‚* which are published in the first week of the Lent Term of the year preceding.

The examination is conducted entirely by printed papers. The papers on the classical subjects and in the Acts of the Apostles, consist of passages to be translated and explained, accompanied by such plain questions in Grammar, History,

*These subjects for the year 1862-3, are Thucydides, Book VII., and Horace, Epistles, Book I

and Geography, as arise immediately out of the subjects; and in the Acts of the Apostles the students are required also to illustrate the subject by reference to the Epistles of the New Testament, in the way shown by Paley in the Horæ Paulinæ.

The papers on the mathematical subjects consist of propositions in Euclid, and of questions in Algebra and Proportion, in Mechanics, and Hydrostatics, according to a prescribed schedule; and also of such questions, applications, and deductions as arise directly out of the said propositions.

It is also ordered, that no student shall be approved by the examiners unless he show a competent knowledge of all the subjects of examination.

The names of the students who pass the examination to the satisfaction of the examiners at the general examination for the ordinary degree, are arranged in four classes, according to merit, the names in each class being arranged alphabetically, and these classes are published in the Senate House. Those who pass the examination in the Lent Term are not classed, but their names are arranged in one list placed alphabetically. The same arrangement is made of those who pass the examination in the Michaelmas Term. Any student who may be unsuccessful in passing the examination at his first trial, may try again as often as he pleases, or until he has been successful in satisfying the examiners. There is no law or statute restricting the number of times a student may attend the examination for the ordinary degree of Bachelor of Arts.

THE MATHEMATICAL TRIPOS.*

All candidates for honours in Mathematics are required to

* The Report of the Royal Commissioners, pp. 111, 112, 23, contains the following remarks:

"The mental discipline resulting from Mathematical Study is of two very distinct kinds, of which one only is commonly apprehended and dwelt upon. Geometry and the Pure Mathematics afford perfect illustrations and examples of deductive reasoning, in which the conclusion is connected with the premises by links of argument, each susceptible of direct and absolute

have passed the Previous Examination, and the examination in the additional subjects, and to have kept nine terms, or, at least, have entered upon the ninth term, having previously kept eight terms; provided that not more than ten terms shall have passed after the first of the said eight terms. And that, excepting candidates for degrees jure natalium, no student of a different standing is allowed to be a candidate for mathematical honours, unless he shall have obtained permission from the Syndicate appointed to consider the cases of persons who have degraded. Powers were also given, by Grace of the Senate, in 1859, to examine into the cases of such students as may be desirous of becoming candidates for honours in the Mathematical Tripos of any year, notwithstanding they have been admitted to the title of Bachelors designate in Arts or Law; and to grant per

verification by the application of simple and easily remembered tests. If fallacy creep in, it is the student's own fault. A given amount of steady thought will always enable him to detect and expose it. Those who have once learned what demonstrative argument really is in this school, will never feel satisfied or secure in accepting as proof any kind of general likelihood, or any arguments drawn from passion, prejudice, or interest. They have learned to break up an argument into its elementary steps, and to apply, if not those exact tests which mathematicians apply, at least some tests, founded on the true relations of the subject, to each of them. And if they find, as they will find, in all the complicated questions of human interest to which reasoning is applied, that these tests fall far short in respect of their applicability and decisive character of what they have been accustomed to see in exact science, they will learn caution and diffidence in adhering to the conclusions. Join to this the length to which the chain of reasoning is carried, the remarkable conclusion to which it leads, the sentiment of unity and coherence in a well-constructed body of knowledge, and the habit of regular study and consecutive thought requisite to impart that sentiment, and we have an account of all that is really beneficial in the Deductive Mathematics in the way of mental training.

"The intellectual discipline imparted by the study of the Mixed Mathematics, and of the Mathematico-Physical Sciences, is different in character from that conveyed by the Pure. The latter exercise no faculties but those of close attention and strict interpretation. The former call into action inductive observation and reasoning on the effect of external conditions. In all their more difficult applications, moreover, approximate conclusions only can be arrived at, and a perpetual exercise of judgment is required as to the extent of deviation from the abstract standard of absolute truth which the nature of their solutions admits. Frinciples as well as raasonings come to be